From adb52a7a2b4f1b2f86e7bb41b68ba03f896b3262 Mon Sep 17 00:00:00 2001
From: SebastianBruijns <>
Date: Fri, 23 Sep 2022 19:48:53 +0200
Subject: [PATCH] increased offset for dirichlet in case things go wrong, makes
things less extreme and less prone to breaking
---
.../pybasicbayes/__init__.py | 2 +
.../pybasicbayes/abstractions.py | 247 +++
.../pybasicbayes/distributions/__init__.py | 13 +
.../pybasicbayes/distributions/binomial.py | 131 ++
.../pybasicbayes/distributions/dynamic_glm.py | 279 +++
.../distributions/dynamic_multinomial.py | 286 ++++
.../dynamic_multinomial_in_progress.py | 265 +++
.../pybasicbayes/distributions/gaussian.py | 1518 +++++++++++++++++
.../pybasicbayes/distributions/geometric.py | 147 ++
.../pybasicbayes/distributions/meta.py | 121 ++
.../pybasicbayes/distributions/multinomial.py | 649 +++++++
.../distributions/negativebinomial.py | 681 ++++++++
.../pybasicbayes/distributions/poisson.py | 186 ++
.../pybasicbayes/distributions/regression.py | 1206 +++++++++++++
.../pybasicbayes/distributions/uniform.py | 137 ++
.../pybasicbayes/models/__init__.py | 2 +
.../pybasicbayes/models/factor_analysis.py | 336 ++++
.../pybasicbayes/models/mixture.py | 841 +++++++++
.../pybasicbayes/models/parallel_mixture.py | 15 +
.../pybasicbayes/testing/__init__.py | 0
.../pybasicbayes/testing/mixins.py | 262 +++
.../pybasicbayes/util/__init__.py | 3 +
.../cstats.cpython-37m-x86_64-linux-gnu.so | Bin 0 -> 1583128 bytes
.../pybasicbayes/util/cyutil.py | 112 ++
.../pybasicbayes/util/general.py | 328 ++++
.../pybasicbayes/util/plot.py | 68 +
.../pybasicbayes/util/profiling.py | 53 +
.../pybasicbayes/util/stats.py | 365 ++++
.../pybasicbayes/util/testing.py | 99 ++
.../pybasicbayes/util/text.py | 59 +
.../pybasicbayes/util/cstats.o | Bin 0 -> 3844888 bytes
pybasicbayes.egg-info/PKG-INFO | 12 +
pybasicbayes.egg-info/SOURCES.txt | 40 +
pybasicbayes.egg-info/dependency_links.txt | 1 +
pybasicbayes.egg-info/requires.txt | 5 +
pybasicbayes.egg-info/top_level.txt | 1 +
pybasicbayes/distributions/multinomial.py | 6 +-
37 files changed, 8473 insertions(+), 3 deletions(-)
create mode 100644 build/lib.linux-x86_64-cpython-37/pybasicbayes/__init__.py
create mode 100644 build/lib.linux-x86_64-cpython-37/pybasicbayes/abstractions.py
create mode 100644 build/lib.linux-x86_64-cpython-37/pybasicbayes/distributions/__init__.py
create mode 100644 build/lib.linux-x86_64-cpython-37/pybasicbayes/distributions/binomial.py
create mode 100644 build/lib.linux-x86_64-cpython-37/pybasicbayes/distributions/dynamic_glm.py
create mode 100644 build/lib.linux-x86_64-cpython-37/pybasicbayes/distributions/dynamic_multinomial.py
create mode 100644 build/lib.linux-x86_64-cpython-37/pybasicbayes/distributions/dynamic_multinomial_in_progress.py
create mode 100644 build/lib.linux-x86_64-cpython-37/pybasicbayes/distributions/gaussian.py
create mode 100644 build/lib.linux-x86_64-cpython-37/pybasicbayes/distributions/geometric.py
create mode 100644 build/lib.linux-x86_64-cpython-37/pybasicbayes/distributions/meta.py
create mode 100644 build/lib.linux-x86_64-cpython-37/pybasicbayes/distributions/multinomial.py
create mode 100644 build/lib.linux-x86_64-cpython-37/pybasicbayes/distributions/negativebinomial.py
create mode 100644 build/lib.linux-x86_64-cpython-37/pybasicbayes/distributions/poisson.py
create mode 100644 build/lib.linux-x86_64-cpython-37/pybasicbayes/distributions/regression.py
create mode 100644 build/lib.linux-x86_64-cpython-37/pybasicbayes/distributions/uniform.py
create mode 100644 build/lib.linux-x86_64-cpython-37/pybasicbayes/models/__init__.py
create mode 100644 build/lib.linux-x86_64-cpython-37/pybasicbayes/models/factor_analysis.py
create mode 100644 build/lib.linux-x86_64-cpython-37/pybasicbayes/models/mixture.py
create mode 100644 build/lib.linux-x86_64-cpython-37/pybasicbayes/models/parallel_mixture.py
create mode 100644 build/lib.linux-x86_64-cpython-37/pybasicbayes/testing/__init__.py
create mode 100644 build/lib.linux-x86_64-cpython-37/pybasicbayes/testing/mixins.py
create mode 100644 build/lib.linux-x86_64-cpython-37/pybasicbayes/util/__init__.py
create mode 100755 build/lib.linux-x86_64-cpython-37/pybasicbayes/util/cstats.cpython-37m-x86_64-linux-gnu.so
create mode 100644 build/lib.linux-x86_64-cpython-37/pybasicbayes/util/cyutil.py
create mode 100644 build/lib.linux-x86_64-cpython-37/pybasicbayes/util/general.py
create mode 100644 build/lib.linux-x86_64-cpython-37/pybasicbayes/util/plot.py
create mode 100644 build/lib.linux-x86_64-cpython-37/pybasicbayes/util/profiling.py
create mode 100644 build/lib.linux-x86_64-cpython-37/pybasicbayes/util/stats.py
create mode 100644 build/lib.linux-x86_64-cpython-37/pybasicbayes/util/testing.py
create mode 100644 build/lib.linux-x86_64-cpython-37/pybasicbayes/util/text.py
create mode 100644 build/temp.linux-x86_64-cpython-37/pybasicbayes/util/cstats.o
create mode 100644 pybasicbayes.egg-info/PKG-INFO
create mode 100644 pybasicbayes.egg-info/SOURCES.txt
create mode 100644 pybasicbayes.egg-info/dependency_links.txt
create mode 100644 pybasicbayes.egg-info/requires.txt
create mode 100644 pybasicbayes.egg-info/top_level.txt
diff --git a/build/lib.linux-x86_64-cpython-37/pybasicbayes/__init__.py b/build/lib.linux-x86_64-cpython-37/pybasicbayes/__init__.py
new file mode 100644
index 0000000..1f8fd26
--- /dev/null
+++ b/build/lib.linux-x86_64-cpython-37/pybasicbayes/__init__.py
@@ -0,0 +1,2 @@
+from __future__ import absolute_import
+from . import abstractions, distributions, models, util
diff --git a/build/lib.linux-x86_64-cpython-37/pybasicbayes/abstractions.py b/build/lib.linux-x86_64-cpython-37/pybasicbayes/abstractions.py
new file mode 100644
index 0000000..853cab0
--- /dev/null
+++ b/build/lib.linux-x86_64-cpython-37/pybasicbayes/abstractions.py
@@ -0,0 +1,247 @@
+from __future__ import print_function
+from builtins import range
+from builtins import object
+import abc
+import numpy as np
+import copy
+
+import pybasicbayes
+from pybasicbayes.util.stats import combinedata
+from pybasicbayes.util.text import progprint_xrange
+from future.utils import with_metaclass
+
+# NOTE: data is always a (possibly masked) np.ndarray or list of (possibly
+# masked) np.ndarrays.
+
+# TODO figure out a data abstraction
+# TODO make an exponential family abc to reduce boilerplate
+
+################
+# Base class #
+################
+
+class Distribution(with_metaclass(abc.ABCMeta, object)):
+ @abc.abstractmethod
+ def rvs(self,size=[]):
+ 'random variates (samples)'
+ pass
+
+ @abc.abstractmethod
+ def log_likelihood(self,x):
+ '''
+ log likelihood (either log probability mass function or log probability
+ density function) of x, which has the same type as the output of rvs()
+ '''
+ pass
+
+class BayesianDistribution(with_metaclass(abc.ABCMeta, Distribution)):
+ def empirical_bayes(self,data):
+ '''
+ (optional) set hyperparameters via empirical bayes
+ e.g. treat argument as a pseudo-dataset for exponential family
+ '''
+ raise NotImplementedError
+
+#########################################################
+# Algorithm interfaces for inference in distributions #
+#########################################################
+
+class GibbsSampling(with_metaclass(abc.ABCMeta, BayesianDistribution)):
+ @abc.abstractmethod
+ def resample(self,data=[]):
+ pass
+
+ def copy_sample(self):
+ '''
+ return an object copy suitable for making lists of posterior samples
+ (override this method to prevent copying shared structures into each sample)
+ '''
+ return copy.deepcopy(self)
+
+ def resample_and_copy(self):
+ self.resample()
+ return self.copy_sample()
+
+class MeanField(with_metaclass(abc.ABCMeta, BayesianDistribution)):
+ @abc.abstractmethod
+ def expected_log_likelihood(self,x):
+ pass
+
+ @abc.abstractmethod
+ def meanfieldupdate(self,data,weights):
+ pass
+
+ def get_vlb(self):
+ raise NotImplementedError
+
+class MeanFieldSVI(with_metaclass(abc.ABCMeta, BayesianDistribution)):
+ @abc.abstractmethod
+ def meanfield_sgdstep(self,expected_suff_stats,prob,stepsize):
+ pass
+
+class Collapsed(with_metaclass(abc.ABCMeta, BayesianDistribution)):
+ @abc.abstractmethod
+ def log_marginal_likelihood(self,data):
+ pass
+
+ def log_predictive(self,newdata,olddata):
+ return self.log_marginal_likelihood(combinedata((newdata,olddata))) \
+ - self.log_marginal_likelihood(olddata)
+
+ def predictive(self,*args,**kwargs):
+ return np.exp(self.log_predictive(*args,**kwargs))
+
+class MaxLikelihood(with_metaclass(abc.ABCMeta, Distribution)):
+ @abc.abstractmethod
+ def max_likelihood(self,data,weights=None):
+ '''
+ sets the parameters set to their maximum likelihood values given the
+ (weighted) data
+ '''
+ pass
+
+ @property
+ def num_parameters(self):
+ raise NotImplementedError
+
+class MAP(with_metaclass(abc.ABCMeta, BayesianDistribution)):
+ @abc.abstractmethod
+ def MAP(self,data,weights=None):
+ '''
+ sets the parameters to their MAP values given the (weighted) data
+ analogous to max_likelihood but includes hyperparameters
+ '''
+ pass
+
+class Tempering(BayesianDistribution):
+ @abc.abstractmethod
+ def log_likelihood(self,data,temperature=1.):
+ pass
+
+ @abc.abstractmethod
+ def resample(self,data,temperature=1.):
+ pass
+
+ def energy(self,data):
+ return -self.log_likelihood(data,temperature=1.)
+
+############
+# Models #
+############
+
+# a "model" is differentiated from a "distribution" in this code by latent state
+# over data: a model attaches a latent variable (like a label or state sequence)
+# to data, and so it 'holds onto' data. Hence the add_data method.
+
+class Model(with_metaclass(abc.ABCMeta, object)):
+ @abc.abstractmethod
+ def add_data(self,data):
+ pass
+
+ @abc.abstractmethod
+ def generate(self,keep=True,**kwargs):
+ '''
+ Like a distribution's rvs, but this also fills in latent state over
+ data and keeps references to the data.
+ '''
+ pass
+
+ def rvs(self,*args,**kwargs):
+ return self.generate(*args,keep=False,**kwargs)[0] # 0th component is data, not latent stuff
+
+##################################################
+# Algorithm interfaces for inference in models #
+##################################################
+
+class ModelGibbsSampling(with_metaclass(abc.ABCMeta, Model)):
+ @abc.abstractmethod
+ def resample_model(self): # TODO niter?
+ pass
+
+ def copy_sample(self):
+ '''
+ return an object copy suitable for making lists of posterior samples
+ (override this method to prevent copying shared structures into each sample)
+ '''
+ return copy.deepcopy(self)
+
+ def resample_and_copy(self):
+ self.resample_model()
+ return self.copy_sample()
+
+class ModelMeanField(with_metaclass(abc.ABCMeta, Model)):
+ @abc.abstractmethod
+ def meanfield_coordinate_descent_step(self):
+ # returns variational lower bound after update, if available
+ pass
+
+ def meanfield_coordinate_descent(self,tol=1e-1,maxiter=250,progprint=False,**kwargs):
+ # NOTE: doesn't re-initialize!
+ scores = []
+ step_iterator = range(maxiter) if not progprint else progprint_xrange(maxiter)
+ for itr in step_iterator:
+ scores.append(self.meanfield_coordinate_descent_step(**kwargs))
+ if scores[-1] is not None and len(scores) > 1:
+ if np.abs(scores[-1]-scores[-2]) < tol:
+ return scores
+ print('WARNING: meanfield_coordinate_descent hit maxiter of %d' % maxiter)
+ return scores
+
+class ModelMeanFieldSVI(with_metaclass(abc.ABCMeta, Model)):
+ @abc.abstractmethod
+ def meanfield_sgdstep(self,minibatch,prob,stepsize):
+ pass
+
+class _EMBase(with_metaclass(abc.ABCMeta, Model)):
+ @abc.abstractmethod
+ def log_likelihood(self):
+ # returns a log likelihood number on attached data
+ pass
+
+ def _EM_fit(self,method,tol=1e-1,maxiter=100,progprint=False):
+ # NOTE: doesn't re-initialize!
+ likes = []
+ step_iterator = range(maxiter) if not progprint else progprint_xrange(maxiter)
+ for itr in step_iterator:
+ method()
+ likes.append(self.log_likelihood())
+ if len(likes) > 1:
+ if likes[-1]-likes[-2] < tol:
+ return likes
+ elif likes[-1] < likes[-2]:
+ # probably oscillation, do one more
+ method()
+ likes.append(self.log_likelihood())
+ return likes
+ print('WARNING: EM_fit reached maxiter of %d' % maxiter)
+ return likes
+
+class ModelEM(with_metaclass(abc.ABCMeta, _EMBase)):
+ def EM_fit(self,tol=1e-1,maxiter=100):
+ return self._EM_fit(self.EM_step,tol=tol,maxiter=maxiter)
+
+ @abc.abstractmethod
+ def EM_step(self):
+ pass
+
+class ModelMAPEM(with_metaclass(abc.ABCMeta, _EMBase)):
+ def MAP_EM_fit(self,tol=1e-1,maxiter=100):
+ return self._EM_fit(self.MAP_EM_step,tol=tol,maxiter=maxiter)
+
+ @abc.abstractmethod
+ def MAP_EM_step(self):
+ pass
+
+class ModelParallelTempering(with_metaclass(abc.ABCMeta, Model)):
+ @abc.abstractproperty
+ def temperature(self):
+ pass
+
+ @abc.abstractproperty
+ def energy(self):
+ pass
+
+ @abc.abstractmethod
+ def swap_sample_with(self,other):
+ pass
+
diff --git a/build/lib.linux-x86_64-cpython-37/pybasicbayes/distributions/__init__.py b/build/lib.linux-x86_64-cpython-37/pybasicbayes/distributions/__init__.py
new file mode 100644
index 0000000..d640135
--- /dev/null
+++ b/build/lib.linux-x86_64-cpython-37/pybasicbayes/distributions/__init__.py
@@ -0,0 +1,13 @@
+from __future__ import absolute_import
+from .meta import *
+
+from .regression import *
+from .gaussian import *
+from .uniform import *
+
+from .binomial import *
+from .multinomial import *
+from .negativebinomial import *
+from .geometric import *
+from .poisson import *
+from .dynamic_glm import *
diff --git a/build/lib.linux-x86_64-cpython-37/pybasicbayes/distributions/binomial.py b/build/lib.linux-x86_64-cpython-37/pybasicbayes/distributions/binomial.py
new file mode 100644
index 0000000..98eb59b
--- /dev/null
+++ b/build/lib.linux-x86_64-cpython-37/pybasicbayes/distributions/binomial.py
@@ -0,0 +1,131 @@
+from __future__ import division
+from builtins import zip
+__all__ = ['Binomial']
+
+import numpy as np
+import scipy.stats as stats
+import scipy.special as special
+from warnings import warn
+
+from pybasicbayes.abstractions import GibbsSampling, MeanField, \
+ MeanFieldSVI
+
+
+class Binomial(GibbsSampling, MeanField, MeanFieldSVI):
+ '''
+ Models a Binomial likelihood and a Beta prior:
+
+ p ~ Beta(alpha_0, beta_0)
+ x | p ~ Binom(p,n)
+
+ where p is the success probability, alpha_0-1 is the prior number of
+ successes, beta_0-1 is the prior number of failures.
+
+ A special case of Multinomial where N is fixed and each observation counts
+ the number of successes and is in {0,1,...,N}.
+ '''
+ def __init__(self,alpha_0,beta_0,alpha_mf=None,beta_mf=None,p=None,n=None):
+ warn('this class is untested!')
+ assert n is not None
+
+ self.n = n
+ self.alpha_0 = alpha_0
+ self.beta_0 = beta_0
+
+ self.alpha_mf = alpha_mf if alpha_mf is not None else alpha_0
+ self.beta_mf = beta_mf if beta_mf is not None else beta_0
+
+ if p is not None:
+ self.p = p
+ else:
+ self.resample()
+
+ def log_likelihood(self,x):
+ return stats.binom.pmf(x,self.n,self.p)
+
+ def rvs(self,size=None):
+ return stats.binom.pmf(self.n,self.p,size=size)
+
+ @property
+ def natural_hypparam(self):
+ return np.array([self.alpha_0 - 1, self.beta_0 - 1])
+
+ @natural_hypparam.setter
+ def natural_hypparam(self,natparam):
+ self.alpha_0, self.beta_0 = natparam + 1
+
+ def _get_statistics(self,data):
+ if isinstance(data,np.ndarray):
+ data = data.ravel()
+ tot = data.sum()
+ return np.array([tot, self.n*data.shape[0] - tot])
+ else:
+ return sum(
+ (self._get_statistics(d) for d in data),
+ self._empty_statistics())
+
+ def _get_weighted_statistics(self,data,weights):
+ if isinstance(data,np.ndarray):
+ data, weights = data.ravel(), weights.ravel()
+ tot = weights.dot(data)
+ return np.array([tot, self.n*weights.sum() - tot])
+ else:
+ return sum(
+ (self._get_weighted_statistics(d,w) for d,w in zip(data,weights)),
+ self._empty_statistics())
+
+ def _empty_statistics(self):
+ return np.zeros(2)
+
+ ### Gibbs
+
+ def resample(self,data=[]):
+ alpha_n, beta_n = self.natural_hypparam + self._get_statistics(data) + 1
+ self.p = np.random.beta(alpha_n,beta_n)
+
+ # use Gibbs to initialize mean field
+ self.alpha_mf = self.p * (self.alpha_0 + self.beta_0)
+ self.beta_mf = (1-self.p) * (self.alpha_0 + self.beta_0)
+
+ ### Mean field and SVI
+
+ def meanfieldupdate(self,data,weights):
+ self.mf_natural_hypparam = \
+ self.natural_hypparam + self._get_weighted_statistics(data,weights)
+
+ # use mean field to initialize Gibbs
+ self.p = self.alpha_mf / (self.alpha_mf + self.beta_mf)
+
+ def meanfield_sgdstep(self,data,weights,minibatchprob,stepsize):
+ self.mf_natural_hypparam = \
+ (1-stepsize) * self.mf_natural_hypparam + stepsize * (
+ self.natural_hypparam
+ + 1./minibatchprob * self._get_weighted_statistics(data,weights))
+
+ @property
+ def mf_natural_hypparam(self):
+ return np.array([self.alpha_mf - 1, self.beta_mf - 1])
+
+ @mf_natural_hypparam.setter
+ def mf_natural_hypparam(self,natparam):
+ self.alpha_mf, self.beta_mf = natparam + 1
+
+ def expected_log_likelihood(self,x):
+ n = self.n
+ Elnp, Eln1mp = self._mf_expected_statistics()
+ return special.gammaln(n+1) - special.gammaln(x+1) - special.gammaln(n-x+1) \
+ + x*Elnp + (n-x)*Eln1mp
+
+ def _mf_expected_statistics(self):
+ return special.digamma([self.alpha_mf, self.beta_mf]) \
+ - special.digamma(self.alpha_mf + self.beta_mf)
+
+ def get_vlb(self):
+ Elnp, Eln1mp = self._mf_expected_statistics()
+ return (self.alpha_0 - self.alpha_mf)*Elnp \
+ + (self.beta_0 - self.beta_mf)*Eln1mp \
+ - (self._log_partition_function(self.alpha_0, self.beta_0)
+ - self._log_partition_function(self.alpha_mf,self.beta_mf))
+
+ def _log_partition_function(self,alpha,beta):
+ return special.betaln(alpha,beta)
diff --git a/build/lib.linux-x86_64-cpython-37/pybasicbayes/distributions/dynamic_glm.py b/build/lib.linux-x86_64-cpython-37/pybasicbayes/distributions/dynamic_glm.py
new file mode 100644
index 0000000..3e1a38b
--- /dev/null
+++ b/build/lib.linux-x86_64-cpython-37/pybasicbayes/distributions/dynamic_glm.py
@@ -0,0 +1,279 @@
+from __future__ import division
+from builtins import zip
+from builtins import range
+__all__ = ['Dynamic_GLM']
+
+from pybasicbayes.abstractions import \
+ GibbsSampling
+
+import numpy as np
+from warnings import warn
+from pypolyagamma import PyPolyaGamma
+
+def local_multivariate_normal_draw(x, sigma, normal):
+ """
+ Cholesky doesn't like 0 cov matrix, but we want it.
+
+ TODO: This might need changing if in practice we see plently of 0 matrices
+ """
+ try:
+ return x + np.linalg.cholesky(sigma).dot(normal)
+ except np.linalg.LinAlgError:
+ if np.isclose(sigma, 0).all():
+ return x
+ else:
+ print("Weird covariance matrix")
+ quit()
+
+
+ppgsseed = 4
+if ppgsseed == 4:
+ print("Using default seed")
+ppgs = PyPolyaGamma(ppgsseed)
+class Dynamic_GLM(GibbsSampling):
+ """
+ This class enables a drifting input output iHMM with logistic link function.
+
+ States are thus dynamic GLMs, giving us more freedom as to the inputs we give the model.
+
+ Hyperparaemters:
+
+ TODO
+
+ Parameters:
+ [weights]
+ """
+
+ def __init__(self, n_inputs, T, prior_mean, P_0, Q, jumplimit=3, seed=4):
+
+ self.n_inputs = n_inputs
+ self.T = T
+ self.jumplimit = jumplimit
+ self.x_0 = prior_mean
+ self.P_0, self.Q = P_0, Q
+ self.psi_diff_saves = []
+ self.noise_mean = np.zeros(self.n_inputs) # save this, so as to not keep creating it
+ self.identity = np.eye(self.n_inputs) # not really needed, but kinda useful for state sampling, mabye delete TODO
+
+ # if seed == 4:
+ # print("Using default seed")
+ # self.ppgs = PyPolyaGamma(seed)
+ self.weights = np.empty((self.T, self.n_inputs)) # one more spot for bias
+ self.weights[0] = np.random.multivariate_normal(mean=self.x_0, cov=self.P_0)
+ for t in range(1, T):
+ self.weights[t] = self.weights[t - 1] + np.random.multivariate_normal(mean=self.noise_mean, cov=self.Q[t - 1])
+
+ def rvs(self, inputs, times):
+ outputs = []
+ for input, t in zip(inputs, times):
+ if input.shape[0] == 0:
+ output = np.zeros((0, self.n_inputs + 1))
+ else:
+ types, inverses, counts = np.unique(input, return_inverse=1, return_counts=True, axis=0)
+ output = np.append(input, np.empty((input.shape[0], 1)), axis=1)
+ for i, (type, c) in enumerate(zip(types, counts)):
+ temp = np.random.rand(c) < 1 / (1 + np.exp(- np.sum(self.weights[t] * type)))
+ output[inverses == i, -1] = temp
+ outputs.append(output)
+ return outputs
+
+ def log_likelihood(self, input, timepoint):
+ predictors, responses = input[:, :-1], input[:, -1]
+ nans = np.isnan(responses)
+ probs = np.zeros((input.shape[0], 2))
+ out = np.zeros(input.shape[0])
+ # I could possibly save the 1 / ..., since it's logged it's just - log (but the other half of the probs is an issue)
+ probs[:, 1] = 1 / (1 + np.exp(- np.sum(self.weights[timepoint] * predictors, axis=1)))
+ probs[:, 0] = 1 - probs[:, 1]
+ # probably not necessary, just fill everything with probs and then have some be 1 - out?
+ out[~nans] = probs[np.arange(input.shape[0])[~nans], responses[~nans].astype(int)]
+ out = np.clip(out, np.spacing(1), 1 - np.spacing(1))
+ out[nans] = 1
+
+ return np.log(out)
+
+ # Gibbs sampling
+ def resample(self, data=[]):
+ # TODO: Clean up this mess, I always have to call delete_obs_data because of all the saved shit!
+ self.psi_diff_saves = []
+ summary_statistics, all_times = self._get_statistics(data)
+ types, pseudo_counts, counts = summary_statistics
+
+ # if state is never active, resample from prior, but without dynamic change
+ if len(counts) == 0:
+ self.weights = np.tile(np.random.multivariate_normal(mean=self.x_0, cov=self.P_0), (self.T, 1))
+ return
+
+ """compute Kalman filter parameters, also sort out which weight vector goes to which timepoint"""
+ timepoint_map = {}
+ total_types = 0
+ actual_obs_count = 0
+ change_points = []
+ prev_t = all_times[0] - 1
+ fake_times = []
+ for type, t in zip(types, all_times):
+ if t > prev_t + 1:
+ add_list = list(range(total_types, min(total_types + t - prev_t - 1, total_types + self.jumplimit)))
+ change_points += add_list
+ fake_times += add_list
+ for i, sub_t in enumerate(range(total_types, total_types + t - prev_t - 1)): # TODO: set up this loop better
+ timepoint_map[prev_t + i + 1] = min(sub_t, total_types + self.jumplimit - 1)
+ total_types += min(t - prev_t - 1, self.jumplimit)
+ total_types += type.shape[0]
+ actual_obs_count += type.shape[0]
+ change_points.append(total_types - 1)
+ timepoint_map[t] = total_types - 1
+ prev_t = t
+
+ # print(total_types)
+ # print(actual_obs_count)
+ # print(change_points)
+ # print(fake_times)
+ # print(all_times)
+ # print(timepoint_map)
+ # return timepoint_map
+
+ self.pseudo_Q = np.zeros((total_types, self.n_inputs, self.n_inputs))
+ # TODO: is it okay to cut off last timepoint here?
+ for k in range(self.T):
+ if k in timepoint_map:
+ self.pseudo_Q[timepoint_map[k]] = self.Q[k] # for every timepoint, map it's variance onto the pseudo_Q
+
+ """sample pseudo obs"""
+ temp = np.empty(actual_obs_count)
+ psis = np.empty(actual_obs_count)
+ psi_count = 0
+ predictors = []
+ for type, time in zip(types, all_times):
+ for t in type:
+ psis[psi_count] = np.sum(self.weights[time] * t)
+ predictors.append(t)
+ psi_count += 1
+
+ ppgs.pgdrawv(np.concatenate(counts).astype(float), psis, temp)
+ self.R = np.zeros(total_types)
+ mask = np.ones(total_types, dtype=np.bool)
+ mask[fake_times] = False
+ self.R[mask] = 1 / temp
+ self.pseudo_obs = np.zeros(total_types)
+ self.pseudo_obs[mask] = np.concatenate(pseudo_counts) / temp
+ self.pseudo_obs = self.pseudo_obs.reshape(total_types, 1)
+ self.H = np.zeros((total_types, self.n_inputs, 1))
+ self.H[mask] = np.array(predictors).reshape(actual_obs_count, self.n_inputs, 1)
+
+ """compute means and sigmas by filtering"""
+ # if there is no obs, sigma_k = sigma_k_k_minus and x_hat_k = x_hat_k_k_minus (because R is infinite at that time)
+ self.compute_sigmas(total_types)
+ self.compute_means(total_types)
+
+ """sample states"""
+ self.weights.fill(0)
+ pseudo_weights = np.empty((total_types, self.n_inputs))
+ pseudo_weights[total_types - 1] = np.random.multivariate_normal(self.x_hat_k[total_types - 1], self.sigma_k[total_types - 1])
+
+ normals = np.random.standard_normal((total_types - 1, self.n_inputs))
+ for k in range(total_types - 2, -1, -1): # normally -1, but we already did first sampling
+ if np.all(self.pseudo_Q[k] == 0):
+ pseudo_weights[k] = pseudo_weights[k + 1]
+ else:
+ updated_x = self.x_hat_k[k].copy() # not sure whether copy is necessary here
+ updated_sigma = self.sigma_k[k].copy()
+
+ for m in range(self.n_inputs):
+ epsilon = pseudo_weights[k + 1, m] - updated_x[m]
+ state_R = updated_sigma[m, m] + self.pseudo_Q[k, m, m]
+
+ updated_x += updated_sigma[:, m] * epsilon / state_R # I don't think it's important, but probs we need the first column
+ updated_sigma -= updated_sigma.dot(np.outer(self.identity[m], self.identity[m])).dot(updated_sigma) / state_R
+
+ pseudo_weights[k] = local_multivariate_normal_draw(updated_x, updated_sigma, normals[k])
+
+ for k in range(self.T):
+ if k in timepoint_map:
+ self.weights[k] = pseudo_weights[timepoint_map[k]]
+
+ """don't forget to sample before and after active times too"""
+ for k in range(all_times[0] - 1, -1, -1):
+ if k > all_times[0] - self.jumplimit - 1:
+ self.weights[k] = self.weights[k + 1] + np.random.multivariate_normal(self.noise_mean, self.Q[k])
+ else:
+ self.weights[k] = self.weights[k + 1]
+ for k in range(all_times[-1] + 1, self.T):
+ if k < min(all_times[-1] + 1 + self.jumplimit, self.T):
+ self.weights[k] = self.weights[k - 1] + np.random.multivariate_normal(self.noise_mean, self.Q[k])
+ else:
+ self.weights[k] = self.weights[k - 1]
+
+ return pseudo_weights
+ # TODO:
+ # self.psi_diff_saves = np.concatenate(self.psi_diff_saves)
+
+ def _get_statistics(self, data):
+ # TODO: improve
+ summary_statistics = [[], [], []]
+ times = []
+ if isinstance(data, np.ndarray):
+ warn('What you are trying is probably stupid, at least the code is not implemented')
+ quit()
+ # assert len(data.shape) == 2
+ # for d in data:
+ # counts[tuple(d)] += 1
+ else:
+ for i, d in enumerate(data):
+ clean_d = d[~np.isnan(d[:, -1])]
+ if len(clean_d) != 0:
+ predictors, responses = clean_d[:, :-1], clean_d[:, -1]
+ types, inverses, counts = np.unique(predictors, return_inverse=True, return_counts=True, axis=0)
+ pseudo_counts = np.zeros(len(types))
+ for j, c in enumerate(counts):
+ mask = inverses == j
+ pseudo_counts[j] = np.sum(responses[mask]) - c / 2
+ summary_statistics[0].append(types)
+ summary_statistics[1].append(pseudo_counts)
+ summary_statistics[2].append(counts)
+ times.append(i)
+
+ return summary_statistics, times
+
+ def compute_sigmas(self, T):
+ """Sigmas can be precomputed (without z), we do this here."""
+ # We rely on the fact that H.T.dot(sigma).dot(H) is just a number, no matrix inversion needed
+ # furthermore we use the fact that many matrices are identities, namely F and G
+ self.sigma_k = [] # we have to reset this for repeating this calculation later for the resampling (R changes)
+ self.sigma_k_k_minus = [self.P_0]
+ self.gain_save = []
+ for k in range(T):
+ if self.R[k] == 0:
+ self.gain_save.append(None)
+ self.sigma_k.append(self.sigma_k_k_minus[k])
+ self.sigma_k_k_minus.append(self.sigma_k[k] + self.pseudo_Q[k])
+ else:
+ sigma, H = self.sigma_k_k_minus[k], self.H[k] # we will need this a lot, so shorten it
+ gain = sigma.dot(H).dot(1 / (H.T.dot(sigma).dot(H) + self.R[k]))
+ self.gain_save.append(gain)
+ self.sigma_k.append(sigma - gain.dot(H.T).dot(sigma))
+ self.sigma_k_k_minus.append(self.sigma_k[k] + self.pseudo_Q[k])
+
+ def compute_means(self, T):
+ """Compute the means, the estimates of the states."""
+ self.x_hat_k = [] # we have to reset this for repeating this calculation later for the resampling
+ self.x_hat_k_k_minus = [self.x_0]
+ for k in range(T): # this will leave out last state which doesn't have observation
+ if self.gain_save[k] is None:
+ self.x_hat_k.append(self.x_hat_k_k_minus[k])
+ self.x_hat_k_k_minus.append(self.x_hat_k[k]) # TODO: still no purpose
+ else:
+ x, H = self.x_hat_k_k_minus[k], self.H[k] # we will need this a lot, so shorten it
+ self.x_hat_k.append(x + self.gain_save[k].dot(self.pseudo_obs[k] - H.T.dot(x)))
+ self.x_hat_k_k_minus.append(self.x_hat_k[k]) # TODO: doesn't really have a purpose if F is identity
+
+ def num_parameters(self):
+ return self.weights.size
+
+ ### Max likelihood
+
+ def max_likelihood(self,data,weights=None):
+ warn('ML not implemented')
+
+ def MAP(self,data,weights=None):
+ warn('MAP not implemented')
diff --git a/build/lib.linux-x86_64-cpython-37/pybasicbayes/distributions/dynamic_multinomial.py b/build/lib.linux-x86_64-cpython-37/pybasicbayes/distributions/dynamic_multinomial.py
new file mode 100644
index 0000000..dbba312
--- /dev/null
+++ b/build/lib.linux-x86_64-cpython-37/pybasicbayes/distributions/dynamic_multinomial.py
@@ -0,0 +1,286 @@
+from __future__ import division
+from builtins import zip
+from builtins import range
+__all__ = ['Dynamic_Input_Categorical']
+
+from pybasicbayes.abstractions import \
+ GibbsSampling
+
+from scipy import sparse
+import numpy as np
+from warnings import warn
+import time
+
+from pgmult.lda import StickbreakingDynamicTopicsLDA
+from pgmult.utils import psi_to_pi
+from scipy.stats import invgamma
+
+
+def enforce_limits(times, limit):
+ times = np.array(times)
+ diffs = np.zeros(len(times), dtype=np.int32)
+ diffs[1:] = np.diff(times)
+ diffs[diffs <= limit] = limit
+ diffs -= limit
+ diffs = np.cumsum(diffs)
+
+ diffs += times[0]
+ times -= diffs
+ return times
+
+
+assert np.array_equal(enforce_limits([0, 1, 2, 3, 4, 5], 3), [0, 1, 2, 3, 4, 5])
+assert np.array_equal(enforce_limits([0, 2, 4, 6, 8, 10, 12, 14, 15], 3), [0, 2, 4, 6, 8, 10, 12, 14, 15])
+assert np.array_equal(enforce_limits([0, 1, 2, 6, 10, 14], 3), [0, 1, 2, 5, 8, 11])
+assert np.array_equal(enforce_limits([0, 1, 8, 20, 100], 3), [0, 1, 4, 7, 10])
+assert np.array_equal(enforce_limits([0, 1, 8, 20, 100, 101, 102], 3), [0, 1, 4, 7, 10, 11, 12])
+assert np.array_equal(enforce_limits([0, 1, 8, 20, 100, 101, 102, 104], 3), [0, 1, 4, 7, 10, 11, 12, 14])
+assert np.array_equal(enforce_limits([0, 1, 8, 20, 100, 101, 102, 104, 110], 3), [0, 1, 4, 7, 10, 11, 12, 14, 17])
+assert np.array_equal(enforce_limits([1, 8, 20, 100, 101, 102, 104, 110], 3), [0, 3, 6, 9, 10, 11, 13, 16])
+
+
+def meh_time_info(all_times, sub_times, limit):
+ # Return time stamps for the needed counts, considering jumps
+ # Return list of mappings, to translate from this states timepoints to the overall timepoints
+ # Return first and last timepoint
+ times = []
+ maps = []
+ first, last = all_times[sub_times[0]], all_times[sub_times[-1]]
+ jump_counter = 0
+ time_counter = 0
+ for i in range(first, last+1):
+ if i in all_times:
+ times.append(i)
+ maps.append((time_counter, i))
+ jump_counter = 0
+ time_counter += 1
+ else:
+ jump_counter += 1
+ if jump_counter <= limit:
+ times.append(i)
+ maps.append((time_counter, i))
+ time_counter += 1
+ else:
+ maps.append((time_counter - 1, i))
+
+ return times, maps, first, last
+
+
+all_times, sub_times, limit = [0, 3, 9], [0, 2], 3
+mya1, mya2, mya3, mya4 = [0, 1, 2, 3, 4, 5, 6, 9], [(0, 0), (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6), (6, 7), (6, 8), (7, 9)], 0, 9
+o1, o2, o3, o4 = meh_time_info(all_times, sub_times, limit)
+assert mya1 == o1
+assert mya2 == o2
+assert mya3 == o3
+assert mya4 == o4
+
+all_times, sub_times, limit = [0, 3, 9], [1], 3
+mya1, mya2, mya3, mya4 = [3], [(0, 3)], 3, 3
+o1, o2, o3, o4 = meh_time_info(all_times, sub_times, limit)
+assert mya1 == o1
+assert mya2 == o2
+assert mya3 == o3
+assert mya4 == o4
+
+
+
+def time_info(all_times, sub_times, limit):
+ # Return list of mappings, to translate from this states timepoints to the overall timepoints
+ # Return first and last timepoint
+ maps = []
+ first, last = all_times[sub_times[0]], all_times[sub_times[-1]]
+ jump_counter = 0
+ time_counter = 0
+ for i in range(first, last+1):
+ if i in all_times:
+ maps.append((time_counter, i))
+ jump_counter = 0
+ time_counter += 1
+ else:
+ jump_counter += 1
+ if jump_counter < limit:
+ maps.append((time_counter, i))
+ time_counter += 1
+ else:
+ maps.append((time_counter - 1, i))
+
+ return maps, first, last
+
+
+all_times, sub_times, limit = [0, 3, 9], [0, 2], 3
+mya2, mya3, mya4 = [(0, 0), (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (5, 6), (5, 7), (5, 8), (6, 9)], 0, 9
+o2, o3, o4 = time_info(all_times, sub_times, limit)
+assert mya1 == o1
+assert mya2 == o2
+assert mya3 == o3
+assert mya4 == o4
+
+all_times, sub_times, limit = [0, 3, 9], [1], 3
+mya2, mya3, mya4 = [(0, 3)], 3, 3 # TODO: I don't think it matters whether first answer is [3] or [0]
+o2, o3, o4 = time_info(all_times, sub_times, limit)
+assert mya2 == o2
+assert mya3 == o3
+assert mya4 == o4
+# TODO: more tests
+
+class Dynamic_Input_Categorical(GibbsSampling):
+ """
+ This class enables a drifting input output iHMM.
+
+ Everything is pretty much like in the input Categorical, but here we also
+ allow drift across sessions for the Categoricals. Similar to a dynamic topic
+ model (with one topic).
+
+ We'll have to tricks quite a bit:
+ - Instead of really resampling we'll reinstate a new dtm for every resampling and resample a couple of times (time killer)
+ - We can't initialize from prior all that easily. We'll just instantiate a constant Dirichlet from prior
+ once data is actually there, we'll use the real model
+ - this will also be a bit hard to copy... maybe really just use package for resampling, otherwise have all that stuff saved in a list of Categoricals?
+ Big problem: how to give log-likelihood for obs in sessions where this state was previously not present?
+ We don't know what value this thing should have there, could be anything...
+ -> if there is no data, we simply have to sample from prior. That is the will of Gibbs
+ That is: sample from prior for first 3 unaccounted sessions, then leave constant
+ But!: How to do this back in time? -> also Gibbs sample just from prior for three sessions
+
+ ! First session cannot contain no data for StickbreakingDynamicTopicsLDA
+
+ Idea: maybe save previously assigned betas (or psi's or whatever directly)
+ then initialize new dtm from there, so as to have to do less resampling
+ (this depends on what gets resampled first, hopefully the auxiliary variables first, then this saving should have an effect)
+
+ Hyperparaemters:
+
+ TODO
+
+ Parameters:
+ [weights, a vector encoding a finite, multidimensional pmf]
+ """
+
+ def __init__(self, n_inputs, n_outputs, T, sigmasq_states, jumplimit=3, n_resample=15):
+
+ self.n_inputs = n_inputs
+ self.n_outputs = n_outputs # could be made different for different inputs
+ if self.n_outputs != 2:
+ warn('this requires adaptions in the row swapping code for the dynamic topic model')
+ # quit()
+ self.T = T
+ self.jumplimit = jumplimit
+ self.sigmasq_states = sigmasq_states
+ self.n_resample = n_resample
+ self.psi_diff_saves = []
+
+ single_weights = np.zeros((self.n_inputs, self.n_outputs))
+ for i in range(self.n_inputs):
+ single_weights[i] = np.random.dirichlet(np.ones(self.n_outputs))
+ self.weights = np.tile(single_weights, (self.T, 1, 1)) # init to constant over timepoints
+
+ def rvs(self, input):
+ print("Looks like simple copy from Input_Categorical, not useful, no dynamics")
+ types, counts = np.unique(input, return_counts=True)
+ output = np.zeros_like(input)
+ for t, c in zip(types, counts):
+ temp = np.random.choice(self.n_outputs, c, p=self.weights[t])
+ output[input == t] = temp
+ return np.array((input, output)).T
+
+ def log_likelihood(self, x, timepoint):
+ out = np.zeros(x.shape[0], dtype=np.double)
+ nans = np.isnan(x[:, -1])
+ err = np.seterr(divide='ignore')
+ out[~nans] = np.log(self.weights[timepoint])[tuple(x[~nans].T.astype(int))]
+ np.seterr(**err)
+ out[nans] = 1
+ return out
+
+ # Gibbs sampling
+ def resample(self, data=[]):
+ self.psi_diff_saves = []
+ counts, all_times = self._get_statistics(data)
+
+ # if state is never active, resample from prior
+ if counts.sum() == 0:
+ single_weights = np.zeros((self.n_inputs, self.n_outputs))
+ for i in range(self.n_inputs):
+ single_weights[i] = np.random.dirichlet(np.ones(self.n_outputs))
+ self.weights = np.tile(single_weights, (self.T, 1, 1)) # init to constant over timepoints
+ return
+
+ fake_times = enforce_limits(all_times, self.jumplimit)
+ self.weights.fill(0)
+
+ for i in range(self.n_inputs):
+ if np.sum(counts[:, i]) == 0:
+ self.weights[:, i] = np.random.dirichlet(np.ones(self.n_outputs))
+ else:
+ temp = np.sum(counts[:, i], axis=1)
+ spec_times = np.where(temp)[0]
+ maps, first_non0, last_non0 = time_info(all_times, spec_times, self.jumplimit)
+ spec_fake_times = fake_times[spec_times]
+ # we shuffle the columns around, so as to have the timeout answer first, for a hopefully more constistent variance estimation
+
+ # dtm = StickbreakingDynamicTopicsLDA(sparse.csr_matrix(counts[spec_times, i][..., [2, 0, 1]]), spec_fake_times, K=1, alpha_theta=1, sigmasq_states=self.sigmasq_states)
+ dtm = StickbreakingDynamicTopicsLDA(sparse.csr_matrix(counts[spec_times, i]), spec_fake_times, K=1, alpha_theta=1, sigmasq_states=self.sigmasq_states)
+
+ for _ in range(self.n_resample):
+ dtm.resample()
+
+ # save for resampling sigma
+ self.psi_diff_saves.append(np.diff(dtm.psi, axis=0).ravel())
+
+ # put dtm weights in right places
+ for m in maps:
+ # shuffle back
+ # self.weights[m[1], i] = dtm.beta[m[0], :, 0][..., [1, 2, 0]]
+ self.weights[m[1], i] = dtm.beta[m[0], :, 0]
+
+ sample = dtm.psi[0]
+ for j in range(min(self.jumplimit, first_non0)):
+ sample += np.random.normal(0, np.sqrt(self.sigmasq_states), size=self.n_outputs - 1)[:, None] # is this the correct way to do this? not sure
+ # self.weights[first_non0 - j - 1, i] = psi_to_pi(sample.T)[..., [1, 2, 0]]
+ self.weights[first_non0 - j - 1, i] = psi_to_pi(sample.T)
+ if first_non0 > self.jumplimit:
+ # self.weights[:first_non0 - self.jumplimit, i] = psi_to_pi(sample.T)[..., [1, 2, 0]]
+ self.weights[:first_non0 - self.jumplimit, i] = psi_to_pi(sample.T)
+
+ sample = dtm.psi[-1]
+ for j in range(min(self.jumplimit, self.T - last_non0 - 1)):
+ sample += np.random.normal(0, np.sqrt(self.sigmasq_states), size=self.n_outputs - 1)[:, None] # is this the correct way to do this? not sure
+ # self.weights[last_non0 + j + 1, i] = psi_to_pi(sample.T)[..., [1, 2, 0]]
+ self.weights[last_non0 + j + 1, i] = psi_to_pi(sample.T)
+ if self.T - last_non0 - 1 > self.jumplimit:
+ # self.weights[last_non0 + self.jumplimit + 1:, i] = psi_to_pi(sample.T)[..., [1, 2, 0]]
+ self.weights[last_non0 + self.jumplimit + 1:, i] = psi_to_pi(sample.T)
+
+ self.psi_diff_saves = np.concatenate(self.psi_diff_saves)
+ assert np.count_nonzero(np.sum(self.weights, axis=2)) == np.sum(self.weights, axis=2).size
+
+ def _get_statistics(self, data):
+ # TODO: improve
+ counts = []
+ times = []
+ timepoint_count = np.empty((self.n_inputs, self.n_outputs), dtype=int)
+ if isinstance(data, np.ndarray):
+ warn('What you are trying is probably stupid, at least the code is not implemented')
+ quit()
+ # assert len(data.shape) == 2
+ # for d in data:
+ # counts[tuple(d)] += 1
+ else:
+ for i, d in enumerate(data):
+ clean_d = (d[~np.isnan(d[:, -1])]).astype(int)
+ if len(clean_d) != 0:
+ timepoint_count[:] = 0
+ for subd in clean_d:
+ timepoint_count[subd[0], subd[1]] += 1
+ counts.append(timepoint_count.copy())
+ times.append(i)
+
+ return np.array(counts), times
+
+ ### Max likelihood
+
+ def max_likelihood(self,data,weights=None):
+ warn('ML not implemented')
+
+ def MAP(self,data,weights=None):
+ warn('MAP not implemented')
diff --git a/build/lib.linux-x86_64-cpython-37/pybasicbayes/distributions/dynamic_multinomial_in_progress.py b/build/lib.linux-x86_64-cpython-37/pybasicbayes/distributions/dynamic_multinomial_in_progress.py
new file mode 100644
index 0000000..46f2b0f
--- /dev/null
+++ b/build/lib.linux-x86_64-cpython-37/pybasicbayes/distributions/dynamic_multinomial_in_progress.py
@@ -0,0 +1,265 @@
+from __future__ import division
+from builtins import zip
+from builtins import range
+__all__ = ['Dynamic_Input_Categorical']
+
+from pybasicbayes.abstractions import \
+ GibbsSampling
+
+from scipy import sparse
+import numpy as np
+from warnings import warn
+import time
+
+from pgmult.lda import StickbreakingDynamicTopicsLDA
+from pgmult.utils import psi_to_pi
+
+
+def enforce_limits(times, limit):
+ times = np.array(times)
+ diffs = np.zeros(len(times), dtype=np.int32)
+ diffs[1:] = np.diff(times)
+ diffs[diffs <= limit] = limit
+ diffs -= limit
+ diffs = np.cumsum(diffs)
+
+ diffs += times[0]
+ times -= diffs
+ return times
+
+
+assert np.array_equal(enforce_limits([0, 1, 2, 3, 4, 5], 3), [0, 1, 2, 3, 4, 5])
+assert np.array_equal(enforce_limits([0, 2, 4, 6, 8, 10, 12, 14, 15], 3), [0, 2, 4, 6, 8, 10, 12, 14, 15])
+assert np.array_equal(enforce_limits([0, 1, 2, 6, 10, 14], 3), [0, 1, 2, 5, 8, 11])
+assert np.array_equal(enforce_limits([0, 1, 8, 20, 100], 3), [0, 1, 4, 7, 10])
+assert np.array_equal(enforce_limits([0, 1, 8, 20, 100, 101, 102], 3), [0, 1, 4, 7, 10, 11, 12])
+assert np.array_equal(enforce_limits([0, 1, 8, 20, 100, 101, 102, 104], 3), [0, 1, 4, 7, 10, 11, 12, 14])
+assert np.array_equal(enforce_limits([0, 1, 8, 20, 100, 101, 102, 104, 110], 3), [0, 1, 4, 7, 10, 11, 12, 14, 17])
+assert np.array_equal(enforce_limits([1, 8, 20, 100, 101, 102, 104, 110], 3), [0, 3, 6, 9, 10, 11, 13, 16])
+
+
+def meh_time_info(all_times, sub_times, limit):
+ # Return time stamps for the needed counts, considering jumps
+ # Return list of mappings, to translate from this states timepoints to the overall timepoints
+ # Return first and last timepoint
+ times = []
+ maps = []
+ first, last = all_times[sub_times[0]], all_times[sub_times[-1]]
+ jump_counter = 0
+ time_counter = 0
+ for i in range(first, last+1):
+ if i in all_times:
+ times.append(i)
+ maps.append((time_counter, i))
+ jump_counter = 0
+ time_counter += 1
+ else:
+ jump_counter += 1
+ if jump_counter <= limit:
+ times.append(i)
+ maps.append((time_counter, i))
+ time_counter += 1
+ else:
+ maps.append((time_counter - 1, i))
+
+ return times, maps, first, last
+
+
+all_times, sub_times, limit = [0, 3, 9], [0, 2], 3
+mya1, mya2, mya3, mya4 = [0, 1, 2, 3, 4, 5, 6, 9], [(0, 0), (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6), (6, 7), (6, 8), (7, 9)], 0, 9
+o1, o2, o3, o4 = meh_time_info(all_times, sub_times, limit)
+assert mya1 == o1
+assert mya2 == o2
+assert mya3 == o3
+assert mya4 == o4
+
+all_times, sub_times, limit = [0, 3, 9], [1], 3
+mya1, mya2, mya3, mya4 = [3], [(0, 3)], 3, 3
+o1, o2, o3, o4 = meh_time_info(all_times, sub_times, limit)
+assert mya1 == o1
+assert mya2 == o2
+assert mya3 == o3
+assert mya4 == o4
+
+
+
+def time_info(all_times, sub_times, limit):
+ # Return list of mappings, to translate from this states timepoints to the overall timepoints
+ # Return first and last timepoint
+ maps = []
+ first, last = all_times[sub_times[0]], all_times[sub_times[-1]]
+ jump_counter = 0
+ time_counter = 0
+ for i in range(first, last+1):
+ if i in all_times:
+ maps.append((time_counter, i))
+ jump_counter = 0
+ time_counter += 1
+ else:
+ jump_counter += 1
+ if jump_counter < limit:
+ maps.append((time_counter, i))
+ time_counter += 1
+ else:
+ maps.append((time_counter - 1, i))
+
+ return maps, first, last
+
+
+all_times, sub_times, limit = [0, 3, 9], [0, 2], 3
+mya2, mya3, mya4 = [(0, 0), (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (5, 6), (5, 7), (5, 8), (6, 9)], 0, 9
+o2, o3, o4 = time_info(all_times, sub_times, limit)
+assert mya1 == o1
+assert mya2 == o2
+assert mya3 == o3
+assert mya4 == o4
+
+all_times, sub_times, limit = [0, 3, 9], [1], 3
+mya2, mya3, mya4 = [(0, 3)], 3, 3 # TODO: I don't think it matters whether first answer is [3] or [0]
+o2, o3, o4 = time_info(all_times, sub_times, limit)
+assert mya2 == o2
+assert mya3 == o3
+assert mya4 == o4
+# TODO: more tests
+
+class Dynamic_Input_Categorical(GibbsSampling):
+ """
+ This class enables a drifting input output iHMM.
+
+ Everything is pretty much like in the input Categorical, but here we also
+ allow drift across sessions for the Categoricals. Similar to a dynamic topic
+ model (with one topic).
+
+ We'll have to tricks quite a bit:
+ - Instead of really resampling we'll reinstate a new dtm for every resampling and resample a couple of times (time killer)
+ - We can't initialize from prior all that easily. We'll just instantiate a constant Dirichlet from prior
+ once data is actually there, we'll use the real model
+ - this will also be a bit hard to copy... maybe really just use package for resampling, otherwise have all that stuff saved in a list of Categoricals?
+ Big problem: how to give log-likelihood for obs in sessions where this state was previously not present?
+ We don't know what value this thing should have there, could be anything...
+ -> if there is no data, we simply have to sample from prior. That is the will of Gibbs
+ That is: sample from prior for first 3 unaccounted sessions, then leave constant
+ But!: How to do this back in time? -> also Gibbs sample just from prior for three sessions
+
+ ! First session cannot contain no data for StickbreakingDynamicTopicsLDA
+
+ Idea: maybe save previously assigned betas (or psi's or whatever directly)
+ then initialize new dtm from there, so as to have to do less resampling
+ (this depends on what gets resampled first, hopefully the auxiliary variables first, then this saving should have an effect)
+
+ Hyperparaemters:
+
+ TODO
+
+ Parameters:
+ [weights, a vector encoding a finite, multidimensional pmf]
+ """
+
+ def __init__(self, n_inputs, n_outputs, T, sigmasq_states=0.01, jumplimit=3):
+
+ self.n_inputs = n_inputs
+ self.n_outputs = n_outputs # could be made different for different inputs
+ self.T = T
+ self.jumplimit = jumplimit
+ self.sigmasq_states = sigmasq_states # !!! this needs to be updated with gibbs estimate of sdev
+ self.psi_save = None
+
+ single_weights = np.zeros((self.n_inputs, self.n_outputs))
+ for i in range(self.n_inputs):
+ single_weights[i] = np.random.dirichlet(np.ones(self.n_outputs))
+ self.weights = np.tile(single_weights, (self.T, 1, 1)) # init to constant over timepoints
+
+ def rvs(self, input):
+ types, counts = np.unique(input, return_counts=True)
+ output = np.zeros_like(input)
+ for t, c in zip(types, counts):
+ temp = np.random.choice(self.n_outputs, c, p=self.weights[t])
+ output[input == t] = temp
+ return np.array((input, output)).T
+
+ def log_likelihood(self, x, timepoint):
+ out = np.zeros_like(x, dtype=np.double)
+ err = np.seterr(divide='ignore')
+ out = np.log(self.weights[timepoint])[tuple(x.T)]
+ np.seterr(**err)
+ return out
+
+ # Gibbs sampling
+ def resample(self, data=[]):
+ counts, all_times = self._get_statistics(data)
+
+ # if state is never active, resample from prior
+ if counts.sum() == 0:
+ single_weights = np.zeros((self.n_inputs, self.n_outputs))
+ for i in range(self.n_inputs):
+ single_weights[i] = np.random.dirichlet(np.ones(self.n_outputs))
+ self.weights = np.tile(single_weights, (self.T, 1, 1)) # init to constant over timepoints
+ return
+
+ fake_times = enforce_limits(all_times, self.jumplimit)
+ self.weights.fill(0)
+
+ for i in range(self.n_inputs):
+ # TODO: case if this counts is always 0
+ if np.sum(counts[:, i]) == 0:
+ self.weights[:, i] = np.random.dirichlet(np.ones(self.n_outputs))
+ else:
+ temp = np.sum(counts[:, i], axis=1)
+ spec_times = np.where(temp)[0]
+ maps, first_non0, last_non0 = time_info(all_times, spec_times, self.jumplimit)
+
+ # represented_sessions = [m[1] for m in maps] # these (add boundary samples) are sessions sampled, for later initialisation
+
+ spec_fake_times = fake_times[spec_times]
+ dtm = StickbreakingDynamicTopicsLDA(sparse.csr_matrix(counts[spec_times, i]), spec_fake_times, K=1, alpha_theta=1, sigmasq_states=self.sigmasq_states)
+
+ dtm.resample()
+
+ for m in maps:
+ self.weights[m[1], i] = dtm.beta[m[0], :, 0]
+
+ sample = dtm.psi[0]
+ for j in range(min(self.jumplimit, first_non0)):
+ sample += np.random.normal(0, np.sqrt(self.sigmasq_states), size=self.n_outputs - 1)[:, None] # is this the correct way to do this? not sure
+ self.weights[first_non0 - j - 1, i] = psi_to_pi(sample.T)
+ if first_non0 > self.jumplimit:
+ self.weights[:first_non0 - self.jumplimit, i] = psi_to_pi(sample.T)
+
+ sample = dtm.psi[-1]
+ for j in range(min(self.jumplimit, self.T - last_non0 - 1)):
+ sample += np.random.normal(0, np.sqrt(self.sigmasq_states), size=self.n_outputs - 1)[:, None] # is this the correct way to do this? not sure
+ self.weights[last_non0 + j + 1, i] = psi_to_pi(sample.T)
+ if self.T - last_non0 - 1 > self.jumplimit:
+ self.weights[last_non0 + self.jumplimit + 1:, i] = psi_to_pi(sample.T)
+
+ assert np.count_nonzero(np.sum(self.weights, axis=2)) == np.sum(self.weights, axis=2).size # weird way to test whether everything is normalised?
+
+ def _get_statistics(self, data):
+ # TODO: improve
+ counts = []
+ times = []
+ timepoint_count = np.empty((self.n_inputs, self.n_outputs), dtype=int)
+ if isinstance(data, np.ndarray):
+ warn('What you are trying is probably stupid, at least the code is not implemented')
+ quit()
+ # assert len(data.shape) == 2
+ # for d in data:
+ # counts[tuple(d)] += 1
+ else:
+ for i, d in enumerate(data):
+ if len(d) != 0:
+ timepoint_count[:] = 0
+ for subd in d:
+ timepoint_count[subd[0], subd[1]] += 1
+ counts.append(timepoint_count.copy())
+ times.append(i)
+
+ return np.array(counts), times
+
+ ### Max likelihood
+
+ def max_likelihood(self,data,weights=None):
+ warn('ML not implemented')
+
+ def MAP(self,data,weights=None):
+ warn('MAP not implemented')
diff --git a/build/lib.linux-x86_64-cpython-37/pybasicbayes/distributions/gaussian.py b/build/lib.linux-x86_64-cpython-37/pybasicbayes/distributions/gaussian.py
new file mode 100644
index 0000000..79d045a
--- /dev/null
+++ b/build/lib.linux-x86_64-cpython-37/pybasicbayes/distributions/gaussian.py
@@ -0,0 +1,1518 @@
+from __future__ import division
+from builtins import map
+from builtins import zip
+from builtins import range
+from builtins import object
+__all__ = \
+ ['Gaussian', 'GaussianFixedMean', 'GaussianFixedCov', 'GaussianFixed',
+ 'GaussianNonConj', 'DiagonalGaussian', 'DiagonalGaussianNonconjNIG',
+ 'IsotropicGaussian', 'ScalarGaussianNIX', 'ScalarGaussianNonconjNIX',
+ 'ScalarGaussianNonconjNIG', 'ScalarGaussianFixedvar']
+
+import numpy as np
+from numpy import newaxis as na
+from numpy.core.umath_tests import inner1d
+import scipy.linalg
+import scipy.stats as stats
+import scipy.special as special
+import copy
+
+from pybasicbayes.abstractions import GibbsSampling, MeanField, \
+ MeanFieldSVI, Collapsed, MaxLikelihood, MAP, Tempering
+from pybasicbayes.distributions.meta import _FixedParamsMixin
+from pybasicbayes.util.stats import sample_niw, invwishart_entropy, \
+ sample_invwishart, invwishart_log_partitionfunction, \
+ getdatasize, flattendata, getdatadimension, \
+ combinedata, multivariate_t_loglik, gi, niw_expectedstats
+
+weps = 1e-12
+
+
+class _GaussianBase(object):
+ @property
+ def params(self):
+ return dict(mu=self.mu, sigma=self.sigma)
+
+ @property
+ def D(self):
+ return self.mu.shape[0]
+
+ ### internals
+
+ def getsigma(self):
+ return self._sigma
+
+ def setsigma(self,sigma):
+ self._sigma = sigma
+ self._sigma_chol = None
+
+ sigma = property(getsigma,setsigma)
+
+ @property
+ def sigma_chol(self):
+ if not hasattr(self,'_sigma_chol') or self._sigma_chol is None:
+ self._sigma_chol = np.linalg.cholesky(self.sigma)
+ return self._sigma_chol
+
+ ### distribution stuff
+
+ def rvs(self,size=None):
+ size = 1 if size is None else size
+ size = size + (self.mu.shape[0],) if isinstance(size,tuple) \
+ else (size,self.mu.shape[0])
+ return self.mu + np.random.normal(size=size).dot(self.sigma_chol.T)
+
+ def log_likelihood(self,x):
+ try:
+ mu, D = self.mu, self.D
+ sigma_chol = self.sigma_chol
+ bads = np.isnan(np.atleast_2d(x)).any(axis=1)
+ x = np.nan_to_num(x).reshape((-1,D)) - mu
+ xs = scipy.linalg.solve_triangular(sigma_chol,x.T,lower=True)
+ out = -1./2. * inner1d(xs.T,xs.T) - D/2*np.log(2*np.pi) \
+ - np.log(sigma_chol.diagonal()).sum()
+ out[bads] = 0
+ return out
+ except np.linalg.LinAlgError:
+ # NOTE: degenerate distribution doesn't have a density
+ return np.repeat(-np.inf,x.shape[0])
+
+ ### plotting
+
+ # TODO making animations, this seems to generate an extra notebook figure
+
+ _scatterplot = None
+ _parameterplot = None
+
+ def plot(self,ax=None,data=None,indices=None,color='b',
+ plot_params=True,label='',alpha=1.,
+ update=False,draw=True):
+ import matplotlib.pyplot as plt
+ from pybasicbayes.util.plot import project_data, \
+ plot_gaussian_projection, plot_gaussian_2D
+ ax = ax if ax else plt.gca()
+ D = self.D
+ if data is not None:
+ data = flattendata(data)
+
+ if data is not None:
+ if D > 2:
+ plot_basis = np.random.RandomState(seed=0).randn(2,D)
+ data = project_data(data,plot_basis)
+ if update and self._scatterplot is not None:
+ self._scatterplot.set_offsets(data)
+ self._scatterplot.set_color(color)
+ else:
+ self._scatterplot = ax.scatter(
+ data[:,0],data[:,1],marker='.',color=color)
+
+ if plot_params:
+ if D > 2:
+ plot_basis = np.random.RandomState(seed=0).randn(2,D)
+ self._parameterplot = \
+ plot_gaussian_projection(
+ self.mu,self.sigma,plot_basis,
+ color=color,label=label,alpha=min(1-1e-3,alpha),
+ ax=ax, artists=self._parameterplot if update else None)
+ else:
+ self._parameterplot = \
+ plot_gaussian_2D(
+ self.mu,self.sigma,color=color,label=label,
+ alpha=min(1-1e-3,alpha), ax=ax,
+ artists=self._parameterplot if update else None)
+
+ if draw:
+ plt.draw()
+
+ return [self._scatterplot] + list(self._parameterplot)
+
+ def to_json_dict(self):
+ D = self.mu.shape[0]
+ assert D == 2
+ U,s,_ = np.linalg.svd(self.sigma)
+ U /= np.linalg.det(U)
+ theta = np.arctan2(U[0,0],U[0,1])*180/np.pi
+ return {'x':self.mu[0],'y':self.mu[1],'rx':np.sqrt(s[0]),
+ 'ry':np.sqrt(s[1]), 'theta':theta}
+
+
+class Gaussian(
+ _GaussianBase, GibbsSampling, MeanField, MeanFieldSVI,
+ Collapsed, MAP, MaxLikelihood):
+ '''
+ Multivariate Gaussian distribution class.
+
+ NOTE: Only works for 2 or more dimensions. For a scalar Gaussian, use a
+ scalar class. Uses a conjugate Normal/Inverse-Wishart prior.
+
+ Hyperparameters mostly follow Gelman et al.'s notation in Bayesian Data
+ Analysis:
+ nu_0, sigma_0, mu_0, kappa_0
+
+ Parameters are mean and covariance matrix:
+ mu, sigma
+ '''
+
+ def __init__(
+ self, mu=None, sigma=None,
+ mu_0=None, sigma_0=None, kappa_0=None, nu_0=None):
+ self.mu = mu
+ self.sigma = sigma
+
+ self.mu_0 = self.mu_mf = mu_0
+ self.sigma_0 = self.sigma_mf = sigma_0
+ self.kappa_0 = self.kappa_mf = kappa_0
+ self.nu_0 = self.nu_mf = nu_0
+
+ # NOTE: resampling will set mu_mf and sigma_mf if necessary
+ if mu is sigma is None \
+ and not any(_ is None for _ in (mu_0,sigma_0,kappa_0,nu_0)):
+ self.resample() # initialize from prior
+ if mu is not None and sigma is not None \
+ and not any(_ is None for _ in (mu_0,sigma_0,kappa_0,nu_0)):
+ self.mu_mf = mu
+ self.sigma_mf = sigma * (self.nu_0 - self.mu_mf.shape[0] - 1)
+
+ @property
+ def hypparams(self):
+ return dict(
+ mu_0=self.mu_0,sigma_0=self.sigma_0,
+ kappa_0=self.kappa_0,nu_0=self.nu_0)
+
+ @property
+ def natural_hypparam(self):
+ return self._standard_to_natural(
+ self.mu_0,self.sigma_0,self.kappa_0,self.nu_0)
+
+ @natural_hypparam.setter
+ def natural_hypparam(self,natparam):
+ self.mu_0, self.sigma_0, self.kappa_0, self.nu_0 = \
+ self._natural_to_standard(natparam)
+
+ def _standard_to_natural(self,mu_mf,sigma_mf,kappa_mf,nu_mf):
+ D = sigma_mf.shape[0]
+ out = np.zeros((D+2,D+2))
+ out[:D,:D] = sigma_mf + kappa_mf * np.outer(mu_mf,mu_mf)
+ out[:D,-2] = out[-2,:D] = kappa_mf * mu_mf
+ out[-2,-2] = kappa_mf
+ out[-1,-1] = nu_mf + 2 + D
+ return out
+
+ def _natural_to_standard(self,natparam):
+ D = natparam.shape[0]-2
+ A = natparam[:D,:D]
+ b = natparam[:D,-2]
+ c = natparam[-2,-2]
+ d = natparam[-1,-1]
+ return b/c, A - np.outer(b,b)/c, c, d - 2 - D
+
+ @property
+ def num_parameters(self):
+ D = self.D
+ return D*(D+1)/2
+
+ @property
+ def D(self):
+ if self.mu is not None:
+ return self.mu.shape[0]
+ elif self.mu_0 is not None:
+ return self.mu_0.shape[0]
+
+ def _get_statistics(self,data,D=None):
+ if D is None:
+ D = self.D if self.D is not None else getdatadimension(data)
+ out = np.zeros((D+2,D+2))
+ if isinstance(data,np.ndarray):
+ out[:D,:D] = data.T.dot(data)
+ out[-2,:D] = out[:D,-2] = data.sum(0)
+ out[-2,-2] = out[-1,-1] = data.shape[0]
+ return out
+ else:
+ return sum(list(map(self._get_statistics,data)),out)
+
+ def _get_weighted_statistics(self,data,weights,D=None):
+ D = getdatadimension(data) if D is None else D
+ out = np.zeros((D+2,D+2))
+ if isinstance(data,np.ndarray):
+ out[:D,:D] = data.T.dot(weights[:,na]*data)
+ out[-2,:D] = out[:D,-2] = weights.dot(data)
+ out[-2,-2] = out[-1,-1] = weights.sum()
+ return out
+ else:
+ return sum(list(map(self._get_weighted_statistics,data,weights)),out)
+
+ def _get_empty_statistics(self, D):
+ out = np.zeros((D+2,D+2))
+ return out
+
+ def empirical_bayes(self,data):
+ self.natural_hypparam = self._get_statistics(data)
+ self.resample() # intialize from prior given new hyperparameters
+ return self
+
+ @staticmethod
+ def _stats_ensure_array(stats):
+ if isinstance(stats, np.ndarray):
+ return stats
+ x, xxT, n = stats
+ D = x.shape[-1]
+ out = np.zeros((D+2,D+2))
+ out[:D,:D] = xxT
+ out[-2,:D] = out[:D,-2] = x
+ out[-2,-2] = out[-1,-1] = n
+ return out
+
+ ### Gibbs sampling
+
+ def resample(self,data=[]):
+ D = len(self.mu_0)
+ self.mu, self.sigma = \
+ sample_niw(*self._natural_to_standard(
+ self.natural_hypparam + self._get_statistics(data,D)))
+ # NOTE: next lines let Gibbs sampling initialize mean
+ nu = self.nu_mf if hasattr(self,'nu_mf') and self.nu_mf \
+ else self.nu_0
+ self.mu_mf, self._sigma_mf = self.mu, self.sigma * (nu - D - 1)
+ return self
+
+ def copy_sample(self):
+ new = copy.copy(self)
+ new.mu = self.mu.copy()
+ new.sigma = self.sigma.copy()
+ return new
+
+ ### Mean Field
+
+ def _resample_from_mf(self):
+ self.mu, self.sigma = \
+ sample_niw(*self._natural_to_standard(
+ self.mf_natural_hypparam))
+ return self
+
+ def meanfieldupdate(self, data=None, weights=None, stats=None):
+ assert (data is not None and weights is not None) ^ (stats is not None)
+ stats = self._stats_ensure_array(stats) if stats is not None else \
+ self._get_weighted_statistics(data, weights, self.mu_0.shape[0])
+ self.mf_natural_hypparam = \
+ self.natural_hypparam + stats
+
+ def meanfield_sgdstep(self,data,weights,prob,stepsize):
+ D = len(self.mu_0)
+ self.mf_natural_hypparam = \
+ (1-stepsize) * self.mf_natural_hypparam + stepsize * (
+ self.natural_hypparam
+ + 1./prob
+ * self._get_weighted_statistics(data,weights,D))
+
+ @property
+ def mf_natural_hypparam(self):
+ return self._standard_to_natural(
+ self.mu_mf,self.sigma_mf,self.kappa_mf,self.nu_mf)
+
+ @mf_natural_hypparam.setter
+ def mf_natural_hypparam(self,natparam):
+ self.mu_mf, self.sigma_mf, self.kappa_mf, self.nu_mf = \
+ self._natural_to_standard(natparam)
+ # NOTE: next line is for plotting
+ self.mu, self.sigma = \
+ self.mu_mf, self.sigma_mf/(self.nu_mf - self.mu_mf.shape[0] - 1)
+
+ @property
+ def sigma_mf(self):
+ return self._sigma_mf
+
+ @sigma_mf.setter
+ def sigma_mf(self,val):
+ self._sigma_mf = val
+ self._sigma_mf_chol = None
+
+ @property
+ def sigma_mf_chol(self):
+ if self._sigma_mf_chol is None:
+ self._sigma_mf_chol = np.linalg.cholesky(self.sigma_mf)
+ return self._sigma_mf_chol
+
+ def get_vlb(self):
+ D = len(self.mu_0)
+ loglmbdatilde = self._loglmbdatilde()
+
+ # see Eq. 10.77 in Bishop
+ q_entropy = -0.5 * (loglmbdatilde + D * (np.log(self.kappa_mf/(2*np.pi))-1)) \
+ + invwishart_entropy(self.sigma_mf,self.nu_mf)
+ # see Eq. 10.74 in Bishop, we aren't summing over K
+ p_avgengy = 0.5 * (D * np.log(self.kappa_0/(2*np.pi)) + loglmbdatilde
+ - D*self.kappa_0/self.kappa_mf - self.kappa_0*self.nu_mf*
+ np.dot(self.mu_mf -
+ self.mu_0,np.linalg.solve(self.sigma_mf,self.mu_mf - self.mu_0))) \
+ - invwishart_log_partitionfunction(self.sigma_0,self.nu_0) \
+ + (self.nu_0 - D - 1)/2*loglmbdatilde - 1/2*self.nu_mf \
+ * np.linalg.solve(self.sigma_mf,self.sigma_0).trace()
+
+ return p_avgengy + q_entropy
+
+ def expected_log_likelihood(self, x=None, stats=None):
+ assert (x is not None) ^ isinstance(stats, (tuple, np.ndarray))
+
+ if x is not None:
+ mu_n, kappa_n, nu_n = self.mu_mf, self.kappa_mf, self.nu_mf
+ D = len(mu_n)
+ x = np.reshape(x,(-1,D)) - mu_n # x is now centered
+ xs = np.linalg.solve(self.sigma_mf_chol,x.T)
+
+ # see Eqs. 10.64, 10.67, and 10.71 in Bishop
+ return self._loglmbdatilde()/2 - D/(2*kappa_n) - nu_n/2 * \
+ inner1d(xs.T,xs.T) - D/2*np.log(2*np.pi)
+ else:
+ D = self.mu_mf.shape[0]
+
+ E_J, E_h, E_muJmuT, E_logdetJ = \
+ niw_expectedstats(
+ self.nu_mf, self.sigma_mf, self.mu_mf, self.kappa_mf)
+
+ if isinstance(stats, np.ndarray):
+ parammat = np.zeros((D+2,D+2))
+ parammat[:D,:D] = E_J
+ parammat[:D,-2] = parammat[-2,:D] = -E_h
+ parammat[-2,-2] = E_muJmuT
+ parammat[-1,-1] = -E_logdetJ
+
+ contract = 'ij,nij->n' if stats.ndim == 3 else 'ij,ij->'
+ return -1./2*np.einsum(contract, parammat, stats) \
+ - D/2.*np.log(2*np.pi)
+ else:
+ x, xxT, n = stats
+ c1, c2 = ('i,i->', 'ij,ij->') if x.ndim == 1 \
+ else ('i,ni->n', 'ij,nij->n')
+
+ out = -1./2 * np.einsum(c2, E_J, xxT)
+ out += np.einsum(c1, E_h, x)
+ out += -n/2.*E_muJmuT
+ out += -D/2.*np.log(2*np.pi) + n/2.*E_logdetJ
+
+ return out
+
+ def _loglmbdatilde(self):
+ # see Eq. 10.65 in Bishop
+ D = len(self.mu_0)
+ chol = self.sigma_mf_chol
+ return special.digamma((self.nu_mf-np.arange(D))/2.).sum() \
+ + D*np.log(2) - 2*np.log(chol.diagonal()).sum()
+
+ ### Collapsed
+
+ def log_marginal_likelihood(self,data):
+ n, D = getdatasize(data), len(self.mu_0)
+ return self._log_partition_function(
+ *self._natural_to_standard(
+ self.natural_hypparam + self._get_statistics(data,D))) \
+ - self._log_partition_function(self.mu_0,self.sigma_0,self.kappa_0,self.nu_0) \
+ - n*D/2 * np.log(2*np.pi)
+
+ def _log_partition_function(self,mu,sigma,kappa,nu):
+ D = len(mu)
+ chol = np.linalg.cholesky(sigma)
+ return nu*D/2*np.log(2) + special.multigammaln(nu/2,D) + D/2*np.log(2*np.pi/kappa) \
+ - nu*np.log(chol.diagonal()).sum()
+
+ def log_predictive_studentt_datapoints(self,datapoints,olddata):
+ D = len(self.mu_0)
+ mu_n, sigma_n, kappa_n, nu_n = \
+ self._natural_to_standard(
+ self.natural_hypparam + self._get_statistics(olddata,D))
+ return multivariate_t_loglik(
+ datapoints,nu_n-D+1,mu_n,(kappa_n+1)/(kappa_n*(nu_n-D+1))*sigma_n)
+
+ def log_predictive_studentt(self,newdata,olddata):
+ newdata = np.atleast_2d(newdata)
+ return sum(self.log_predictive_studentt_datapoints(
+ d,combinedata((olddata,newdata[:i])))[0] for i,d in enumerate(newdata))
+
+ ### Max likelihood
+
+ def max_likelihood(self,data,weights=None):
+ D = getdatadimension(data)
+ if weights is None:
+ statmat = self._get_statistics(data,D)
+ else:
+ statmat = self._get_weighted_statistics(data,weights,D)
+
+ n, x, xxt = statmat[-1,-1], statmat[-2,:D], statmat[:D,:D]
+
+ # this SVD is necessary to check if the max likelihood solution is
+ # degenerate, which can happen in the EM algorithm
+ if n < D or (np.linalg.svd(xxt,compute_uv=False) > 1e-6).sum() < D:
+ self.broken = True
+ self.mu = 99999999*np.ones(D)
+ self.sigma = np.eye(D)
+ else:
+ self.mu = x/n
+ self.sigma = xxt/n - np.outer(self.mu,self.mu)
+
+ return self
+
+ def MAP(self,data,weights=None):
+ D = getdatadimension(data)
+ # max likelihood with prior pseudocounts included in data
+ if weights is None:
+ statmat = self._get_statistics(data)
+ else:
+ statmat = self._get_weighted_statistics(data,weights)
+ statmat += self.natural_hypparam
+
+ n, x, xxt = statmat[-1,-1], statmat[-2,:D], statmat[:D,:D]
+
+ self.mu = x/n
+ self.sigma = xxt/n - np.outer(self.mu,self.mu)
+
+ return self
+
+
+class GaussianFixedMean(_GaussianBase, GibbsSampling, MaxLikelihood):
+ def __init__(self,mu=None,sigma=None,nu_0=None,lmbda_0=None):
+ self.sigma = sigma
+
+ self.mu = mu
+
+ self.nu_0 = nu_0
+ self.lmbda_0 = lmbda_0
+
+ if sigma is None and not any(_ is None for _ in (nu_0,lmbda_0)):
+ self.resample() # initialize from prior
+
+ @property
+ def hypparams(self):
+ return dict(nu_0=self.nu_0,lmbda_0=self.lmbda_0)
+
+ @property
+ def num_parameters(self):
+ D = len(self.mu)
+ return D*(D+1)/2
+
+ def _get_statistics(self,data):
+ n = getdatasize(data)
+ if n > 1e-4:
+ if isinstance(data,np.ndarray):
+ centered = data[gi(data)] - self.mu
+ sumsq = centered.T.dot(centered)
+ n = len(centered)
+ else:
+ sumsq = sum((d[gi(d)]-self.mu).T.dot(d[gi(d)]-self.mu) for d in data)
+ else:
+ sumsq = None
+ return n, sumsq
+
+ def _get_weighted_statistics(self,data,weights):
+ if isinstance(data,np.ndarray):
+ neff = weights.sum()
+ if neff > weps:
+ centered = data - self.mu
+ sumsq = centered.T.dot(weights[:,na]*centered)
+ else:
+ sumsq = None
+ else:
+ neff = sum(w.sum() for w in weights)
+ if neff > weps:
+ sumsq = sum((d-self.mu).T.dot(w[:,na]*(d-self.mu)) for w,d in zip(weights,data))
+ else:
+ sumsq = None
+
+ return neff, sumsq
+
+ def _posterior_hypparams(self,n,sumsq):
+ nu_0, lmbda_0 = self.nu_0, self.lmbda_0
+ if n > 1e-4:
+ nu_0 = nu_0 + n
+ sigma_n = self.lmbda_0 + sumsq
+ return sigma_n, nu_0
+ else:
+ return lmbda_0, nu_0
+
+ ### Gibbs sampling
+
+ def resample(self, data=[]):
+ self.sigma = sample_invwishart(*self._posterior_hypparams(
+ *self._get_statistics(data)))
+ return self
+
+ ### Max likelihood
+
+ def max_likelihood(self,data,weights=None):
+ D = getdatadimension(data)
+ if weights is None:
+ n, sumsq = self._get_statistics(data)
+ else:
+ n, sumsq = self._get_weighted_statistics(data,weights)
+
+ if n < D or (np.linalg.svd(sumsq,compute_uv=False) > 1e-6).sum() < D:
+ # broken!
+ self.sigma = np.eye(D)*1e-9
+ self.broken = True
+ else:
+ self.sigma = sumsq/n
+
+ return self
+
+
+class GaussianFixedCov(_GaussianBase, GibbsSampling, MaxLikelihood):
+ # See Gelman's Bayesian Data Analysis notation around Eq. 3.18, p. 85
+ # in 2nd Edition. We replaced \Lambda_0 with sigma_0 since it is a prior
+ # *covariance* matrix rather than a precision matrix.
+ def __init__(self,mu=None,sigma=None,mu_0=None,sigma_0=None):
+ self.mu = mu
+
+ self.sigma = sigma
+
+ self.mu_0 = mu_0
+ self.sigma_0 = sigma_0
+
+ if mu is None and not any(_ is None for _ in (mu_0,sigma_0)):
+ self.resample()
+
+ @property
+ def hypparams(self):
+ return dict(mu_0=self.mu_0,sigma_0=self.sigma_0)
+
+ @property
+ def sigma_inv(self):
+ if not hasattr(self,'_sigma_inv'):
+ self._sigma_inv = np.linalg.inv(self.sigma)
+ return self._sigma_inv
+
+ @property
+ def sigma_inv_0(self):
+ if not hasattr(self,'_sigma_inv_0'):
+ self._sigma_inv_0 = np.linalg.inv(self.sigma_0)
+ return self._sigma_inv_0
+
+ @property
+ def num_parameters(self):
+ return len(self.mu)
+
+ def _get_statistics(self,data):
+ n = getdatasize(data)
+ if n > 0:
+ if isinstance(data,np.ndarray):
+ xbar = data.mean(0)
+ else:
+ xbar = sum(d.sum(0) for d in data) / n
+ else:
+ xbar = None
+
+ return n, xbar
+
+ def _get_weighted_statistics(self,data,weights):
+ if isinstance(data,np.ndarray):
+ neff = weights.sum()
+ if neff > weps:
+ xbar = weights.dot(data) / neff
+ else:
+ xbar = None
+ else:
+ neff = sum(w.sum() for w in weights)
+ if neff > weps:
+ xbar = sum(w.dot(d) for w,d in zip(weights,data)) / neff
+ else:
+ xbar = None
+
+ return neff, xbar
+
+ def _posterior_hypparams(self,n,xbar):
+ # It seems we should be working with lmbda and sigma inv (unless lmbda
+ # is a covariance, not a precision)
+ sigma_inv, mu_0, sigma_inv_0 = self.sigma_inv, self.mu_0, self.sigma_inv_0
+ if n > 0:
+ sigma_inv_n = n*sigma_inv + sigma_inv_0
+ mu_n = np.linalg.solve(
+ sigma_inv_n, sigma_inv_0.dot(mu_0) + n*sigma_inv.dot(xbar))
+ return mu_n, sigma_inv_n
+ else:
+ return mu_0, sigma_inv_0
+
+ ### Gibbs sampling
+
+ def resample(self,data=[]):
+ mu_n, sigma_n_inv = self._posterior_hypparams(*self._get_statistics(data))
+ D = len(mu_n)
+ L = np.linalg.cholesky(sigma_n_inv)
+ self.mu = scipy.linalg.solve_triangular(L,np.random.normal(size=D),lower=True) \
+ + mu_n
+ return self
+
+ ### Max likelihood
+
+ def max_likelihood(self,data,weights=None):
+ if weights is None:
+ n, xbar = self._get_statistics(data)
+ else:
+ n, xbar = self._get_weighted_statistics(data,weights)
+
+ self.mu = xbar
+ return self
+
+
+class GaussianFixed(_FixedParamsMixin, Gaussian):
+ def __init__(self,mu,sigma):
+ self.mu = mu
+ self.sigma = sigma
+
+class GaussianNonConj(_GaussianBase, GibbsSampling):
+ def __init__(self,mu=None,sigma=None,
+ mu_0=None,mu_lmbda_0=None,nu_0=None,sigma_lmbda_0=None):
+ self._sigma_distn = GaussianFixedMean(mu=mu,
+ nu_0=nu_0,lmbda_0=sigma_lmbda_0,sigma=sigma)
+ self._mu_distn = GaussianFixedCov(sigma=self._sigma_distn.sigma,
+ mu_0=mu_0, sigma_0=mu_lmbda_0,mu=mu)
+ self._sigma_distn.mu = self._mu_distn.mu
+
+ @property
+ def hypparams(self):
+ d = self._mu_distn.hypparams
+ d.update(**self._sigma_distn.hypparams)
+ return d
+
+ def _get_mu(self):
+ return self._mu_distn.mu
+
+ def _set_mu(self,val):
+ self._mu_distn.mu = val
+ self._sigma_distn.mu = val
+
+ mu = property(_get_mu,_set_mu)
+
+ def _get_sigma(self):
+ return self._sigma_distn.sigma
+
+ def _set_sigma(self,val):
+ self._sigma_distn.sigma = val
+ self._mu_distn.sigma = val
+
+ sigma = property(_get_sigma,_set_sigma)
+
+ ### Gibbs sampling
+
+ def resample(self,data=[],niter=1):
+ if getdatasize(data) == 0:
+ niter = 1
+
+ # TODO this is kinda dumb because it collects statistics over and over
+ # instead of updating them...
+ for itr in range(niter):
+ # resample mu
+ self._mu_distn.sigma = self._sigma_distn.sigma
+ self._mu_distn.resample(data)
+
+ # resample sigma
+ self._sigma_distn.mu = self._mu_distn.mu
+ self._sigma_distn.resample(data)
+
+ return self
+
+
+# TODO collapsed
+class DiagonalGaussian(_GaussianBase,GibbsSampling,MaxLikelihood,MeanField,Tempering):
+ '''
+ Product of normal-inverse-gamma priors over mu (mean vector) and sigmas
+ (vector of scalar variances).
+
+ The prior follows
+ sigmas ~ InvGamma(alphas_0,betas_0) iid
+ mu | sigma ~ N(mu_0,1/nus_0 * diag(sigmas))
+
+ It allows placing different prior hyperparameters on different components.
+ '''
+
+ def __init__(self,mu=None,sigmas=None,mu_0=None,nus_0=None,alphas_0=None,betas_0=None):
+ # all the s's refer to the fact that these are vectors of length
+ # len(mu_0) OR scalars
+ if mu_0 is not None:
+ D = mu_0.shape[0]
+ if nus_0 is not None and \
+ (isinstance(nus_0,int) or isinstance(nus_0,float)):
+ nus_0 = nus_0*np.ones(D)
+ if alphas_0 is not None and \
+ (isinstance(alphas_0,int) or isinstance(alphas_0,float)):
+ alphas_0 = alphas_0*np.ones(D)
+ if betas_0 is not None and \
+ (isinstance(betas_0,int) or isinstance(betas_0,float)):
+ betas_0 = betas_0*np.ones(D)
+
+ self.mu_0 = self.mf_mu = mu_0
+ self.nus_0 = self.mf_nus = nus_0
+ self.alphas_0 = self.mf_alphas = alphas_0
+ self.betas_0 = self.mf_betas = betas_0
+
+ self.mu = mu
+ self.sigmas = sigmas
+
+ assert self.mu is None or (isinstance(self.mu,np.ndarray) and not isinstance(self.mu,np.ma.MaskedArray))
+ assert self.sigmas is None or (isinstance(self.sigmas,np.ndarray) and not isinstance(self.sigmas,np.ma.MaskedArray))
+
+ if mu is sigmas is None \
+ and not any(_ is None for _ in (mu_0,nus_0,alphas_0,betas_0)):
+ self.resample() # intialize from prior
+
+ ### the basics!
+
+ @property
+ def parameters(self):
+ return self.mu, self.sigmas
+
+ @parameters.setter
+ def parameters(self, mu_sigmas_tuple):
+ (mu,sigmas) = mu_sigmas_tuple
+ self.mu, self.sigmas = mu, sigmas
+
+ @property
+ def sigma(self):
+ return np.diag(self.sigmas)
+
+ @sigma.setter
+ def sigma(self,val):
+ val = np.array(val)
+ assert val.ndim in (1,2)
+ if val.ndim == 1:
+ self.sigmas = val
+ else:
+ self.sigmas = np.diag(val)
+
+ @property
+ def hypparams(self):
+ return dict(mu_0=self.mu_0,nus_0=self.nus_0,
+ alphas_0=self.alphas_0,betas_0=self.betas_0)
+
+ def rvs(self,size=None):
+ size = np.array(size,ndmin=1)
+ return np.sqrt(self.sigmas)*\
+ np.random.normal(size=np.concatenate((size,self.mu.shape))) + self.mu
+
+ def log_likelihood(self,x,temperature=1.):
+ mu, sigmas, D = self.mu, self.sigmas * temperature, self.mu.shape[0]
+ x = np.reshape(x,(-1,D))
+ Js = -1./(2*sigmas)
+ return (np.einsum('ij,ij,j->i',x,x,Js) - np.einsum('ij,j,j->i',x,2*mu,Js)) \
+ + (mu**2*Js - 1./2*np.log(2*np.pi*sigmas)).sum()
+
+ ### posterior updating stuff
+
+ @property
+ def natural_hypparam(self):
+ return self._standard_to_natural(self.alphas_0,self.betas_0,self.mu_0,self.nus_0)
+
+ @natural_hypparam.setter
+ def natural_hypparam(self,natparam):
+ self.alphas_0, self.betas_0, self.mu_0, self.nus_0 = \
+ self._natural_to_standard(natparam)
+
+ def _standard_to_natural(self,alphas,betas,mu,nus):
+ return np.array([2*betas + nus * mu**2, nus*mu, nus, 2*alphas])
+
+ def _natural_to_standard(self,natparam):
+ nus = natparam[2]
+ mu = natparam[1] / nus
+ alphas = natparam[3]/2.
+ betas = (natparam[0] - nus*mu**2) / 2.
+ return alphas, betas, mu, nus
+
+ def _get_statistics(self,data):
+ if isinstance(data,np.ndarray) and data.shape[0] > 0:
+ data = data[gi(data)]
+ ns = np.repeat(*data.shape)
+ return np.array([
+ np.einsum('ni,ni->i',data,data),
+ np.einsum('ni->i',data),
+ ns,
+ ns,
+ ])
+ else:
+ return sum((self._get_statistics(d) for d in data), self._empty_stats())
+
+ def _get_weighted_statistics(self,data,weights):
+ if isinstance(data,np.ndarray):
+ idx = ~np.isnan(data).any(1)
+ data = data[idx]
+ weights = weights[idx]
+ assert data.ndim == 2 and weights.ndim == 1 \
+ and data.shape[0] == weights.shape[0]
+ neff = np.repeat(weights.sum(),data.shape[1])
+ return np.array([weights.dot(data**2), weights.dot(data), neff, neff])
+ else:
+ return sum(
+ (self._get_weighted_statistics(d,w) for d, w in zip(data,weights)),
+ self._empty_stats())
+
+ def _empty_stats(self):
+ return np.zeros_like(self.natural_hypparam)
+
+ ### Gibbs sampling
+
+ def resample(self,data=[],temperature=1.,stats=None):
+ stats = self._get_statistics(data) if stats is None else stats
+
+ alphas_n, betas_n, mu_n, nus_n = self._natural_to_standard(
+ self.natural_hypparam + stats / temperature)
+
+ D = mu_n.shape[0]
+ self.sigmas = 1/np.random.gamma(alphas_n,scale=1/betas_n)
+ self.mu = np.sqrt(self.sigmas/nus_n)*np.random.randn(D) + mu_n
+
+ assert not np.isnan(self.mu).any()
+ assert not np.isnan(self.sigmas).any()
+
+ # NOTE: next line is to use Gibbs sampling to initialize mean field
+ self.mf_mu = self.mu
+
+ assert self.sigmas.ndim == 1
+ return self
+
+ def copy_sample(self):
+ new = copy.copy(self)
+ new.mu = self.mu.copy()
+ new.sigmas = self.sigmas.copy()
+ return new
+
+ ### max likelihood
+
+ def max_likelihood(self,data,weights=None):
+ if weights is None:
+ n, muhat, sumsq = self._get_statistics(data)
+ else:
+ n, muhat, sumsq = self._get_weighted_statistics_old(data,weights)
+
+ self.mu = muhat
+ self.sigmas = sumsq/n
+
+ return self
+
+ ### Mean Field
+
+ @property
+ def mf_natural_hypparam(self):
+ return self._standard_to_natural(self.mf_alphas,self.mf_betas,self.mf_mu,self.mf_nus)
+
+ @mf_natural_hypparam.setter
+ def mf_natural_hypparam(self,natparam):
+ self.mf_alphas, self.mf_betas, self.mf_mu, self.mf_nus = \
+ self._natural_to_standard(natparam)
+ # NOTE: this part is for plotting
+ self.mu = self.mf_mu
+ self.sigmas = np.where(self.mf_alphas > 1,self.mf_betas / (self.mf_alphas - 1),100000)
+
+ def meanfieldupdate(self,data,weights):
+ self.mf_natural_hypparam = \
+ self.natural_hypparam + self._get_weighted_statistics(data,weights)
+
+ def meanfield_sgdstep(self,data,weights,prob,stepsize):
+ self.mf_natural_hypparam = \
+ (1-stepsize) * self.mf_natural_hypparam + stepsize * (
+ self.natural_hypparam
+ + 1./prob * self._get_weighted_statistics(data,weights))
+
+ def get_vlb(self):
+ natparam_diff = self.natural_hypparam - self.mf_natural_hypparam
+ expected_stats = self._expected_statistics(
+ self.mf_alphas,self.mf_betas,self.mf_mu,self.mf_nus)
+ linear_term = sum(v1.dot(v2) for v1, v2 in zip(natparam_diff, expected_stats))
+
+ normalizer_term = \
+ self._log_Z(self.alphas_0,self.betas_0,self.mu_0,self.nus_0) \
+ - self._log_Z(self.mf_alphas,self.mf_betas,self.mf_mu,self.mf_nus)
+
+ return linear_term - normalizer_term - len(self.mf_mu)/2. * np.log(2*np.pi)
+
+ def expected_log_likelihood(self,x):
+ x = np.atleast_2d(x).reshape((-1,len(self.mf_mu)))
+ a,b,c,d = self._expected_statistics(
+ self.mf_alphas,self.mf_betas,self.mf_mu,self.mf_nus)
+ return (x**2).dot(a) + x.dot(b) + c.sum() + d.sum() \
+ - len(self.mf_mu)/2. * np.log(2*np.pi)
+
+ def _expected_statistics(self,alphas,betas,mu,nus):
+ return np.array([
+ -1./2 * alphas/betas,
+ mu * alphas/betas,
+ -1./2 * (1./nus + mu**2 * alphas/betas),
+ -1./2 * (np.log(betas) - special.digamma(alphas))])
+
+ def _log_Z(self,alphas,betas,mu,nus):
+ return (special.gammaln(alphas) - alphas*np.log(betas) - 1./2*np.log(nus)).sum()
+
+# TODO meanfield
+class DiagonalGaussianNonconjNIG(_GaussianBase,GibbsSampling):
+ '''
+ Product of normal priors over mu and product of gamma priors over sigmas.
+ Note that while the conjugate prior in DiagonalGaussian is of the form
+ p(mu,sigmas), this prior is of the form p(mu)p(sigmas). Therefore its
+ resample() update has to perform inner iterations.
+
+ The prior follows
+ mu ~ N(mu_0,diag(sigmas_0))
+ sigmas ~ InvGamma(alpha_0,beta_0) iid
+ '''
+
+ def __init__(self,mu=None,sigmas=None,mu_0=None,sigmas_0=None,alpha_0=None,beta_0=None,
+ niter=20):
+ self.mu_0, self.sigmas_0 = mu_0, sigmas_0
+ self.alpha_0, self.beta_0 = alpha_0, beta_0
+
+ self.niter = niter
+
+ if None in (mu,sigmas):
+ self.resample()
+ else:
+ self.mu, self.sigmas = mu, sigmas
+
+ @property
+ def hypparams(self):
+ return dict(mu_0=self.mu_0,sigmas_0=self.sigmas_0,alpha_0=self.alpha_0,beta_0=self.beta_0)
+
+ # TODO next three methods are copied from DiagonalGaussian, factor them out
+
+ @property
+ def sigma(self):
+ return np.diag(self.sigmas)
+
+ def rvs(self,size=None):
+ size = np.array(size,ndmin=1)
+ return np.sqrt(self.sigmas)*\
+ np.random.normal(size=np.concatenate((size,self.mu.shape))) + self.mu
+
+ def log_likelihood(self,x):
+ mu, sigmas, D = self.mu, self.sigmas, self.mu.shape[0]
+ x = np.reshape(x,(-1,D))
+ Js = -1./(2*sigmas)
+ return (np.einsum('ij,ij,j->i',x,x,Js) - np.einsum('ij,j,j->i',x,2*mu,Js)) \
+ + (mu**2*Js - 1./2*np.log(2*np.pi*sigmas)).sum()
+
+
+ def resample(self,data=[]):
+ n, y, ysq = self._get_statistics(data)
+ if n == 0:
+ self.mu = np.sqrt(self.sigmas_0) * np.random.randn(self.mu_0.shape[0]) + self.mu_0
+ self.sigmas = 1./np.random.gamma(self.alpha_0,scale=1./self.beta_0)
+ else:
+ for itr in range(self.niter):
+ sigmas_n = 1./(1./self.sigmas_0 + n / self.sigmas)
+ mu_n = (self.mu_0 / self.sigmas_0 + y / self.sigmas) * sigmas_n
+ self.mu = np.sqrt(sigmas_n) * np.random.randn(mu_n.shape[0]) + mu_n
+
+ alphas_n = self.alpha_0 + 1./2*n
+ betas_n = self.beta_0 + 1./2*(ysq + n*self.mu**2 - 2*self.mu*y)
+ self.sigmas = 1./np.random.gamma(alphas_n,scale=1./betas_n)
+ return self
+
+ def _get_statistics(self,data):
+ # TODO dont forget to handle nans
+ assert isinstance(data,(list,np.ndarray)) and not isinstance(data,np.ma.MaskedArray)
+ if isinstance(data,np.ndarray):
+ data = data[gi(data)]
+ n = data.shape[0]
+ y = np.einsum('ni->i',data)
+ ysq = np.einsum('ni,ni->i',data,data)
+ return np.array([n,y,ysq],dtype=np.object)
+ else:
+ return sum((self._get_statistics(d) for d in data),self._empty_stats)
+
+ @property
+ def _empty_stats(self):
+ return np.array([0.,np.zeros_like(self.mu_0),np.zeros_like(self.mu_0)],
+ dtype=np.object)
+
+# TODO collapsed, meanfield, max_likelihood
+class IsotropicGaussian(GibbsSampling):
+ '''
+ Normal-Inverse-Gamma prior over mu (mean vector) and sigma (scalar
+ variance). Essentially, all coordinates of all observations inform the
+ variance.
+
+ The prior follows
+ sigma ~ InvGamma(alpha_0,beta_0)
+ mu | sigma ~ N(mu_0,sigma/nu_0 * I)
+ '''
+
+ def __init__(self,mu=None,sigma=None,mu_0=None,nu_0=None,alpha_0=None,beta_0=None):
+ self.mu = mu
+ self.sigma = sigma
+
+ self.mu_0 = mu_0
+ self.nu_0 = nu_0
+ self.alpha_0 = alpha_0
+ self.beta_0 = beta_0
+
+ if mu is sigma is None and not any(_ is None for _ in (mu_0,nu_0,alpha_0,beta_0)):
+ self.resample() # intialize from prior
+
+ @property
+ def hypparams(self):
+ return dict(mu_0=self.mu_0,nu_0=self.nu_0,alpha_0=self.alpha_0,beta_0=self.beta_0)
+
+ def rvs(self,size=None):
+ return np.sqrt(self.sigma)*np.random.normal(size=tuple(size)+self.mu.shape) + self.mu
+
+ def log_likelihood(self,x):
+ mu, sigma, D = self.mu, self.sigma, self.mu.shape[0]
+ x = np.reshape(x,(-1,D))
+ return (-0.5*((x-mu)**2).sum(1)/sigma - D*np.log(np.sqrt(2*np.pi*sigma)))
+
+ def _posterior_hypparams(self,n,xbar,sumsq):
+ mu_0, nu_0, alpha_0, beta_0 = self.mu_0, self.nu_0, self.alpha_0, self.beta_0
+ D = mu_0.shape[0]
+ if n > 0:
+ nu_n = D*n + nu_0
+ alpha_n = alpha_0 + D*n/2
+ beta_n = beta_0 + 1/2*sumsq + (n*D*nu_0)/(n*D+nu_0) * 1/2 * ((xbar - mu_0)**2).sum()
+ mu_n = (n*xbar + nu_0*mu_0)/(n+nu_0)
+
+ return mu_n, nu_n, alpha_n, beta_n
+ else:
+ return mu_0, nu_0, alpha_0, beta_0
+
+ ### Gibbs sampling
+
+ def resample(self,data=[]):
+ mu_n, nu_n, alpha_n, beta_n = self._posterior_hypparams(
+ *self._get_statistics(data, D=self.mu_0.shape[0]))
+ D = mu_n.shape[0]
+ self.sigma = 1/np.random.gamma(alpha_n,scale=1/beta_n)
+ self.mu = np.sqrt(self.sigma/nu_n)*np.random.randn(D)+mu_n
+ return self
+
+ def _get_statistics(self,data, D=None):
+ n = getdatasize(data)
+ if n > 0:
+ D = D if D else getdatadimension(data)
+ if isinstance(data,np.ndarray):
+ assert (data.ndim == 1 and data.shape == (D,)) \
+ or (data.ndim == 2 and data.shape[1] == D)
+ data = np.reshape(data,(-1,D))
+ xbar = data.mean(0)
+ sumsq = ((data-xbar)**2).sum()
+ else:
+ xbar = sum(np.reshape(d,(-1,D)).sum(0) for d in data) / n
+ sumsq = sum(((np.reshape(data,(-1,D)) - xbar)**2).sum() for d in data)
+ else:
+ xbar, sumsq = None, None
+ return n, xbar, sumsq
+
+
+class _ScalarGaussianBase(object):
+ @property
+ def params(self):
+ return dict(mu=self.mu,sigmasq=self.sigmasq)
+
+ def rvs(self,size=None):
+ return np.sqrt(self.sigmasq)*np.random.normal(size=size)+self.mu
+
+ def log_likelihood(self,x):
+ x = np.reshape(x,(-1,1))
+ return (-0.5*(x-self.mu)**2/self.sigmasq - np.log(np.sqrt(2*np.pi*self.sigmasq))).ravel()
+
+ def __repr__(self):
+ return self.__class__.__name__ + '(mu=%f,sigmasq=%f)' % (self.mu,self.sigmasq)
+
+ def plot(self,data=None,indices=None,color='b',plot_params=True,label=None):
+ import matplotlib.pyplot as plt
+ data = np.concatenate(data) if data is not None else None
+ indices = np.concatenate(indices) if indices is not None else None
+
+ if data is not None:
+ assert indices is not None
+ plt.plot(indices,data,color=color,marker='x',linestyle='')
+
+ if plot_params:
+ assert indices is not None
+ if len(indices) > 1:
+ from util.general import rle
+ vals, lens = rle(np.diff(indices))
+ starts = np.concatenate(((0,),lens.cumsum()[:-1]))
+ for start, blocklen in zip(starts[vals == 1], lens[vals == 1]):
+ plt.plot(indices[start:start+blocklen],
+ np.repeat(self.mu,blocklen),color=color,linestyle='--')
+ else:
+ plt.plot(indices,[self.mu],color=color,marker='+')
+
+ ### mostly shared statistics gathering
+
+ def _get_statistics(self,data):
+ n = getdatasize(data)
+ if n > 0:
+ if isinstance(data,np.ndarray):
+ ybar = data.mean()
+ centered = data.ravel() - ybar
+ sumsqc = centered.dot(centered)
+ elif isinstance(data,list):
+ ybar = sum(d.sum() for d in data)/n
+ sumsqc = sum((d.ravel()-ybar).dot(d.ravel()-ybar) for d in data)
+ else:
+ ybar = data
+ sumsqc = 0
+ else:
+ ybar = None
+ sumsqc = None
+
+ return n, ybar, sumsqc
+
+ def _get_weighted_statistics(self,data,weights):
+ if isinstance(data,np.ndarray):
+ neff = weights.sum()
+ if neff > weps:
+ ybar = weights.dot(data.ravel()) / neff
+ centered = data.ravel() - ybar
+ sumsqc = centered.dot(weights*centered)
+ else:
+ ybar = None
+ sumsqc = None
+ elif isinstance(data,list):
+ neff = sum(w.sum() for w in weights)
+ if neff > weps:
+ ybar = sum(w.dot(d.ravel()) for d,w in zip(data,weights)) / neff
+ sumsqc = sum((d.ravel()-ybar).dot(w*(d.ravel()-ybar))
+ for d,w in zip(data,weights))
+ else:
+ ybar = None
+ sumsqc = None
+ else:
+ ybar = data
+ sumsqc = 0
+
+ return neff, ybar, sumsqc
+
+ ### max likelihood
+
+ def max_likelihood(self,data,weights=None):
+ if weights is None:
+ n, ybar, sumsqc = self._get_statistics(data)
+ else:
+ n, ybar, sumsqc = self._get_weighted_statistics(data,weights)
+
+ if sumsqc > 0:
+ self.mu = ybar
+ self.sigmasq = sumsqc/n
+ else:
+ self.broken = True
+ self.mu = 999999999.
+ self.sigmsq = 1.
+
+ return self
+
+class ScalarGaussianNIX(_ScalarGaussianBase, GibbsSampling, Collapsed):
+ '''
+ Conjugate Normal-(Scaled-)Inverse-ChiSquared prior. (Another parameterization is the
+ Normal-Inverse-Gamma.)
+ '''
+ def __init__(self,mu=None,sigmasq=None,mu_0=None,kappa_0=None,sigmasq_0=None,nu_0=None):
+ self.mu = mu
+ self.sigmasq = sigmasq
+
+ self.mu_0 = mu_0
+ self.kappa_0 = kappa_0
+ self.sigmasq_0 = sigmasq_0
+ self.nu_0 = nu_0
+
+ if mu is sigmasq is None \
+ and not any(_ is None for _ in (mu_0,kappa_0,sigmasq_0,nu_0)):
+ self.resample() # intialize from prior
+
+ @property
+ def hypparams(self):
+ return dict(mu_0=self.mu_0,kappa_0=self.kappa_0,
+ sigmasq_0=self.sigmasq_0,nu_0=self.nu_0)
+
+ def _posterior_hypparams(self,n,ybar,sumsqc):
+ mu_0, kappa_0, sigmasq_0, nu_0 = self.mu_0, self.kappa_0, self.sigmasq_0, self.nu_0
+ if n > 0:
+ kappa_n = kappa_0 + n
+ mu_n = (kappa_0 * mu_0 + n * ybar) / kappa_n
+ nu_n = nu_0 + n
+ sigmasq_n = 1/nu_n * (nu_0 * sigmasq_0 + sumsqc + kappa_0 * n / (kappa_0 + n) * (ybar - mu_0)**2)
+
+ return mu_n, kappa_n, sigmasq_n, nu_n
+ else:
+ return mu_0, kappa_0, sigmasq_0, nu_0
+
+ ### Gibbs sampling
+
+ def resample(self,data=[]):
+ mu_n, kappa_n, sigmasq_n, nu_n = self._posterior_hypparams(*self._get_statistics(data))
+ self.sigmasq = nu_n * sigmasq_n / np.random.chisquare(nu_n)
+ self.mu = np.sqrt(self.sigmasq / kappa_n) * np.random.randn() + mu_n
+ return self
+
+ ### Collapsed
+
+ def log_marginal_likelihood(self,data):
+ n = getdatasize(data)
+ kappa_0, sigmasq_0, nu_0 = self.kappa_0, self.sigmasq_0, self.nu_0
+ mu_n, kappa_n, sigmasq_n, nu_n = self._posterior_hypparams(*self._get_statistics(data))
+ return special.gammaln(nu_n/2) - special.gammaln(nu_0/2) \
+ + 0.5*(np.log(kappa_0) - np.log(kappa_n)
+ + nu_0 * (np.log(nu_0) + np.log(sigmasq_0))
+ - nu_n * (np.log(nu_n) + np.log(sigmasq_n))
+ - n*np.log(np.pi))
+
+ def log_predictive_single(self,y,olddata):
+ # mostly for testing or speed
+ mu_n, kappa_n, sigmasq_n, nu_n = self._posterior_hypparams(*self._get_statistics(olddata))
+ return stats.t.logpdf(y,nu_n,loc=mu_n,scale=np.sqrt((1+kappa_n)*sigmasq_n/kappa_n))
+
+
+class ScalarGaussianNonconjNIX(_ScalarGaussianBase, GibbsSampling):
+ '''
+ Non-conjugate separate priors on mean and variance parameters, via
+ mu ~ Normal(mu_0,tausq_0)
+ sigmasq ~ (Scaled-)Inverse-ChiSquared(sigmasq_0,nu_0)
+ '''
+ def __init__(self,mu=None,sigmasq=None,mu_0=None,tausq_0=None,sigmasq_0=None,nu_0=None,
+ niter=1):
+ self.mu, self.sigmasq = mu, sigmasq
+ self.mu_0, self.tausq_0 = mu_0, tausq_0
+ self.sigmasq_0, self.nu_0 = sigmasq_0, nu_0
+
+ self.niter = niter
+
+ if mu is sigmasq is None \
+ and not any(_ is None for _ in (mu_0, tausq_0, sigmasq_0, nu_0)):
+ self.resample() # intialize from prior
+
+ @property
+ def hypparams(self):
+ return dict(mu_0=self.mu_0,tausq_0=self.tausq_0,
+ sigmasq_0=self.sigmasq_0,nu_0=self.nu_0)
+
+ def resample(self,data=[],niter=None):
+ n = getdatasize(data)
+ niter = self.niter if niter is None else niter
+ if n > 0:
+ data = flattendata(data)
+ datasum = data[gi(data)].sum()
+ datasqsum = (data[gi(data)]**2).sum()
+ nu_n = self.nu_0 + n
+ for itr in range(niter):
+ # resample mean
+ tausq_n = 1/(1/self.tausq_0 + n/self.sigmasq)
+ mu_n = tausq_n*(self.mu_0/self.tausq_0 + datasum/self.sigmasq)
+ self.mu = np.sqrt(tausq_n)*np.random.normal() + mu_n
+ # resample variance
+ sigmasq_n = (self.nu_0*self.sigmasq_0 + (datasqsum + n*self.mu**2-2*datasum*self.mu))/nu_n
+ self.sigmasq = sigmasq_n*nu_n/np.random.chisquare(nu_n)
+ else:
+ self.mu = np.sqrt(self.tausq_0) * np.random.normal() + self.mu_0
+ self.sigmasq = self.sigmasq_0*self.nu_0/np.random.chisquare(self.nu_0)
+
+ return self
+
+class ScalarGaussianNonconjNIG(_ScalarGaussianBase, MeanField, MeanFieldSVI):
+ # NOTE: this is like ScalarGaussianNonconjNiIG except prior is in natural
+ # coordinates
+
+ def __init__(self,h_0,J_0,alpha_0,beta_0,
+ mu=None,sigmasq=None,
+ h_mf=None,J_mf=None,alpha_mf=None,beta_mf=None,niter=1):
+ self.h_0, self.J_0 = h_0, J_0
+ self.alpha_0, self.beta_0 = alpha_0, beta_0
+
+ self.h_mf = h_mf if h_mf is not None else J_0 * np.random.normal(h_0/J_0,1./np.sqrt(J_0))
+ self.J_mf = J_mf if J_mf is not None else J_0
+ self.alpha_mf = alpha_mf if alpha_mf is not None else alpha_0
+ self.beta_mf = beta_mf if beta_mf is not None else beta_0
+
+ self.niter = niter
+
+ self.mu = mu if mu is not None else np.random.normal(h_0/J_0,1./np.sqrt(J_0))
+ self.sigmasq = sigmasq if sigmasq is not None else 1./np.random.gamma(alpha_0,1./beta_0)
+
+ @property
+ def hypparams(self):
+ return dict(h_0=self.h_0,J_0=self.J_0,alpha_0=self.alpha_0,beta_0=self.beta_0)
+
+ @property
+ def _E_mu(self):
+ # E[mu], E[mu**2]
+ return self.h_mf / self.J_mf, 1./self.J_mf + (self.h_mf / self.J_mf)**2
+
+ @property
+ def _E_sigmasq(self):
+ # E[1/sigmasq], E[ln sigmasq]
+ return self.alpha_mf / self.beta_mf, \
+ np.log(self.beta_mf) - special.digamma(self.alpha_mf)
+
+ @property
+ def natural_hypparam(self):
+ return np.array([self.alpha_0,self.beta_0,self.h_0,self.J_0])
+
+ @natural_hypparam.setter
+ def natural_hypparam(self,natural_hypparam):
+ self.alpha_0, self.beta_0, self.h_0, self.J_0 = natural_hypparam
+
+ @property
+ def mf_natural_hypparam(self):
+ return np.array([self.alpha_mf,self.beta_mf,self.h_mf,self.J_mf])
+
+ @mf_natural_hypparam.setter
+ def mf_natural_hypparam(self,mf_natural_hypparam):
+ self.alpha_mf, self.beta_mf, self.h_mf, self.J_mf = mf_natural_hypparam
+ # set point estimates of (mu, sigmasq) for plotting and stuff
+ self.mu, self.sigmasq = self.h_mf / self.J_mf, self.beta_mf / (self.alpha_mf-1)
+
+ def _resample_from_mf(self):
+ self.mu, self.sigmasq = np.random.normal(self.h_mf/self.J_mf,np.sqrt(1./self.J_mf)), \
+ np.random.gamma(self.alpha_mf,1./self.beta_mf)
+ return self
+
+ def expected_log_likelihood(self,x):
+ (Emu, Emu2), (Esigmasqinv, Elnsigmasq) = self._E_mu, self._E_sigmasq
+ return -1./2 * Esigmasqinv * (x**2 + Emu2 - 2*x*Emu) \
+ - 1./2*Elnsigmasq - 1./2*np.log(2*np.pi)
+
+ def get_vlb(self):
+ # E[ln p(mu) / q(mu)] part
+ h_0, J_0, J_mf = self.h_0, self.J_0, self.J_mf
+ Emu, Emu2 = self._E_mu
+ p_mu_avgengy = -1./2*J_0*Emu2 + h_0*Emu \
+ - 1./2*(h_0**2/J_0) + 1./2*np.log(J_0) - 1./2*np.log(2*np.pi)
+ q_mu_entropy = 1./2*np.log(2*np.pi*np.e/J_mf)
+
+ # E[ln p(sigmasq) / q(sigmasq)] part
+ alpha_0, beta_0, alpha_mf, beta_mf = \
+ self.alpha_0, self.beta_0, self.alpha_mf, self.beta_mf
+ (Esigmasqinv, Elnsigmasq) = self._E_sigmasq
+ p_sigmasq_avgengy = (-alpha_0-1)*Elnsigmasq + (-beta_0)*Esigmasqinv \
+ - (special.gammaln(alpha_0) - alpha_0*np.log(beta_0))
+ q_sigmasq_entropy = alpha_mf + np.log(beta_mf) + special.gammaln(alpha_mf) \
+ - (1+alpha_mf)*special.digamma(alpha_mf)
+
+ return p_mu_avgengy + q_mu_entropy + p_sigmasq_avgengy + q_sigmasq_entropy
+
+ def meanfield_sgdstep(self,data,weights,prob,stepsize):
+ # like meanfieldupdate except we step the factors simultaneously
+
+ # NOTE: unlike the fully conjugate case, there are interaction terms, so
+ # we work on the destructured pieces
+ neff, y, ysq = self._get_weighted_statistics(data,weights)
+ Emu, _ = self._E_mu
+ Esigmasqinv, _ = self._E_sigmasq
+
+
+ # form new natural hyperparameters as if doing a batch update
+ alpha_new = self.alpha_0 + 1./prob * 1./2*neff
+ beta_new = self.beta_0 + 1./prob * 1./2*(ysq + neff*Emu**2 - 2*Emu*y)
+
+ h_new = self.h_0 + 1./prob * Esigmasqinv * y
+ J_new = self.J_0 + 1./prob * Esigmasqinv * neff
+
+
+ # take a step
+ self.alpha_mf = (1-stepsize)*self.alpha_mf + stepsize*alpha_new
+ self.beta_mf = (1-stepsize)*self.beta_mf + stepsize*beta_new
+
+ self.h_mf = (1-stepsize)*self.h_mf + stepsize*h_new
+ self.J_mf = (1-stepsize)*self.J_mf + stepsize*J_new
+
+ # calling this setter will set point estimates for (mu,sigmasq) for
+ # plotting and sampling and stuff
+ self.mf_natural_hypparam = (self.alpha_mf, self.beta_mf, self.h_mf, self.J_mf)
+
+ return self
+
+ def meanfieldupdate(self,data,weights,niter=None):
+ niter = niter if niter is not None else self.niter
+ neff, y, ysq = self._get_weighted_statistics(data,weights)
+ for niter in range(niter):
+ # update q(sigmasq)
+ Emu, _ = self._E_mu
+
+ self.alpha_mf = self.alpha_0 + 1./2*neff
+ self.beta_mf = self.beta_0 + 1./2*(ysq + neff*Emu**2 - 2*Emu*y)
+
+ # update q(mu)
+ Esigmasqinv, _ = self._E_sigmasq
+
+ self.h_mf = self.h_0 + Esigmasqinv * y
+ self.J_mf = self.J_0 + Esigmasqinv * neff
+
+ # calling this setter will set point estimates for (mu,sigmasq) for
+ # plotting and sampling and stuff
+ self.mf_natural_hypparam = \
+ (self.alpha_mf, self.beta_mf, self.h_mf, self.J_mf)
+
+ return self
+
+ def _get_weighted_statistics(self,data,weights):
+ if isinstance(data,np.ndarray):
+ neff = weights.sum()
+ y = weights.dot(data)
+ ysq = weights.dot(data**2)
+ else:
+ return sum(
+ self._get_weighted_statistics(d,w) for d,w in zip(data,weights))
+ return np.array([neff,y,ysq])
+
+
+class ScalarGaussianFixedvar(_ScalarGaussianBase, GibbsSampling):
+ '''
+ Conjugate normal prior on mean.
+ '''
+ def __init__(self,mu=None,sigmasq=None,mu_0=None,tausq_0=None):
+ self.mu = mu
+
+ self.sigmasq = sigmasq
+
+ self.mu_0 = mu_0
+ self.tausq_0 = tausq_0
+
+ if mu is None and not any(_ is None for _ in (mu_0,tausq_0)):
+ self.resample() # intialize from prior
+
+ @property
+ def hypparams(self):
+ return dict(mu_0=self.mu_0,tausq_0=self.tausq_0)
+
+ def _posterior_hypparams(self,n,xbar):
+ mu_0, tausq_0 = self.mu_0, self.tausq_0
+ sigmasq = self.sigmasq
+ if n > 0:
+ tausq_n = 1/(1/tausq_0 + n/sigmasq)
+ mu_n = (mu_0/tausq_0 + n*xbar/sigmasq)*tausq_n
+
+ return mu_n, tausq_n
+ else:
+ return mu_0, tausq_0
+
+ def resample(self,data=[]):
+ mu_n, tausq_n = self._posterior_hypparams(*self._get_statistics(data))
+ self.mu = np.sqrt(tausq_n)*np.random.randn()+mu_n
+ return self
+
+ def _get_statistics(self,data):
+ n = getdatasize(data)
+ if n > 0:
+ if isinstance(data,np.ndarray):
+ xbar = data.mean()
+ else:
+ xbar = sum(d.sum() for d in data)/n
+ else:
+ xbar = None
+ return n, xbar
+
+ def _get_weighted_statistics(self,data,weights):
+ if isinstance(data,np.ndarray):
+ neff = weights.sum()
+ else:
+ neff = sum(w.sum() for w in weights)
+
+ if neff > weps:
+ if isinstance(data,np.ndarray):
+ xbar = data.dot(weights) / neff
+ else:
+ xbar = sum(w.dot(d) for d,w in zip(data,weights)) / neff
+ else:
+ xbar = None
+
+ return neff, xbar
+
+ def max_likelihood(self,data,weights=None):
+ if weights is None:
+ _, xbar = self._get_statistics(data)
+ else:
+ _, xbar = self._get_weighted_statistics(data,weights)
+
+ self.mu = xbar
diff --git a/build/lib.linux-x86_64-cpython-37/pybasicbayes/distributions/geometric.py b/build/lib.linux-x86_64-cpython-37/pybasicbayes/distributions/geometric.py
new file mode 100644
index 0000000..8841300
--- /dev/null
+++ b/build/lib.linux-x86_64-cpython-37/pybasicbayes/distributions/geometric.py
@@ -0,0 +1,147 @@
+from __future__ import division
+from builtins import zip
+__all__ = ['Geometric']
+
+import numpy as np
+import scipy.stats as stats
+import scipy.special as special
+from warnings import warn
+
+from pybasicbayes.abstractions import GibbsSampling, MeanField, \
+ Collapsed, MaxLikelihood
+
+
+class Geometric(GibbsSampling, MeanField, Collapsed, MaxLikelihood):
+ '''
+ Geometric distribution with a conjugate beta prior.
+ The support is {1,2,3,...}.
+
+ Hyperparameters:
+ alpha_0, beta_0
+
+ Parameter is the success probability:
+ p
+ '''
+ def __init__(self,alpha_0=None,beta_0=None,p=None):
+ self.p = p
+
+ self.alpha_0 = self.mf_alpha_0 = alpha_0
+ self.beta_0 = self.mf_beta_0 = beta_0
+
+ if p is None and not any(_ is None for _ in (alpha_0,beta_0)):
+ self.resample() # intialize from prior
+
+ @property
+ def params(self):
+ return dict(p=self.p)
+
+ @property
+ def hypparams(self):
+ return dict(alpha_0=self.alpha_0,beta_0=self.beta_0)
+
+ def _posterior_hypparams(self,n,tot):
+ return self.alpha_0 + n, self.beta_0 + tot
+
+ def log_likelihood(self,x):
+ x = np.array(x,ndmin=1)
+ raw = np.empty(x.shape)
+ raw[x>0] = (x[x>0]-1.)*np.log(1.-self.p) + np.log(self.p)
+ raw[x<1] = -np.inf
+ return raw if isinstance(x,np.ndarray) else raw[0]
+
+ def log_sf(self,x):
+ return stats.geom.logsf(x,self.p)
+
+ def pmf(self,x):
+ return stats.geom.pmf(x,self.p)
+
+ def rvs(self,size=None):
+ return np.random.geometric(self.p,size=size)
+
+ def _get_statistics(self,data):
+ if isinstance(data,np.ndarray):
+ n = data.shape[0]
+ tot = data.sum() - n
+ elif isinstance(data,list):
+ n = sum(d.shape[0] for d in data)
+ tot = sum(d.sum() for d in data) - n
+ else:
+ assert np.isscalar(data)
+ n = 1
+ tot = data-1
+ return n, tot
+
+ def _get_weighted_statistics(self,data,weights):
+ if isinstance(data,np.ndarray):
+ n = weights.sum()
+ tot = weights.dot(data) - n
+ elif isinstance(data,list):
+ n = sum(w.sum() for w in weights)
+ tot = sum(w.dot(d) for w,d in zip(weights,data)) - n
+ else:
+ assert np.isscalar(data) and np.isscalar(weights)
+ n = weights
+ tot = weights*data - 1
+
+ return n, tot
+
+ ### Gibbs sampling
+
+ def resample(self,data=[]):
+ self.p = np.random.beta(*self._posterior_hypparams(*self._get_statistics(data)))
+
+ # initialize mean field
+ self.alpha_mf = self.p*(self.alpha_0+self.beta_0)
+ self.beta_mf = (1-self.p)*(self.alpha_0+self.beta_0)
+
+ return self
+
+ ### mean field
+
+ def meanfieldupdate(self,data,weights,stats=None):
+ warn('untested')
+ n, tot = self._get_weighted_statistics(data,weights) if stats is None else stats
+ self.alpha_mf = self.alpha_0 + n
+ self.beta_mf = self.beta_0 + tot
+
+ # initialize Gibbs
+ self.p = self.alpha_mf / (self.alpha_mf + self.beta_mf)
+
+ def get_vlb(self):
+ warn('untested')
+ Elnp, Eln1mp = self._expected_statistics(self.alpha_mf,self.beta_mf)
+ return (self.alpha_0 - self.alpha_mf)*Elnp \
+ + (self.beta_0 - self.beta_mf)*Eln1mp \
+ - (self._log_partition_function(self.alpha_0,self.beta_0)
+ - self._log_partition_function(self.alpha_mf,self.beta_mf))
+
+ def expected_log_likelihood(self,x):
+ warn('untested')
+ Elnp, Eln1mp = self._expected_statistics(self.alpha_mf,self.beta_mf)
+ return (x-1)*Eln1mp + Elnp1mp
+
+ def _expected_statistics(self,alpha,beta):
+ warn('untested')
+ Elnp = special.digamma(alpha) - special.digamma(alpha+beta)
+ Eln1mp = special.digamma(beta) - special.digamma(alpha+beta)
+ return Elnp, Eln1mp
+
+ ### Max likelihood
+
+ def max_likelihood(self,data,weights=None):
+ if weights is None:
+ n, tot = self._get_statistics(data)
+ else:
+ n, tot = self._get_weighted_statistics(data,weights)
+
+ self.p = n/tot
+ return self
+
+ ### Collapsed
+
+ def log_marginal_likelihood(self,data):
+ return self._log_partition_function(*self._posterior_hypparams(*self._get_statistics(data))) \
+ - self._log_partition_function(self.alpha_0,self.beta_0)
+
+ def _log_partition_function(self,alpha,beta):
+ return special.betaln(alpha,beta)
diff --git a/build/lib.linux-x86_64-cpython-37/pybasicbayes/distributions/meta.py b/build/lib.linux-x86_64-cpython-37/pybasicbayes/distributions/meta.py
new file mode 100644
index 0000000..f2ee519
--- /dev/null
+++ b/build/lib.linux-x86_64-cpython-37/pybasicbayes/distributions/meta.py
@@ -0,0 +1,121 @@
+from __future__ import division
+from builtins import zip
+from builtins import range
+__all__ = ['_FixedParamsMixin', 'ProductDistribution']
+
+import numpy as np
+
+from pybasicbayes.abstractions import Distribution, \
+ GibbsSampling, MeanField, MeanFieldSVI, MaxLikelihood
+from pybasicbayes.util.stats import atleast_2d
+
+
+class _FixedParamsMixin(Distribution):
+ @property
+ def num_parameters(self):
+ return 0
+
+ def resample(self, *args, **kwargs):
+ return self
+
+ def meanfieldupdate(self, *args, **kwargs):
+ return self
+
+ def get_vlb(self):
+ return 0.
+
+ def copy_sample(self):
+ return self
+
+
+class ProductDistribution(
+ GibbsSampling, MeanField, MeanFieldSVI, MaxLikelihood):
+ def __init__(self, distns, slices=None):
+ self._distns = distns
+ self._slices = slices if slices is not None else \
+ [slice(i, i+1) for i in range(len(distns))]
+
+ @property
+ def params(self):
+ return {idx:distn.params for idx, distn in enumerate(self._distns)}
+
+ @property
+ def hypparams(self):
+ return {idx:distn.hypparams for idx, distn in enumerate(self._distns)}
+
+ @property
+ def num_parameters(self):
+ return sum(d.num_parameters for d in self._distns)
+
+ def rvs(self,size=[]):
+ return np.concatenate(
+ [atleast_2d(distn.rvs(size=size))
+ for distn in self._distns],axis=-1)
+
+ def log_likelihood(self,x):
+ return sum(
+ distn.log_likelihood(x[...,sl])
+ for distn,sl in zip(self._distns,self._slices))
+
+ ### Gibbs
+
+ def resample(self,data=[]):
+ assert isinstance(data,(np.ndarray,list))
+ if isinstance(data,np.ndarray):
+ for distn,sl in zip(self._distns,self._slices):
+ distn.resample(data[...,sl])
+ else:
+ for distn,sl in zip(self._distns,self._slices):
+ distn.resample([d[...,sl] for d in data])
+ return self
+
+ ### Max likelihood
+
+ def max_likelihood(self,data,weights=None):
+ assert isinstance(data,(np.ndarray,list))
+ if isinstance(data,np.ndarray):
+ for distn,sl in zip(self._distns,self._slices):
+ distn.max_likelihood(data[...,sl],weights=weights)
+ else:
+ for distn,sl in zip(self._distns,self._slices):
+ distn.max_likelihood([d[...,sl] for d in data],weights=weights)
+ return self
+
+ ### Mean field
+
+ def get_vlb(self):
+ return sum(distn.get_vlb() for distn in self._distns)
+
+ def expected_log_likelihood(self,x):
+ return np.sum(
+ [distn.expected_log_likelihood(x[...,sl])
+ for distn,sl in zip(self._distns,self._slices)], axis=0).ravel()
+
+ def meanfieldupdate(self,data,weights,**kwargs):
+ assert isinstance(data,(np.ndarray,list))
+ if isinstance(data,np.ndarray):
+ for distn,sl in zip(self._distns,self._slices):
+ distn.meanfieldupdate(data[...,sl],weights)
+ else:
+ for distn,sl in zip(self._distns,self._slices):
+ distn.meanfieldupdate(
+ [d[...,sl] for d in data],weights=weights)
+ return self
+
+ def _resample_from_mf(self):
+ for distn in self._distns:
+ distn._resample_from_mf()
+
+ ### SVI
+
+ def meanfield_sgdstep(self,data,weights,prob,stepsize):
+ assert isinstance(data,(np.ndarray,list))
+ if isinstance(data,np.ndarray):
+ for distn,sl in zip(self._distns,self._slices):
+ distn.meanfield_sgdstep(
+ data[...,sl],weights,prob,stepsize)
+ else:
+ for distn,sl in zip(self._distns,self._slices):
+ distn.meanfield_sgdstep(
+ [d[...,sl] for d in data],weights,prob,stepsize)
+ return self
diff --git a/build/lib.linux-x86_64-cpython-37/pybasicbayes/distributions/multinomial.py b/build/lib.linux-x86_64-cpython-37/pybasicbayes/distributions/multinomial.py
new file mode 100644
index 0000000..477675b
--- /dev/null
+++ b/build/lib.linux-x86_64-cpython-37/pybasicbayes/distributions/multinomial.py
@@ -0,0 +1,649 @@
+from __future__ import division
+from builtins import zip
+from builtins import map
+from builtins import range
+import copy
+__all__ = ['Categorical', 'CategoricalAndConcentration', 'Multinomial',
+ 'MultinomialAndConcentration', 'GammaCompoundDirichlet', 'CRP',
+ 'Input_Categorical', 'Input_Categorical_Normal']
+
+from pybasicbayes.distributions import gaussian
+import numpy as np
+from warnings import warn
+import scipy.stats as stats
+import scipy.special as special
+
+from pybasicbayes.abstractions import \
+ GibbsSampling, MeanField, MeanFieldSVI, MaxLikelihood, MAP
+
+from pybasicbayes.util.stats import sample_discrete
+
+try:
+ from pybasicbayes.util.cstats import sample_crp_tablecounts
+except ImportError:
+ warn('using slow sample_crp_tablecounts')
+ from pybasicbayes.util.stats import sample_crp_tablecounts
+
+
+class Categorical(GibbsSampling, MeanField, MeanFieldSVI, MaxLikelihood, MAP):
+ '''
+ This class represents a categorical distribution over labels, where the
+ parameter is weights and the prior is a Dirichlet distribution.
+ For example, if K == 3, then five samples may look like
+ [0,1,0,2,1]
+ Each entry is the label of a sample, like the outcome of die rolls. In other
+ words, generated data or data passed to log_likelihood are indices, not
+ indicator variables! (But when 'weighted data' is passed, like in mean
+ field or weighted max likelihood, the weights are over indicator
+ variables...)
+
+ This class can be used as a weak limit approximation for a DP, particularly by
+ calling __init__ with alpha_0 and K arguments, in which case the prior will be
+ a symmetric Dirichlet with K components and parameter alpha_0/K; K is then the
+ weak limit approximation parameter.
+
+ Hyperparaemters:
+ alphav_0 (vector) OR alpha_0 (scalar) and K
+
+ Parameters:
+ weights, a vector encoding a finite pmf
+ '''
+ def __init__(self,weights=None,alpha_0=None,K=None,alphav_0=None,alpha_mf=None):
+ self.K = K
+ self.alpha_0 = alpha_0
+ self.alphav_0 = alphav_0
+
+ self._alpha_mf = alpha_mf if alpha_mf is not None else self.alphav_0
+
+ self.weights = weights
+
+ if weights is None and self.alphav_0 is not None:
+ self.resample() # intialize from prior
+
+ def _get_alpha_0(self):
+ return self._alpha_0
+
+ def _set_alpha_0(self,alpha_0):
+ self._alpha_0 = alpha_0
+ if not any(_ is None for _ in (self.K, self._alpha_0)):
+ self.alphav_0 = np.repeat(self._alpha_0/self.K,self.K)
+
+ alpha_0 = property(_get_alpha_0,_set_alpha_0)
+
+ def _get_alphav_0(self):
+ return self._alphav_0 if hasattr(self,'_alphav_0') else None
+
+ def _set_alphav_0(self,alphav_0):
+ if alphav_0 is not None:
+ self._alphav_0 = alphav_0
+ self.K = len(alphav_0)
+
+ alphav_0 = property(_get_alphav_0,_set_alphav_0)
+
+ @property
+ def params(self):
+ return dict(weights=self.weights)
+
+ @property
+ def hypparams(self):
+ return dict(alphav_0=self.alphav_0)
+
+ @property
+ def num_parameters(self):
+ return len(self.weights)
+
+ def rvs(self,size=None):
+ return sample_discrete(self.weights,size)
+
+ def log_likelihood(self,x):
+ out = np.zeros_like(x, dtype=np.double)
+ nanidx = np.isnan(x)
+ err = np.seterr(divide='ignore')
+ out[~nanidx] = np.log(self.weights)[list(x[~nanidx])] # log(0) can happen, no warning
+ np.seterr(**err)
+ return out
+
+ ### Gibbs sampling
+
+ def resample(self,data=[],counts=None):
+ counts = self._get_statistics(data) if counts is None else counts
+ try:
+ self.weights = np.random.dirichlet(self.alphav_0 + counts)
+ except ZeroDivisionError as e:
+ # print("ZeroDivisionError {}".format(e))
+ self.weights = np.random.dirichlet(self.alphav_0 + 0.01 + counts)
+ except ValueError as e:
+ # print("ValueError {}".format(e))
+ self.weights = np.random.dirichlet(self.alphav_0 + 0.01 + counts)
+ if np.isnan(self.weights).any():
+ self.weights = np.random.dirichlet(self.alphav_0 + 0.01 + counts)
+ np.clip(self.weights, np.spacing(1.), np.inf, out=self.weights)
+ # NOTE: next line is so we can use Gibbs sampling to initialize mean field
+ self._alpha_mf = self.weights * self.alphav_0.sum()
+ assert (self._alpha_mf >= 0.).all()
+ return self
+
+ def _get_statistics(self,data,K=None):
+ K = K if K else self.K
+ if isinstance(data,np.ndarray) or \
+ (isinstance(data,list) and len(data) > 0
+ and not isinstance(data[0],(np.ndarray,list))):
+ counts = np.bincount(data,minlength=K)
+ else:
+ counts = sum(np.bincount(d,minlength=K) for d in data)
+ return counts
+
+ def _get_weighted_statistics(self,data,weights):
+ if isinstance(weights,np.ndarray):
+ assert weights.ndim in (1,2)
+ if data is None or weights.ndim == 2:
+ # when weights is 2D or data is None, the weights are expected
+ # indicators and data is just a placeholder; nominally data
+ # should be np.arange(K)[na,:].repeat(N,axis=0)
+ counts = np.atleast_2d(weights).sum(0)
+ else:
+ # when weights is 1D, data is indices and we do a weighted
+ # bincount
+ counts = np.bincount(data,weights,minlength=self.K)
+ else:
+ if len(weights) == 0:
+ counts = np.zeros(self.K,dtype=int)
+ else:
+ data = data if data else [None]*len(weights)
+ counts = sum(self._get_weighted_statistics(d,w)
+ for d, w in zip(data,weights))
+ return counts
+
+ ### Mean Field
+
+ def meanfieldupdate(self,data,weights):
+ # update
+ self._alpha_mf = self.alphav_0 + self._get_weighted_statistics(data,weights)
+ self.weights = self._alpha_mf / self._alpha_mf.sum() # for plotting
+ assert (self._alpha_mf > 0.).all()
+ return self
+
+ def get_vlb(self):
+ # return avg energy plus entropy, our contribution to the vlb
+ # see Eq. 10.66 in Bishop
+ logpitilde = self.expected_log_likelihood() # default is on np.arange(self.K)
+ q_entropy = -1* (
+ (logpitilde*(self._alpha_mf-1)).sum()
+ + special.gammaln(self._alpha_mf.sum()) - special.gammaln(self._alpha_mf).sum())
+ p_avgengy = special.gammaln(self.alphav_0.sum()) - special.gammaln(self.alphav_0).sum() \
+ + ((self.alphav_0-1)*logpitilde).sum()
+
+ return p_avgengy + q_entropy
+
+ def expected_log_likelihood(self,x=None):
+ # usually called when np.all(x == np.arange(self.K))
+ x = x if x is not None else slice(None)
+ return special.digamma(self._alpha_mf[x]) - special.digamma(self._alpha_mf.sum())
+
+ ### Mean Field SGD
+
+ def meanfield_sgdstep(self,data,weights,prob,stepsize):
+ self._alpha_mf = \
+ (1-stepsize) * self._alpha_mf + stepsize * (
+ self.alphav_0
+ + 1./prob * self._get_weighted_statistics(data,weights))
+ self.weights = self._alpha_mf / self._alpha_mf.sum() # for plotting
+ return self
+
+ def _resample_from_mf(self):
+ self.weights = np.random.dirichlet(self._alpha_mf)
+
+ ### Max likelihood
+
+ def max_likelihood(self,data,weights=None):
+ if weights is None:
+ counts = self._get_statistics(data)
+ else:
+ counts = self._get_weighted_statistics(data,weights)
+ self.weights = counts/counts.sum()
+ return self
+
+ def MAP(self,data,weights=None):
+ if weights is None:
+ counts = self._get_statistics(data)
+ else:
+ counts = self._get_weighted_statistics(data,weights)
+ counts += self.alphav_0
+ self.weights = counts/counts.sum()
+ return self
+
+
+class CategoricalAndConcentration(Categorical):
+ '''
+ Categorical with resampling of the symmetric Dirichlet concentration
+ parameter.
+
+ concentration ~ Gamma(a_0,b_0)
+
+ The Dirichlet prior over pi is then
+
+ pi ~ Dir(concentration/K)
+ '''
+ def __init__(self,a_0,b_0,K,alpha_0=None,weights=None):
+ self.alpha_0_obj = GammaCompoundDirichlet(a_0=a_0,b_0=b_0,K=K,concentration=alpha_0)
+ super(CategoricalAndConcentration,self).__init__(alpha_0=self.alpha_0,
+ K=K,weights=weights)
+
+ def _get_alpha_0(self):
+ return self.alpha_0_obj.concentration
+
+ def _set_alpha_0(self,alpha_0):
+ self.alpha_0_obj.concentration = alpha_0
+ self.alphav_0 = np.repeat(alpha_0/self.K,self.K)
+
+ alpha_0 = property(_get_alpha_0, _set_alpha_0)
+
+ @property
+ def params(self):
+ return dict(alpha_0=self.alpha_0,weights=self.weights)
+
+ @property
+ def hypparams(self):
+ return dict(a_0=self.a_0,b_0=self.b_0,K=self.K)
+
+ def resample(self,data=[]):
+ counts = self._get_statistics(data,self.K)
+ self.alpha_0_obj.resample(counts)
+ self.alpha_0 = self.alpha_0 # for the effect on alphav_0
+ return super(CategoricalAndConcentration,self).resample(data)
+
+ def resample_just_weights(self,data=[]):
+ return super(CategoricalAndConcentration,self).resample(data)
+
+ def meanfieldupdate(self,*args,**kwargs): # TODO
+ warn('MeanField not implemented for %s; concentration parameter will stay fixed')
+ return super(CategoricalAndConcentration,self).meanfieldupdate(*args,**kwargs)
+
+ def max_likelihood(self,*args,**kwargs):
+ raise NotImplementedError
+
+
+class Multinomial(Categorical):
+ '''
+ Like Categorical but the data are counts, so _get_statistics is overridden
+ (though _get_weighted_statistics can stay the same!). log_likelihood also
+ changes since, just like for the binomial special case, we sum over all
+ possible orderings.
+
+ For example, if K == 3, then a sample with n=5 might be
+ array([2,2,1])
+
+ A Poisson process conditioned on the number of points emitted.
+ '''
+ def __init__(self,weights=None,alpha_0=None,K=None,alphav_0=None,alpha_mf=None,
+ N=1):
+ self.N = N
+ super(Multinomial, self).__init__(weights,alpha_0,K,alphav_0,alpha_mf)
+
+ def log_likelihood(self,x):
+ assert isinstance(x,np.ndarray) and x.ndim == 2 and x.shape[1] == self.K
+ return np.where(x,x*np.log(self.weights),0.).sum(1) \
+ + special.gammaln(x.sum(1)+1) - special.gammaln(x+1).sum(1)
+
+ def rvs(self,size=None,N=None):
+ N = N if N else self.N
+ return np.random.multinomial(N, self.weights, size=size)
+
+ def _get_statistics(self,data,K=None):
+ K = K if K else self.K
+ if isinstance(data,np.ndarray):
+ return np.atleast_2d(data).sum(0)
+ else:
+ if len(data) == 0:
+ return np.zeros(K,dtype=int)
+ return np.concatenate(data).sum(0)
+
+ def expected_log_likelihood(self,x=None):
+ if x is not None and (not x.ndim == 2 or not np.all(x == np.eye(x.shape[0]))):
+ raise NotImplementedError # TODO nontrivial expected log likelihood
+ return super(Multinomial,self).expected_log_likelihood()
+
+
+class MultinomialAndConcentration(CategoricalAndConcentration,Multinomial):
+ pass
+
+
+class CRP(GibbsSampling):
+ '''
+ concentration ~ Gamma(a_0,b_0) [b_0 is inverse scale, inverse of numpy scale arg]
+ rvs ~ CRP(concentration)
+
+ This class models CRPs. The parameter is the concentration parameter (proportional
+ to probability of starting a new table given some number of customers in the
+ restaurant), which has a Gamma prior.
+ '''
+
+ def __init__(self,a_0,b_0,concentration=None):
+ self.a_0 = a_0
+ self.b_0 = b_0
+
+ if concentration is not None:
+ self.concentration = concentration
+ else:
+ self.resample(niter=1)
+
+ @property
+ def params(self):
+ return dict(concentration=self.concentration)
+
+ @property
+ def hypparams(self):
+ return dict(a_0=self.a_0,b_0=self.b_0)
+
+ def rvs(self,customer_counts):
+ # could replace this with one of the faster C versions I have lying
+ # around, but at least the Python version is clearer
+ assert isinstance(customer_counts,list) or isinstance(customer_counts,int)
+ if isinstance(customer_counts,int):
+ customer_counts = [customer_counts]
+
+ restaurants = []
+ for num in customer_counts:
+ # a CRP with num customers
+ tables = []
+ for c in range(num):
+ newidx = sample_discrete(np.array(tables + [self.concentration]))
+ if newidx == len(tables):
+ tables += [1]
+ else:
+ tables[newidx] += 1
+
+ restaurants.append(tables)
+
+ return restaurants if len(restaurants) > 1 else restaurants[0]
+
+ def log_likelihood(self,restaurants):
+ assert isinstance(restaurants,list) and len(restaurants) > 0
+ if not isinstance(restaurants[0],list): restaurants=[restaurants]
+
+ likes = []
+ for counts in restaurants:
+ counts = np.array([c for c in counts if c > 0]) # remove zero counts b/c of gammaln
+ K = len(counts) # number of tables
+ N = sum(counts) # number of customers
+ likes.append(K*np.log(self.concentration) + np.sum(special.gammaln(counts)) +
+ special.gammaln(self.concentration) -
+ special.gammaln(N+self.concentration))
+
+ return np.asarray(likes) if len(likes) > 1 else likes[0]
+
+ def resample(self,data=[],niter=50):
+ for itr in range(niter):
+ a_n, b_n = self._posterior_hypparams(*self._get_statistics(data))
+ try:
+ self.concentration = np.random.gamma(a_n,scale=1./b_n)
+ except Exception:
+ print("have to apply weird bug fix in /apps/conda/sbruijns/envs/hdp_pg_env/lib/python3.4/site-packages/pybasicbayes/distributions/multinomial")
+ self.concentration += 0.00001
+ a_n, b_n = self._posterior_hypparams(*self._get_statistics(data))
+ self.concentration = np.random.gamma(a_n,scale=1./b_n)
+
+ def _posterior_hypparams(self,sample_numbers,total_num_distinct):
+ # NOTE: this is a stochastic function: it samples auxiliary variables
+ if total_num_distinct > 0:
+ sample_numbers = np.array(sample_numbers)
+ sample_numbers = sample_numbers[sample_numbers > 0]
+
+ wvec = np.random.beta(self.concentration+1,sample_numbers)
+ svec = np.array(stats.bernoulli.rvs(sample_numbers/(sample_numbers+self.concentration)))
+ return self.a_0 + total_num_distinct-svec.sum(), (self.b_0 - np.log(wvec).sum())
+ else:
+ return self.a_0, self.b_0
+ return self
+
+ def _get_statistics(self,data):
+ assert isinstance(data,list)
+ if len(data) == 0:
+ sample_numbers = 0
+ total_num_distinct = 0
+ else:
+ if isinstance(data[0],list):
+ sample_numbers = np.array(list(map(sum,data)))
+ total_num_distinct = sum(map(len,data))
+ else:
+ sample_numbers = np.array(sum(data))
+ total_num_distinct = len(data)
+
+ return sample_numbers, total_num_distinct
+
+
+class GammaCompoundDirichlet(CRP):
+ # TODO this class is a bit ugly
+ '''
+ Implements a Gamma(a_0,b_0) prior over finite dirichlet concentration
+ parameter. The concentration is scaled according to the weak-limit sequence.
+
+ For each set of counts i, the model is
+ concentration ~ Gamma(a_0,b_0)
+ pi_i ~ Dir(concentration/K)
+ data_i ~ Multinomial(pi_i)
+
+ K is a free parameter in that with big enough K (relative to the size of the
+ sampled data) everything starts to act like a DP; K is just the size of the
+ size of the mesh projection.
+ '''
+ def __init__(self,K,a_0,b_0,concentration=None):
+ self.K = K
+ super(GammaCompoundDirichlet,self).__init__(a_0=a_0,b_0=b_0,
+ concentration=concentration)
+
+ @property
+ def params(self):
+ return dict(concentration=self.concentration)
+
+ @property
+ def hypparams(self):
+ return dict(a_0=self.a_0,b_0=self.b_0,K=self.K)
+
+ def rvs(self, sample_counts=None, size=None):
+ if sample_counts is None:
+ sample_counts = size
+ if isinstance(sample_counts,int):
+ sample_counts = [sample_counts]
+ out = np.empty((len(sample_counts),self.K),dtype=int)
+ for idx,c in enumerate(sample_counts):
+ out[idx] = np.random.multinomial(c,
+ np.random.dirichlet(np.repeat(self.concentration/self.K,self.K)))
+ return out if out.shape[0] > 1 else out[0]
+
+ def resample(self,data=[],niter=50,weighted_cols=None):
+ if weighted_cols is not None:
+ self.weighted_cols = weighted_cols
+ else:
+ self.weighted_cols = np.ones(self.K)
+
+ # all this is to check if data is empty
+ if isinstance(data,np.ndarray):
+ size = data.sum()
+ elif isinstance(data,list):
+ size = sum(d.sum() for d in data)
+ else:
+ assert data == 0
+ size = 0
+
+ if size > 0:
+ return super(GammaCompoundDirichlet,self).resample(data,niter=niter)
+ else:
+ return super(GammaCompoundDirichlet,self).resample(data,niter=1)
+
+ def _get_statistics(self,data):
+ # NOTE: this is a stochastic function: it samples auxiliary variables
+ counts = np.array(data,ndmin=2,order='C')
+
+ # sample m's, which sample an inverse of the weak limit projection
+ if counts.sum() == 0:
+ return 0, 0
+ else:
+ m = sample_crp_tablecounts(self.concentration,counts,self.weighted_cols)
+ return counts.sum(1), m.sum()
+
+ def _get_statistics_python(self,data):
+ counts = np.array(data,ndmin=2)
+
+ # sample m's
+ if counts.sum() == 0:
+ return 0, 0
+ else:
+ m = 0
+ for (i,j), n in np.ndenumerate(counts):
+ m += (np.random.rand(n) < self.concentration*self.K*self.weighted_cols[j] \
+ / (np.arange(n)+self.concentration*self.K*self.weighted_cols[j])).sum()
+ return counts.sum(1), m
+
+
+class Input_Categorical():
+ '''
+ This class enables an input output HMM structure, where the observation distribution
+ that we sample from is dictated by the input at that time step, so this input must be an
+ integer. Parameters are weights and the prior is a Dirichlet distribution.
+ Inspired by Matt's other distributions.
+
+ Hyperparaemters:
+
+ TODO
+
+ Parameters:
+ [weights, a vector encoding a finite, multidimensional pmf]
+ '''
+ def __init__(self, n_inputs, n_outputs, modulate=100):
+
+ self.n_inputs = n_inputs
+ self.n_outputs = n_outputs # could be made different for different inputs
+ self.modulate = modulate # high modulation (take modulo of first row data) means no effect, modulation = stimulus set size means no conditinoning
+ #print("Input data is taken mod {}".format(self.modulate))
+ self.weights = np.zeros((n_inputs, n_outputs))
+
+ self.resample() # intialize from prior
+
+ def rvs(self, input):
+ input = copy.copy(input)
+ input = input % self.modulate
+ types, counts = np.unique(input, return_counts=True)
+ output = np.zeros_like(input)
+ for t, c in zip(types, counts):
+ temp = np.random.choice(self.n_outputs, c, p=self.weights[t])
+ output[input == t] = temp
+ return np.array((input, output)).T
+
+ def log_likelihood(self, x):
+ x = copy.copy(x)
+ x[:, 0] %= self.modulate
+ out = np.zeros_like(x, dtype=np.double)
+ err = np.seterr(divide='ignore')
+ out = np.log(self.weights)[tuple(x.T)]
+ np.seterr(**err)
+ return out
+
+ # Gibbs sampling
+ def resample(self, data=[]):
+ counts = self._get_statistics(data)
+
+ for i in range(self.n_inputs):
+ self.weights[i] = np.random.dirichlet(np.ones(self.n_outputs) + counts[i])
+
+ def _get_statistics(self, data):
+ # TODO: improve
+ data = copy.copy(data)
+ counts = np.zeros_like(self.weights, dtype=np.int32)
+ if isinstance(data, np.ndarray):
+ assert len(data.shape) == 2
+ data[:, 0] %= self.modulate
+ for d in data:
+ counts[tuple(d)] += 1
+ else:
+ for d in data:
+ d[:, 0] %= self.modulate
+ for subd in d:
+ counts[tuple(subd)] += 1
+ return counts
+
+
+ ### Max likelihood
+
+ def max_likelihood(self,data,weights=None):
+ warn('ML not implemented')
+
+ def MAP(self,data,weights=None):
+ warn('MAP not implemented')
+
+
+class Input_Categorical_Normal():
+ '''
+ This class enables an input output HMM structure, where the observation distribution
+ that we sample from is dictated by the input at that time step, so this input must be an
+ integer.
+ Here, One output is from a Categorical, the other from a normal.
+ Parameters are weights and the prior is a Dirichlet distribution.
+ Inspired by Matt's other distributions.
+
+ Hyperparaemters:
+
+ TODO
+
+ Parameters:
+ [weights, a vector encoding a finite, multidimensional pmf]
+ '''
+ def __init__(self, n_inputs, n_outputs, normal_hypparams):
+
+ self.n_inputs = n_inputs
+ self.n_outputs = n_outputs # could be made different for different inputs
+ self.cats = Input_Categorical(n_inputs, n_outputs)
+ self.normals = [gaussian.Gaussian(**normal_hypparams) for state in range(n_inputs)]
+
+ def rvs(self, input):
+ types, counts = np.unique(input, return_counts=True)
+ output = np.zeros((len(input), 2))
+ output[:, 0] = self.cats.rvs(input)[:, 1]
+
+ for t, c in zip(types, counts):
+ temp = self.normals[t].rvs(c)
+ output[input == t, 1] = temp[:, 0]
+
+ return np.concatenate((np.array(input)[None].T, output), axis=1)
+
+ def log_likelihood(self, x):
+ out = self.cats.log_likelihood(x[:, [0, 1]].astype(int))
+
+ # Filter out negative or 0 reaction times
+ bad_nums = x[:, 2] == -np.inf
+ x[bad_nums, 2] = 0
+
+ means = np.zeros(x.shape[0])
+ stds = np.zeros(x.shape[0])
+ normal_ll = np.zeros(x.shape[0])
+ for i, n in enumerate(self.normals):
+ mask = x[:, 0] == i
+ # don't consider negative RTs in ll calculation
+ means[mask], stds[mask] = n.mu, n.sigma[0]
+
+ normal_ll = stats.norm().logpdf((x[:, 2] - means) / stds) / stds
+ normal_ll[bad_nums] = 0
+
+ return out
+
+ # Gibbs sampling
+ def resample(self, data=[]):
+ if isinstance(data, np.ndarray):
+ pass
+ if isinstance(data, list):
+ data = np.concatenate(data)
+ self.cats.resample(data[:, [0, 1]].astype(int))
+
+ bad_nums = data[:, 2] == -np.inf
+ for i, n in enumerate(self.normals):
+ mask = data[:, 0] == i
+ n.resample(data=data[np.logical_and(mask, ~bad_nums), 2])
+
+
+ ### Max likelihood
+
+ def max_likelihood(self,data,weights=None):
+ warn('ML not implemented')
+
+ def MAP(self,data,weights=None):
+ warn('MAP not implemented')
diff --git a/build/lib.linux-x86_64-cpython-37/pybasicbayes/distributions/negativebinomial.py b/build/lib.linux-x86_64-cpython-37/pybasicbayes/distributions/negativebinomial.py
new file mode 100644
index 0000000..9336a2a
--- /dev/null
+++ b/build/lib.linux-x86_64-cpython-37/pybasicbayes/distributions/negativebinomial.py
@@ -0,0 +1,681 @@
+from __future__ import division
+from builtins import zip
+from builtins import range
+from builtins import object
+__all__ = [
+ 'NegativeBinomial', 'NegativeBinomialFixedR', 'NegativeBinomialIntegerR2',
+ 'NegativeBinomialIntegerR', 'NegativeBinomialFixedRVariant',
+ 'NegativeBinomialIntegerRVariant', 'NegativeBinomialIntegerRVariant',
+ 'NegativeBinomialIntegerR2Variant']
+
+import numpy as np
+from numpy import newaxis as na
+import scipy.special as special
+from scipy.special import logsumexp
+from warnings import warn
+
+from pybasicbayes.abstractions import Distribution, GibbsSampling, \
+ MeanField, MeanFieldSVI, MaxLikelihood
+from pybasicbayes.util.stats import getdatasize, flattendata, \
+ sample_discrete_from_log, sample_discrete, atleast_2d
+
+try:
+ from pybasicbayes.util.cstats import sample_crp_tablecounts
+except ImportError:
+ warn('using slow sample_crp_tablecounts')
+ from pybasicbayes.util.stats import sample_crp_tablecounts
+
+
+class _NegativeBinomialBase(Distribution):
+ '''
+ Negative Binomial distribution with a conjugate beta prior on p and a
+ separate gamma prior on r. The parameter r does not need to be an integer.
+ If r is an integer, then x ~ NegBin(r,p) is the same as
+ x = np.random.geometric(1-p,size=r).sum() - r
+ where r is subtracted to make the geometric support be {0,1,2,...}
+ Mean is r*p/(1-p), var is r*p/(1-p)**2
+
+ Uses the data augemntation sampling method from Zhou et al. ICML 2012
+
+ NOTE: the support is {0,1,2,...}.
+
+ Hyperparameters:
+ k_0, theta_0: r ~ Gamma(k, theta)
+ or r = np.random.gamma(k,theta)
+ alpha_0, beta_0: p ~ Beta(alpha,beta)
+ or p = np.random.beta(alpha,beta)
+
+ Parameters:
+ r
+ p
+ '''
+ def __init__(self,r=None,p=None,k_0=None,theta_0=None,alpha_0=None,beta_0=None):
+ self.r = r
+ self.p = p
+
+ self.k_0 = k_0
+ self.theta_0 = theta_0
+ self.alpha_0 = alpha_0
+ self.beta_0 = beta_0
+
+ if r is p is None and not any(_ is None for _ in (k_0,theta_0,alpha_0,beta_0)):
+ self.resample() # intialize from prior
+
+ @property
+ def params(self):
+ return dict(r=self.r,p=self.p)
+
+ @property
+ def hypparams(self):
+ return dict(k_0=self.k_0,theta_0=self.theta_0,
+ alpha_0=self.alpha_0,beta_0=self.beta_0)
+
+ def log_likelihood(self,x,r=None,p=None):
+ r = r if r is not None else self.r
+ p = p if p is not None else self.p
+ x = np.array(x,ndmin=1)
+
+ if self.p > 0:
+ xnn = x[x >= 0]
+ raw = np.empty(x.shape)
+ raw[x>=0] = special.gammaln(r + xnn) - special.gammaln(r) \
+ - special.gammaln(xnn+1) + r*np.log(1-p) + xnn*np.log(p)
+ raw[x<0] = -np.inf
+ return raw if isinstance(x,np.ndarray) else raw[0]
+ else:
+ raw = np.log(np.zeros(x.shape))
+ raw[x == 0] = 0.
+ return raw if isinstance(x,np.ndarray) else raw[0]
+
+ def log_sf(self,x):
+ scalar = not isinstance(x,np.ndarray)
+ x = np.atleast_1d(x)
+ errs = np.seterr(divide='ignore')
+ ret = np.log(special.betainc(x+1,self.r,self.p))
+ np.seterr(**errs)
+ ret[x < 0] = np.log(1.)
+ if scalar:
+ return ret[0]
+ else:
+ return ret
+
+ def rvs(self,size=None):
+ return np.random.poisson(np.random.gamma(self.r,self.p/(1-self.p),size=size))
+
+class NegativeBinomial(_NegativeBinomialBase, GibbsSampling):
+ def resample(self,data=[],niter=20):
+ if getdatasize(data) == 0:
+ self.p = np.random.beta(self.alpha_0,self.beta_0)
+ self.r = np.random.gamma(self.k_0,self.theta_0)
+ else:
+ data = atleast_2d(flattendata(data))
+ N = len(data)
+ for itr in range(niter):
+ ### resample r
+ msum = sample_crp_tablecounts(self.r,data).sum()
+ self.r = np.random.gamma(self.k_0 + msum, 1/(1/self.theta_0 - N*np.log(1-self.p)))
+ ### resample p
+ self.p = np.random.beta(self.alpha_0 + data.sum(), self.beta_0 + N*self.r)
+ return self
+
+ def resample_python(self,data=[],niter=20):
+ if getdatasize(data) == 0:
+ self.p = np.random.beta(self.alpha_0,self.beta_0)
+ self.r = np.random.gamma(self.k_0,self.theta_0)
+ else:
+ data = flattendata(data)
+ N = len(data)
+ for itr in range(niter):
+ ### resample r
+ msum = 0.
+ for n in data:
+ msum += (np.random.rand(n) < self.r/(np.arange(n)+self.r)).sum()
+ self.r = np.random.gamma(self.k_0 + msum, 1/(1/self.theta_0 - N*np.log(1-self.p)))
+ ### resample p
+ self.p = np.random.beta(self.alpha_0 + data.sum(), self.beta_0 + N*self.r)
+ return self
+
+ ### OLD unused alternatives
+
+ def resample_logseriesaug(self,data=[],niter=20):
+ # an alternative algorithm, kind of opaque and no advantages...
+ if getdatasize(data) == 0:
+ self.p = np.random.beta(self.alpha_0,self.beta_0)
+ self.r = np.random.gamma(self.k_0,self.theta_0)
+ else:
+ data = flattendata(data)
+ N = data.shape[0]
+ logF = self.logF
+ L_i = np.zeros(N)
+ data_nz = data[data > 0]
+ for itr in range(niter):
+ logR = np.arange(1,logF.shape[1]+1)*np.log(self.r) + logF
+ L_i[data > 0] = sample_discrete_from_log(logR[data_nz-1,:data_nz.max()],axis=1)+1
+ self.r = np.random.gamma(self.k_0 + L_i.sum(), 1/(1/self.theta_0 - np.log(1-self.p)*N))
+ self.p = np.random.beta(self.alpha_0 + data.sum(), self.beta_0 + N*self.r)
+ return self
+
+ @classmethod
+ def _set_up_logF(cls):
+ if not hasattr(cls,'logF'):
+ # actually indexes logF[0,0] to correspond to log(F(1,1)) in Zhou
+ # paper, but keeps track of that alignment with the other code!
+ # especially arange(1,...), only using nonzero data and shifting it
+ SIZE = 500
+
+ logF = -np.inf * np.ones((SIZE,SIZE))
+ logF[0,0] = 0.
+ for m in range(1,logF.shape[0]):
+ prevrow = np.exp(logF[m-1] - logF[m-1].max())
+ logF[m] = np.log(np.convolve(prevrow,[0,m,1],'same')) + logF[m-1].max()
+ cls.logF = logF
+
+
+class NegativeBinomialFixedR(_NegativeBinomialBase, GibbsSampling, MeanField, MeanFieldSVI, MaxLikelihood):
+ def __init__(self,r=None,p=None,alpha_0=None,beta_0=None,alpha_mf=None,beta_mf=None):
+ self.p = p
+
+ self.r = r
+
+ self.alpha_0 = alpha_0
+ self.beta_0 = beta_0
+
+ if p is None and not any(_ is None for _ in (alpha_0,beta_0)):
+ self.resample() # intialize from prior
+
+ if not any(_ is None for _ in (alpha_mf,beta_mf)):
+ self.alpha_mf = alpha_mf
+ self.beta_mf = beta_mf
+
+ @property
+ def hypparams(self):
+ return dict(alpha_0=self.alpha_0,beta_0=self.beta_0)
+
+ @property
+ def natural_hypparam(self):
+ return np.array([self.alpha_0,self.beta_0]) - 1
+
+ @natural_hypparam.setter
+ def natural_hypparam(self,natparam):
+ self.alpha_0, self.beta_0 = natparam + 1
+
+ ### Mean Field
+
+ def _resample_from_mf(self):
+ self.p = np.random.beta(self.alpha_mf,self.beta_mf)
+ return self
+
+ def meanfieldupdate(self,data,weights):
+ self.alpha_mf, self.beta_mf = \
+ self._posterior_hypparams(*self._get_weighted_statistics(data,weights))
+ self.p = self.alpha_mf / (self.alpha_mf + self.beta_mf)
+
+ def meanfield_sgdstep(self,data,weights,prob,stepsize):
+ alpha_new, beta_new = \
+ self._posterior_hypparams(*(
+ 1./prob * self._get_weighted_statistics(data,weights)))
+ self.alpha_mf = (1-stepsize)*self.alpha_mf + stepsize*alpha_new
+ self.beta_mf = (1-stepsize)*self.beta_mf + stepsize*beta_new
+ self.p = self.alpha_mf / (self.alpha_mf + self.beta_mf)
+
+ def get_vlb(self):
+ Elnp, Eln1mp = self._mf_expected_statistics()
+ p_avgengy = (self.alpha_0-1)*Elnp + (self.beta_0-1)*Eln1mp \
+ - (special.gammaln(self.alpha_0) + special.gammaln(self.beta_0)
+ - special.gammaln(self.alpha_0 + self.beta_0))
+ q_entropy = special.betaln(self.alpha_mf,self.beta_mf) \
+ - (self.alpha_mf-1)*special.digamma(self.alpha_mf) \
+ - (self.beta_mf-1)*special.digamma(self.beta_mf) \
+ + (self.alpha_mf+self.beta_mf-2)*special.digamma(self.alpha_mf+self.beta_mf)
+ return p_avgengy + q_entropy
+
+ def _mf_expected_statistics(self):
+ Elnp, Eln1mp = special.digamma([self.alpha_mf,self.beta_mf]) \
+ - special.digamma(self.alpha_mf + self.beta_mf)
+ return Elnp, Eln1mp
+
+ def expected_log_likelihood(self,x):
+ Elnp, Eln1mp = self._mf_expected_statistics()
+ x = np.atleast_1d(x)
+ errs = np.seterr(invalid='ignore')
+ out = x*Elnp + self.r*Eln1mp + self._log_base_measure(x,self.r)
+ np.seterr(**errs)
+ out[np.isnan(out)] = -np.inf
+ return out if out.shape[0] > 1 else out[0]
+
+ @staticmethod
+ def _log_base_measure(x,r):
+ return special.gammaln(x+r) - special.gammaln(x+1) - special.gammaln(r)
+
+ ### Gibbs
+
+ def resample(self,data=[]):
+ self.p = np.random.beta(*self._posterior_hypparams(*self._get_statistics(data)))
+ # set mean field params to something reasonable for initialization
+ fakedata = self.rvs(10)
+ self.alpha_mf, self.beta_mf = self._posterior_hypparams(*self._get_statistics(fakedata))
+
+ ### Max likelihood
+
+ def max_likelihood(self,data,weights=None):
+ if weights is None:
+ n, tot = self._get_statistics(data)
+ else:
+ n, tot = self._get_weighted_statistics(data,weights)
+
+ self.p = (tot/n) / (self.r + tot/n)
+ return self
+
+ ### Statistics and posterior hypparams
+
+ def _get_statistics(self,data):
+ if getdatasize(data) == 0:
+ n, tot = 0, 0
+ elif isinstance(data,np.ndarray):
+ assert np.all(data >= 0)
+ data = np.atleast_1d(data)
+ n, tot = data.shape[0], data.sum()
+ elif isinstance(data,list):
+ assert all(np.all(d >= 0) for d in data)
+ n = sum(d.shape[0] for d in data)
+ tot = sum(d.sum() for d in data)
+ else:
+ assert np.isscalar(data)
+ n = 1
+ tot = data
+
+ return np.array([n, tot])
+
+ def _get_weighted_statistics(self,data,weights):
+ if isinstance(weights,np.ndarray):
+ assert np.all(data >= 0) and data.ndim == 1
+ n, tot = weights.sum(), weights.dot(data)
+ else:
+ assert all(np.all(d >= 0) for d in data)
+ n = sum(w.sum() for w in weights)
+ tot = sum(w.dot(d) for d,w in zip(data,weights))
+
+ return np.array([n, tot])
+
+ def _posterior_hypparams(self,n,tot):
+ return np.array([self.alpha_0 + tot, self.beta_0 + n*self.r])
+
+class NegativeBinomialIntegerR2(_NegativeBinomialBase,MeanField,MeanFieldSVI,GibbsSampling):
+ # NOTE: this class should replace NegativeBinomialFixedR completely...
+ _fixedr_class = NegativeBinomialFixedR
+
+ def __init__(self,alpha_0=None,beta_0=None,alphas_0=None,betas_0=None,
+ r_support=None,r_probs=None,r_discrete_distn=None,
+ r=None,ps=None):
+
+ assert (r_discrete_distn is not None) ^ (r_support is not None and r_probs is not None)
+ if r_discrete_distn is not None:
+ r_support, = np.where(r_discrete_distn)
+ r_probs = r_discrete_distn[r_support]
+ r_support += 1
+ self.r_support = np.asarray(r_support)
+ self.rho_0 = self.rho_mf = np.log(r_probs)
+
+ assert (alpha_0 is not None and beta_0 is not None) \
+ ^ (alphas_0 is not None and betas_0 is not None)
+ alphas_0 = alphas_0 if alphas_0 is not None else [alpha_0]*len(r_support)
+ betas_0 = betas_0 if betas_0 is not None else [beta_0]*len(r_support)
+ ps = ps if ps is not None else [None]*len(r_support)
+ self._fixedr_distns = \
+ [self._fixedr_class(r=r,p=p,alpha_0=alpha_0,beta_0=beta_0)
+ for r,p,alpha_0,beta_0 in zip(r_support,ps,alphas_0,betas_0)]
+
+ # for init
+ self.ridx = sample_discrete(r_probs)
+ self.r = r_support[self.ridx]
+
+ def __repr__(self):
+ return 'NB(r=%d,p=%0.3f)' % (self.r,self.p)
+
+ @property
+ def alphas_0(self):
+ return np.array([d.alpha_0 for d in self._fixedr_distns]) \
+ if len(self._fixedr_distns) > 0 else None
+
+ @property
+ def betas_0(self):
+ return np.array([d.beta_0 for d in self._fixedr_distns]) \
+ if len(self._fixedr_distns) > 0 else None
+
+ @property
+ def p(self):
+ return self._fixedr_distns[self.ridx].p
+
+ @p.setter
+ def p(self,val):
+ self._fixedr_distns[self.ridx].p = val
+
+ def _resample_from_mf(self):
+ self._resample_r_from_mf()
+ self._resample_p_from_mf()
+
+ def _resample_r_from_mf(self):
+ lognorm = logsumexp(self.rho_mf)
+ self.ridx = sample_discrete(np.exp(self.rho_mf - lognorm))
+ self.r = self.r_support[self.ridx]
+
+ def _resample_p_from_mf(self):
+ d = self._fixedr_distns[self.ridx]
+ self.p = np.random.beta(d.alpha_mf,d.beta_mf)
+
+ def get_vlb(self):
+ return self._r_vlb() + sum(np.exp(rho)*d.get_vlb()
+ for rho,d in zip(self.rho_mf,self._fixedr_distns))
+
+ def _r_vlb(self):
+ return np.exp(self.rho_mf).dot(self.rho_0) \
+ - np.exp(self.rho_mf).dot(self.rho_mf)
+
+ def num_parameters(self):
+ return 2
+
+ def meanfieldupdate(self,data,weights):
+ for d in self._fixedr_distns:
+ d.meanfieldupdate(data,weights)
+ self._update_rho_mf(data,weights)
+ # everything below here is for plotting
+ ridx = self.rho_mf.argmax()
+ d = self._fixedr_distns[ridx]
+ self.r = d.r
+ self.p = d.alpha_mf / (d.alpha_mf + d.beta_mf)
+
+ def _update_rho_mf(self,data,weights):
+ self.rho_mf = self.rho_0.copy()
+ for idx, d in enumerate(self._fixedr_distns):
+ n, tot = d._get_weighted_statistics(data,weights)
+ Elnp, Eln1mp = d._mf_expected_statistics()
+ self.rho_mf[idx] += (d.alpha_0-1+tot)*Elnp + (d.beta_0-1+n*d.r)*Eln1mp
+ if isinstance(data,np.ndarray):
+ self.rho_mf[idx] += weights.dot(d._log_base_measure(data,d.r))
+ else:
+ self.rho_mf[idx] += sum(w.dot(d._log_base_measure(dt,d.r))
+ for dt,w in zip(data,weights))
+
+ def expected_log_likelihood(self,x):
+ lognorm = logsumexp(self.rho_mf)
+ return sum(np.exp(rho-lognorm)*d.expected_log_likelihood(x)
+ for rho,d in zip(self.rho_mf,self._fixedr_distns))
+
+ def meanfield_sgdstep(self,data,weights,prob,stepsize):
+ rho_mf_orig = self.rho_mf.copy()
+ if isinstance(data,np.ndarray):
+ self._update_rho_mf(data,prob*weights)
+ else:
+ self._update_rho_mf(data,[w*prob for w in weights])
+ rho_mf_new = self.rho_mf
+
+ for d in self._fixedr_distns:
+ d.meanfield_sgdstep(data,weights,prob,stepsize)
+
+ self.rho_mf = (1-stepsize)*rho_mf_orig + stepsize*rho_mf_new
+
+ # for plotting
+ ridx = self.rho_mf.argmax()
+ d = self._fixedr_distns[ridx]
+ self.r = d.r
+ self.p = d.alpha_mf / (d.alpha_mf + d.beta_mf)
+
+ def resample(self,data=[]):
+ self._resample_r(data) # marginalizes out p values
+ self._resample_p(data) # resample p given sampled r
+ return self
+
+ def _resample_r(self,data):
+ self.ridx = sample_discrete(
+ self._posterior_hypparams(self._get_statistics(data)))
+ self.r = self.r_support[self.ridx]
+ return self
+
+ def _resample_p(self,data):
+ self._fixedr_distns[self.ridx].resample(data)
+ return self
+
+ def _get_statistics(self,data=[]):
+ n, tot = self._fixedr_distns[0]._get_statistics(data)
+ if n > 0:
+ data = flattendata(data)
+ alphas_n, betas_n = self.alphas_0 + tot, self.betas_0 + self.r_support*n
+ log_marg_likelihoods = \
+ special.betaln(alphas_n, betas_n) \
+ - special.betaln(self.alphas_0, self.betas_0) \
+ + (special.gammaln(data[:,na]+self.r_support)
+ - special.gammaln(data[:,na]+1) \
+ - special.gammaln(self.r_support)).sum(0)
+ else:
+ log_marg_likelihoods = np.zeros_like(self.r_support)
+ return log_marg_likelihoods
+
+ def _posterior_hypparams(self,log_marg_likelihoods):
+ log_posterior_discrete = self.rho_0 + log_marg_likelihoods
+ return np.exp(log_posterior_discrete - log_posterior_discrete.max())
+
+class NegativeBinomialIntegerR(NegativeBinomialFixedR, GibbsSampling, MaxLikelihood):
+ '''
+ Nonconjugate Discrete+Beta prior
+ r_discrete_distribution is an array where index i is p(r=i+1)
+ '''
+ def __init__(self,r_discrete_distn=None,r_support=None,
+ alpha_0=None,beta_0=None,r=None,p=None):
+ self.r_support = r_support
+ self.r_discrete_distn = r_discrete_distn
+ self.alpha_0 = alpha_0
+ self.beta_0 = beta_0
+ self.r = r
+ self.p = p
+
+ if r is p is None \
+ and not any(_ is None for _ in (r_discrete_distn,alpha_0,beta_0)):
+ self.resample() # intialize from prior
+
+ @property
+ def hypparams(self):
+ return dict(r_discrete_distn=self.r_discrete_distn,
+ alpha_0=self.alpha_0,beta_0=self.beta_0)
+
+ def get_r_discrete_distn(self):
+ return self._r_discrete_distn
+
+ def set_r_discrete_distn(self,r_discrete_distn):
+ if r_discrete_distn is not None:
+ r_discrete_distn = np.asarray(r_discrete_distn,dtype=np.float)
+ r_support, = np.where(r_discrete_distn)
+ r_probs = r_discrete_distn[r_support]
+ r_probs /= r_probs.sum()
+ r_support += 1 # r_probs[0] corresponds to r=1
+
+ self.r_support = r_support
+ self.r_probs = r_probs
+ self._r_discrete_distn = r_discrete_distn
+
+ r_discrete_distn = property(get_r_discrete_distn,set_r_discrete_distn)
+
+ def rvs(self,size=None):
+ out = np.random.geometric(1-self.p,size=size)-1
+ for i in range(self.r-1):
+ out += np.random.geometric(1-self.p,size=size)-1
+ return out
+
+ def resample(self,data=[]):
+ alpha_n, betas_n, posterior_discrete = self._posterior_hypparams(
+ *self._get_statistics(data))
+
+ r_idx = sample_discrete(posterior_discrete)
+ self.r = self.r_support[r_idx]
+ self.p = np.random.beta(alpha_n, betas_n[r_idx])
+
+ # NOTE: this class has a conjugate prior even though it's not in the
+ # exponential family, so I wrote _get_statistics and _get_weighted_statistics
+ # (which integrate out p) for the resample() and meanfield_update() methods,
+ # though these aren't statistics in the exponential family sense
+
+ def _get_statistics(self,data):
+ # NOTE: since this isn't really in exponential family, this method needs
+ # to look at hyperparameters. form posterior hyperparameters for the p
+ # parameters here so we can integrate them out and get the r statistics
+ n, tot = super(NegativeBinomialIntegerR,self)._get_statistics(data)
+ if n > 0:
+ alpha_n, betas_n = self.alpha_0 + tot, self.beta_0 + self.r_support*n
+ data = flattendata(data)
+ log_marg_likelihoods = \
+ special.betaln(alpha_n, betas_n) \
+ - special.betaln(self.alpha_0, self.beta_0) \
+ + (special.gammaln(data[:,na]+self.r_support)
+ - special.gammaln(data[:,na]+1) \
+ - special.gammaln(self.r_support)).sum(0)
+ else:
+ log_marg_likelihoods = np.zeros_like(self.r_support)
+
+ return n, tot, log_marg_likelihoods
+
+ def _get_weighted_statistics(self,data,weights):
+ n, tot = super(NegativeBinomialIntegerR,self)._get_weighted_statistics(data,weights)
+ if n > 0:
+ alpha_n, betas_n = self.alpha_0 + tot, self.beta_0 + self.r_support*n
+ data, weights = flattendata(data), flattendata(weights)
+ log_marg_likelihoods = \
+ special.betaln(alpha_n, betas_n) \
+ - special.betaln(self.alpha_0, self.beta_0) \
+ + (special.gammaln(data[:,na]+self.r_support)
+ - special.gammaln(data[:,na]+1) \
+ - special.gammaln(self.r_support)).dot(weights)
+ else:
+ log_marg_likelihoods = np.zeros_like(self.r_support)
+
+ return n, tot, log_marg_likelihoods
+
+ def _posterior_hypparams(self,n,tot,log_marg_likelihoods):
+ alpha_n = self.alpha_0 + tot
+ betas_n = self.beta_0 + n*self.r_support
+ log_posterior_discrete = np.log(self.r_probs) + log_marg_likelihoods
+ posterior_discrete = np.exp(log_posterior_discrete - log_posterior_discrete.max())
+ return alpha_n, betas_n, posterior_discrete
+
+ def max_likelihood(self,data,weights=None,stats=None):
+ if stats is not None:
+ n, tot = stats
+ elif weights is None:
+ n, tot = super(NegativeBinomialIntegerR,self)._get_statistics(data)
+ else:
+ n, tot = super(NegativeBinomialIntegerR,self)._get_weighted_statistics(data,weights)
+
+ if n > 1:
+ rs = self.r_support
+ ps = self._max_likelihood_ps(n,tot,rs)
+
+ # TODO TODO this isn't right for weighted data: do weighted sums
+ if isinstance(data,np.ndarray):
+ likelihoods = np.array([self.log_likelihood(data,r=r,p=p).sum()
+ for r,p in zip(rs,ps)])
+ else:
+ likelihoods = np.array([sum(self.log_likelihood(d,r=r,p=p).sum()
+ for d in data) for r,p in zip(rs,ps)])
+
+ argmax = likelihoods.argmax()
+ self.r = self.r_support[argmax]
+ self.p = ps[argmax]
+ return self
+
+ def _log_base_measure(self,data):
+ return [(special.gammaln(r+data) - special.gammaln(r) - special.gammaln(data+1)).sum()
+ for r in self.r_support]
+
+ def _max_likelihood_ps(self,n,tot,rs):
+ ps = (tot/n) / (rs + tot/n)
+ assert (ps >= 0).all()
+ return ps
+
+class _StartAtRMixin(object):
+ def log_likelihood(self,x,**kwargs):
+ r = kwargs['r'] if 'r' in kwargs else self.r
+ return super(_StartAtRMixin,self).log_likelihood(x-r,**kwargs)
+
+ def log_sf(self,x,**kwargs):
+ return super(_StartAtRMixin,self).log_sf(x-self.r,**kwargs)
+
+ def expected_log_likelihood(self,x,**kwargs):
+ r = kwargs['r'] if 'r' in kwargs else self.r
+ return super(_StartAtRMixin,self).expected_log_likelihood(x-r,**kwargs)
+
+ def rvs(self,size=[]):
+ return super(_StartAtRMixin,self).rvs(size)+self.r
+
+class NegativeBinomialFixedRVariant(_StartAtRMixin,NegativeBinomialFixedR):
+ def _get_statistics(self,data):
+ n, tot = super(NegativeBinomialFixedRVariant,self)._get_statistics(data)
+ n, tot = n, tot-n*self.r
+ assert tot >= 0
+ return np.array([n, tot])
+
+ def _get_weighted_statistics(self,data,weights):
+ n, tot = super(NegativeBinomialFixedRVariant,self)._get_weighted_statistics(data,weights)
+ n, tot = n, tot-n*self.r
+ assert tot >= 0
+ return np.array([n, tot])
+
+class NegativeBinomialIntegerRVariant(NegativeBinomialIntegerR):
+ def resample(self,data=[]):
+ n, alpha_n, posterior_discrete, r_support = self._posterior_hypparams(
+ *self._get_statistics(data)) # NOTE: pass out r_support b/c feasible subset
+ self.r = r_support[sample_discrete(posterior_discrete)]
+ self.p = np.random.beta(alpha_n - n*self.r, self.beta_0 + n*self.r)
+
+ def _get_statistics(self,data):
+ n = getdatasize(data)
+ if n > 0:
+ data = flattendata(data)
+ feasible = self.r_support <= data.min()
+ assert np.any(feasible)
+ r_support = self.r_support[feasible]
+ normalizers = (special.gammaln(data[:,na]) - special.gammaln(data[:,na]-r_support+1)
+ - special.gammaln(r_support)).sum(0)
+ return n, data.sum(), normalizers, feasible
+ else:
+ return n, None, None, None
+
+ def _posterior_hypparams(self,n,tot,normalizers,feasible):
+ if n == 0:
+ return n, self.alpha_0, self.r_probs, self.r_support
+ else:
+ r_probs = self.r_probs[feasible]
+ r_support = self.r_support[feasible]
+ log_marg_likelihoods = special.betaln(self.alpha_0 + tot - n*r_support,
+ self.beta_0 + r_support*n) \
+ - special.betaln(self.alpha_0, self.beta_0) \
+ + normalizers
+ log_marg_probs = np.log(r_probs) + log_marg_likelihoods
+ log_marg_probs -= log_marg_probs.max()
+ marg_probs = np.exp(log_marg_probs)
+
+ return n, self.alpha_0 + tot, marg_probs, r_support
+
+ def _max_likelihood_ps(self,n,tot,rs):
+ ps = 1-(rs*n)/tot
+ assert (ps >= 0).all()
+ return ps
+
+ def rvs(self,size=[]):
+ return super(NegativeBinomialIntegerRVariant,self).rvs(size) + self.r
+
+class NegativeBinomialIntegerR2Variant(NegativeBinomialIntegerR2):
+ _fixedr_class = NegativeBinomialFixedRVariant
+
+ def _update_rho_mf(self,data,weights):
+ self.rho_mf = self.rho_0.copy()
+ for idx, d in enumerate(self._fixedr_distns):
+ n, tot = d._get_weighted_statistics(data,weights)
+ Elnp, Eln1mp = d._mf_expected_statistics()
+ self.rho_mf[idx] += (d.alpha_0-1+tot)*Elnp + (d.beta_0-1+n*d.r)*Eln1mp
+ self.rho_mf_temp = self.rho_mf.copy()
+
+ # NOTE: this method only needs to override parent in the base measure
+ # part, i.e. data -> data-r
+ if isinstance(data,np.ndarray):
+ self.rho_mf[idx] += weights.dot(d._log_base_measure(data-d.r,d.r))
+ else:
+ self.rho_mf[idx] += sum(w.dot(d._log_base_measure(dt-d.r,d.r))
+ for dt,w in zip(data,weights))
diff --git a/build/lib.linux-x86_64-cpython-37/pybasicbayes/distributions/poisson.py b/build/lib.linux-x86_64-cpython-37/pybasicbayes/distributions/poisson.py
new file mode 100644
index 0000000..ee6099e
--- /dev/null
+++ b/build/lib.linux-x86_64-cpython-37/pybasicbayes/distributions/poisson.py
@@ -0,0 +1,186 @@
+from __future__ import division
+from builtins import zip
+__all__ = ['Poisson']
+import numpy as np
+import scipy.stats as stats
+import scipy.special as special
+
+from pybasicbayes.abstractions import GibbsSampling, Collapsed, \
+ MaxLikelihood, MeanField, MeanFieldSVI
+
+
+class Poisson(GibbsSampling, Collapsed, MaxLikelihood, MeanField, MeanFieldSVI):
+ '''
+ Poisson distribution with a conjugate Gamma prior.
+
+ NOTE: the support is {0,1,2,...}
+
+ Hyperparameters (following Wikipedia's notation):
+ alpha_0, beta_0
+
+ Parameter is the mean/variance parameter:
+ lmbda
+ '''
+ def __init__(self,lmbda=None,alpha_0=None,beta_0=None,mf_alpha_0=None,mf_beta_0=None):
+ self.lmbda = lmbda
+
+ self.alpha_0 = alpha_0
+ self.beta_0 = beta_0
+ self.mf_alpha_0 = mf_alpha_0 if mf_alpha_0 is not None else alpha_0
+ self.mf_beta_0 = mf_beta_0 if mf_beta_0 is not None else beta_0
+
+ if lmbda is None and not any(_ is None for _ in (alpha_0,beta_0)):
+ self.resample() # intialize from prior
+
+ @property
+ def params(self):
+ return dict(lmbda=self.lmbda)
+
+ @property
+ def hypparams(self):
+ return dict(alpha_0=self.alpha_0,beta_0=self.beta_0)
+
+ def log_sf(self,x):
+ return stats.poisson.logsf(x,self.lmbda)
+
+ def _posterior_hypparams(self,n,tot):
+ return self.alpha_0 + tot, self.beta_0 + n
+
+ def rvs(self,size=None):
+ return np.random.poisson(self.lmbda,size=size)
+
+ def log_likelihood(self,x):
+ lmbda = self.lmbda
+ x = np.array(x,ndmin=1)
+ raw = np.empty(x.shape)
+ raw[x>=0] = -lmbda + x[x>=0]*np.log(lmbda) - special.gammaln(x[x>=0]+1)
+ raw[x<0] = -np.inf
+ return raw if isinstance(x,np.ndarray) else raw[0]
+
+ def _get_statistics(self,data):
+ if isinstance(data,np.ndarray):
+ n = data.shape[0]
+ tot = data.sum()
+ elif isinstance(data,list):
+ n = sum(d.shape[0] for d in data)
+ tot = sum(d.sum() for d in data)
+ else:
+ assert np.isscalar(data)
+ n = 1
+ tot = data
+
+ return n, tot
+
+ def _get_weighted_statistics(self,data,weights):
+ if isinstance(data,np.ndarray):
+ n = weights.sum()
+ tot = weights.dot(data)
+ elif isinstance(data,list):
+ n = sum(w.sum() for w in weights)
+ tot = sum(w.dot(d) for w,d in zip(weights,data))
+ else:
+ assert np.isscalar(data) and np.isscalar(weights)
+ n = weights
+ tot = weights*data
+
+ return np.array([n, tot])
+
+ ### Gibbs Sampling
+
+ def resample(self,data=[],stats=None):
+ stats = self._get_statistics(data) if stats is None else stats
+ alpha_n, beta_n = self._posterior_hypparams(*stats)
+ self.lmbda = np.random.gamma(alpha_n,1/beta_n)
+
+ # next line is for mean field initialization
+ self.mf_alpha_0, self.mf_beta_0 = self.lmbda * self.beta_0, self.beta_0
+
+ return self
+
+ ### Mean Field
+
+ def _resample_from_mf(self):
+ mf_alpha_0, mf_beta_0 = self._natural_to_standard(self.mf_natural_hypparam)
+ self.lmbda = np.random.gamma(mf_alpha_0, 1./mf_beta_0)
+
+ def meanfieldupdate(self,data,weights):
+ self.mf_natural_hypparam = \
+ self.natural_hypparam + self._get_weighted_statistics(data,weights)
+ self.lmbda = self.mf_alpha_0 / self.mf_beta_0
+
+ def meanfield_sgdstep(self,data,weights,prob,stepsize):
+ self.mf_natural_hypparam = \
+ (1-stepsize) * self.mf_natural_hypparam + stepsize * (
+ self.natural_hypparam
+ + 1./prob * self._get_weighted_statistics(data,weights))
+
+ def get_vlb(self):
+ return (self.natural_hypparam - self.mf_natural_hypparam).dot(self._mf_expected_statistics) \
+ - (self._log_partition_fn(self.alpha_0,self.beta_0)
+ - self._log_partition_fn(self.mf_alpha_0,self.mf_beta_0))
+
+ def expected_log_likelihood(self,x):
+ Emlmbda, Elnlmbda = self._mf_expected_statistics
+ return -special.gammaln(x+1) + Elnlmbda * x + Emlmbda
+
+ @property
+ def _mf_expected_statistics(self):
+ alpha, beta = self.mf_alpha_0, self.mf_beta_0
+ return np.array([-alpha/beta, special.digamma(alpha) - np.log(beta)])
+
+
+ @property
+ def natural_hypparam(self):
+ return self._standard_to_natural(self.alpha_0,self.beta_0)
+
+ @property
+ def mf_natural_hypparam(self):
+ return self._standard_to_natural(self.mf_alpha_0,self.mf_beta_0)
+
+ @mf_natural_hypparam.setter
+ def mf_natural_hypparam(self,natparam):
+ self.mf_alpha_0, self.mf_beta_0 = self._natural_to_standard(natparam)
+
+
+ def _standard_to_natural(self,alpha,beta):
+ return np.array([beta, alpha-1])
+
+ def _natural_to_standard(self,natparam):
+ return natparam[1]+1, natparam[0]
+
+ ### Collapsed
+
+ def log_marginal_likelihood(self,data):
+ return self._log_partition_fn(*self._posterior_hypparams(*self._get_statistics(data))) \
+ - self._log_partition_fn(self.alpha_0,self.beta_0) \
+ - self._get_sum_of_gammas(data)
+
+ def _log_partition_fn(self,alpha,beta):
+ return special.gammaln(alpha) - alpha * np.log(beta)
+
+ def _get_sum_of_gammas(self,data):
+ if isinstance(data,np.ndarray):
+ return special.gammaln(data+1).sum()
+ elif isinstance(data,list):
+ return sum(special.gammaln(d+1).sum() for d in data)
+ else:
+ assert isinstance(data,int)
+ return special.gammaln(data+1)
+
+ ### Max likelihood
+
+ def max_likelihood(self,data,weights=None):
+ if weights is None:
+ n, tot = self._get_statistics(data)
+ else:
+ n, tot = self._get_weighted_statistics(data,weights)
+
+ if n > 1e-2:
+ self.lmbda = tot/n
+ assert self.lmbda > 0
+ else:
+ self.broken = True
+ self.lmbda = 999999
+
+ return self
+
diff --git a/build/lib.linux-x86_64-cpython-37/pybasicbayes/distributions/regression.py b/build/lib.linux-x86_64-cpython-37/pybasicbayes/distributions/regression.py
new file mode 100644
index 0000000..b524061
--- /dev/null
+++ b/build/lib.linux-x86_64-cpython-37/pybasicbayes/distributions/regression.py
@@ -0,0 +1,1206 @@
+from __future__ import division
+from builtins import zip
+from builtins import range
+__all__ = ['Regression', 'RegressionNonconj', 'ARDRegression',
+ 'AutoRegression', 'ARDAutoRegression', 'DiagonalRegression',
+ 'RobustRegression', 'RobustAutoRegression']
+
+from warnings import warn
+
+import numpy as np
+from numpy import newaxis as na
+
+from scipy.linalg import solve_triangular
+from scipy.special import gammaln, digamma, polygamma
+
+from pybasicbayes.abstractions import GibbsSampling, MaxLikelihood, \
+ MeanField, MeanFieldSVI
+from pybasicbayes.util.stats import sample_gaussian, sample_mniw, \
+ sample_invwishart, getdatasize, mniw_expectedstats, mniw_log_partitionfunction, \
+ sample_invgamma, update_param
+
+from pybasicbayes.util.general import blockarray, inv_psd, cumsum, \
+ all_none, any_none, AR_striding, objarray
+
+
+class Regression(GibbsSampling, MeanField, MaxLikelihood):
+ def __init__(
+ self, nu_0=None,S_0=None,M_0=None,K_0=None,
+ affine=False,
+ A=None,sigma=None):
+ self.affine = affine
+
+ self._check_shapes(A, sigma, nu_0, S_0, M_0, K_0)
+
+ self.A = A
+ self.sigma = sigma
+
+ have_hypers = not any_none(nu_0,S_0,M_0,K_0)
+
+ if have_hypers:
+ self.natural_hypparam = self.mf_natural_hypparam = \
+ self._standard_to_natural(nu_0,S_0,M_0,K_0)
+
+ if A is sigma is None and have_hypers:
+ self.resample() # initialize from prior
+
+ @staticmethod
+ def _check_shapes(A, sigma, nu, S, M, K):
+ is_2d = lambda x: isinstance(x, np.ndarray) and x.ndim == 2
+ not_none = lambda x: x is not None
+ assert all(map(is_2d, filter(not_none, [A, sigma, S, M, K]))), 'Matrices must be 2D'
+
+ get_dim = lambda x, i: x.shape[i] if x is not None else None
+ get_dim_list = lambda pairs: filter(not_none, map(get_dim, *zip(*pairs)))
+ is_consistent = lambda dimlist: len(set(dimlist)) == 1
+ dims_agree = lambda pairs: is_consistent(get_dim_list(pairs))
+ assert dims_agree([(A, 1), (M, 1), (K, 0), (K, 1)]), 'Input dimensions not consistent'
+ assert dims_agree([(A, 0), (sigma, 0), (sigma, 1), (S, 0), (S, 1), (M, 0)]), \
+ 'Output dimensions not consistent'
+
+ @property
+ def parameters(self):
+ return (self.A, self.sigma)
+
+ @parameters.setter
+ def parameters(self, A_sigma_tuple):
+ (A,sigma) = A_sigma_tuple
+ self.A = A
+ self.sigma = sigma
+
+ @property
+ def D_in(self):
+ # NOTE: D_in includes the extra affine coordinate
+ mat = self.A if self.A is not None else self.natural_hypparam[1]
+ return mat.shape[1]
+
+ @property
+ def D_out(self):
+ mat = self.A if self.A is not None else self.natural_hypparam[1]
+ return mat.shape[0]
+
+ ### converting between natural and standard parameters
+
+ @staticmethod
+ def _standard_to_natural(nu,S,M,K):
+ Kinv = inv_psd(K)
+ A = S + M.dot(Kinv).dot(M.T)
+ B = M.dot(Kinv)
+ C = Kinv
+ d = nu
+ return np.array([A,B,C,d])
+
+ @staticmethod
+ def _natural_to_standard(natparam):
+ A,B,C,d = natparam # natparam is roughly (yyT, yxT, xxT, n)
+ nu = d
+ Kinv = C
+ K = inv_psd(Kinv)
+ # M = B.dot(K)
+ M = np.linalg.solve(Kinv, B.T).T
+ # This subtraction seems unstable!
+ # It does not necessarily return a PSD matrix
+ S = A - M.dot(B.T)
+
+ # numerical padding here...
+ K += 1e-8*np.eye(K.shape[0])
+ S += 1e-8*np.eye(S.shape[0])
+ assert np.all(0 < np.linalg.eigvalsh(S))
+ assert np.all(0 < np.linalg.eigvalsh(K))
+
+ # standard is degrees of freedom, mean of sigma (ish), mean of A, cov of rows of A
+ return nu, S, M, K
+
+ ### getting statistics
+
+ # NOTE: stats object arrays depend on the last element being a scalar,
+ # otherwise numpy will try to create a dense array and fail
+
+ def _get_statistics(self,data):
+ assert isinstance(data, (list, tuple, np.ndarray))
+ if isinstance(data,list):
+ return sum((self._get_statistics(d) for d in data),
+ self._empty_statistics())
+ elif isinstance(data, tuple):
+ x, y = data
+ bad = np.isnan(x).any(1) | np.isnan(y).any(1)
+ x, y = x[~bad], y[~bad]
+
+ n, D = y.shape
+
+ xxT, yxT, yyT = \
+ x.T.dot(x), y.T.dot(x), y.T.dot(y)
+
+ if self.affine:
+ x, y = x.sum(0), y.sum(0)
+ xxT = blockarray([[xxT,x[:,na]],[x[na,:],np.atleast_2d(n)]])
+ yxT = np.hstack((yxT,y[:,na]))
+
+ return np.array([yyT, yxT, xxT, n])
+ else:
+ # data passed in like np.hstack((x, y))
+ data = data[~np.isnan(data).any(1)]
+ n, D = data.shape[0], self.D_out
+
+ statmat = data.T.dot(data)
+ xxT, yxT, yyT = \
+ statmat[:-D,:-D], statmat[-D:,:-D], statmat[-D:,-D:]
+
+ if self.affine:
+ xy = data.sum(0)
+ x, y = xy[:-D], xy[-D:]
+ xxT = blockarray([[xxT,x[:,na]],[x[na,:],np.atleast_2d(n)]])
+ yxT = np.hstack((yxT,y[:,na]))
+
+ return np.array([yyT, yxT, xxT, n])
+
+ def _get_weighted_statistics(self,data,weights):
+ assert isinstance(data, (list, tuple, np.ndarray))
+ if isinstance(data,list):
+ return sum((self._get_statistics(d) for d in data),
+ self._empty_statistics())
+ elif isinstance(data, tuple):
+ x, y = data
+ bad = np.isnan(x).any(1) | np.isnan(y).any(1)
+ x, y, weights = x[~bad], y[~bad], weights[~bad]
+
+ n, D = weights.sum(), y.shape[1]
+ wx = weights[:,na]*x
+
+ xxT, yxT, yyT = \
+ x.T.dot(wx), y.T.dot(wx), y.T.dot(weights[:,na]*y)
+
+ if self.affine:
+ x, y = weights.dot(x), weights.dot(y)
+ xxT = blockarray([[xxT,x[:,na]],[x[na,:],np.atleast_2d(n)]])
+ yxT = np.hstack((yxT,y[:,na]))
+
+ return np.array([yyT, yxT, xxT, n])
+ else:
+ # data passed in like np.hstack((x, y))
+ gi = ~np.isnan(data).any(1)
+ data, weights = data[gi], weights[gi]
+ n, D = weights.sum(), self.D_out
+
+ statmat = data.T.dot(weights[:,na]*data)
+ xxT, yxT, yyT = \
+ statmat[:-D,:-D], statmat[-D:,:-D], statmat[-D:,-D:]
+
+ if self.affine:
+ xy = weights.dot(data)
+ x, y = xy[:-D], xy[-D:]
+ xxT = blockarray([[xxT,x[:,na]],[x[na,:],np.atleast_2d(n)]])
+ yxT = np.hstack((yxT,y[:,na]))
+
+ return np.array([yyT, yxT, xxT, n])
+
+ def _empty_statistics(self):
+ D_in, D_out = self.D_in, self.D_out
+ return np.array(
+ [np.zeros((D_out,D_out)), np.zeros((D_out,D_in)),
+ np.zeros((D_in,D_in)),0])
+
+ @staticmethod
+ def _stats_ensure_array(stats):
+ if isinstance(stats, np.ndarray):
+ return stats
+ affine = len(stats) > 4
+
+ yyT, yxT, xxT, n = stats[-4:]
+ if affine:
+ y, x = stats[:2]
+ yxT = np.hstack((yxT, y[:,None]))
+ xxT = blockarray([[xxT, x[:,None]], [x[None,:], 1.]])
+
+ return np.array([yyT, yxT, xxT, n])
+
+ ### distribution
+
+ def log_likelihood(self,xy):
+ assert isinstance(xy, (tuple,np.ndarray))
+ A, sigma, D = self.A, self.sigma, self.D_out
+ x, y = (xy[:,:-D], xy[:,-D:]) if isinstance(xy,np.ndarray) else xy
+
+ if self.affine:
+ A, b = A[:,:-1], A[:,-1]
+
+ sigma_inv, L = inv_psd(sigma, return_chol=True)
+ parammat = -1./2 * blockarray([
+ [A.T.dot(sigma_inv).dot(A), -A.T.dot(sigma_inv)],
+ [-sigma_inv.dot(A), sigma_inv]])
+
+ contract = 'ni,ni->n' if x.ndim == 2 else 'i,i->'
+ if isinstance(xy, np.ndarray):
+ out = np.einsum(contract,xy.dot(parammat),xy)
+ else:
+ out = np.einsum(contract,x.dot(parammat[:-D,:-D]),x)
+ out += np.einsum(contract,y.dot(parammat[-D:,-D:]),y)
+ out += 2*np.einsum(contract,x.dot(parammat[:-D,-D:]),y)
+
+ out -= D/2*np.log(2*np.pi) + np.log(np.diag(L)).sum()
+
+ if self.affine:
+ out += y.dot(sigma_inv).dot(b)
+ out -= x.dot(A.T).dot(sigma_inv).dot(b)
+ out -= 1./2*b.dot(sigma_inv).dot(b)
+
+ return out
+
+ def predict(self, x):
+ A, sigma = self.A, self.sigma
+
+ if self.affine:
+ A, b = A[:, :-1], A[:, -1]
+ y = x.dot(A.T) + b.T
+ else:
+ y = x.dot(A.T)
+
+ return y
+
+ def rvs(self,x=None,size=1,return_xy=True):
+ A, sigma = self.A, self.sigma
+
+ if self.affine:
+ A, b = A[:,:-1], A[:,-1]
+
+ x = np.random.normal(size=(size,A.shape[1])) if x is None else x
+ y = self.predict(x)
+ y += np.random.normal(size=(x.shape[0], self.D_out)) \
+ .dot(np.linalg.cholesky(sigma).T)
+
+ return np.hstack((x,y)) if return_xy else y
+
+ ### Gibbs sampling
+
+ def resample(self,data=[],stats=None):
+ stats = self._get_statistics(data) if stats is None else stats
+ self.A, self.sigma = sample_mniw(
+ *self._natural_to_standard(self.natural_hypparam + stats))
+ self._initialize_mean_field()
+
+ ### Max likelihood
+
+ def max_likelihood(self,data,weights=None,stats=None):
+ if stats is None:
+ stats = self._get_statistics(data) if weights is None \
+ else self._get_weighted_statistics(data,weights)
+
+ yyT, yxT, xxT, n = stats
+
+ if n > 0:
+ try:
+ self.A = np.linalg.solve(xxT, yxT.T).T
+ self.sigma = (yyT - self.A.dot(yxT.T))/n
+
+ def symmetrize(A):
+ return (A + A.T)/2.
+ self.sigma = 1e-10*np.eye(self.D_out) \
+ + symmetrize(self.sigma) # numerical
+ except np.linalg.LinAlgError:
+ self.broken = True
+ else:
+ self.broken = True
+
+ assert np.allclose(self.sigma,self.sigma.T)
+ assert np.all(np.linalg.eigvalsh(self.sigma) > 0.)
+
+ self._initialize_mean_field()
+
+ return self
+
+ ### Mean Field
+
+ def meanfieldupdate(self, data=None, weights=None, stats=None):
+ assert (data is not None and weights is not None) ^ (stats is not None)
+ stats = self._stats_ensure_array(stats) if stats is not None \
+ else self._get_weighted_statistics(data, weights)
+ self.mf_natural_hypparam = self.natural_hypparam + stats
+ self._set_params_from_mf()
+
+ def meanfield_sgdstep(self, data, weights, prob, stepsize, stats=None):
+ if stats is None:
+ stats = self._get_weighted_statistics(data, weights)
+ self.mf_natural_hypparam = \
+ (1-stepsize) * self.mf_natural_hypparam + stepsize \
+ * (self.natural_hypparam + 1./prob * stats)
+ self._set_params_from_mf()
+
+ def meanfield_expectedstats(self):
+ from pybasicbayes.util.stats import mniw_expectedstats
+ return mniw_expectedstats(
+ *self._natural_to_standard(self.mf_natural_hypparam))
+
+ def expected_log_likelihood(self, xy=None, stats=None):
+ # TODO test values, test for the affine case
+ assert isinstance(xy, (tuple, np.ndarray)) ^ isinstance(stats, tuple)
+
+ D = self.D_out
+ E_Sigmainv, E_Sigmainv_A, E_AT_Sigmainv_A, E_logdetSigmainv = \
+ mniw_expectedstats(
+ *self._natural_to_standard(self.mf_natural_hypparam))
+
+ if self.affine:
+ E_Sigmainv_A, E_Sigmainv_b = \
+ E_Sigmainv_A[:,:-1], E_Sigmainv_A[:,-1]
+ E_AT_Sigmainv_A, E_AT_Sigmainv_b, E_bT_Sigmainv_b = \
+ E_AT_Sigmainv_A[:-1,:-1], E_AT_Sigmainv_A[:-1,-1], \
+ E_AT_Sigmainv_A[-1,-1]
+
+ if xy is not None:
+ x, y = (xy[:,:-D], xy[:,-D:]) if isinstance(xy, np.ndarray) \
+ else xy
+
+ parammat = -1./2 * blockarray([
+ [E_AT_Sigmainv_A, -E_Sigmainv_A.T],
+ [-E_Sigmainv_A, E_Sigmainv]])
+
+ contract = 'ni,ni->n' if x.ndim == 2 else 'i,i->'
+ if isinstance(xy, np.ndarray):
+ out = np.einsum('ni,ni->n', xy.dot(parammat), xy)
+ else:
+ out = np.einsum(contract,x.dot(parammat[:-D,:-D]),x)
+ out += np.einsum(contract,y.dot(parammat[-D:,-D:]),y)
+ out += 2*np.einsum(contract,x.dot(parammat[:-D,-D:]),y)
+
+ out += -D/2*np.log(2*np.pi) + 1./2*E_logdetSigmainv
+
+ if self.affine:
+ out += y.dot(E_Sigmainv_b)
+ out -= x.dot(E_AT_Sigmainv_b)
+ out -= 1./2 * E_bT_Sigmainv_b
+ else:
+ if self.affine:
+ Ey, Ex = stats[:2]
+ yyT, yxT, xxT, n = stats[-4:]
+
+ contract = 'ij,nij->n' if yyT.ndim == 3 else 'ij,ij->'
+
+ out = -1./2 * np.einsum(contract, E_AT_Sigmainv_A, xxT)
+ out += np.einsum(contract, E_Sigmainv_A, yxT)
+ out += -1./2 * np.einsum(contract, E_Sigmainv, yyT)
+ out += -D/2*np.log(2*np.pi) + n/2.*E_logdetSigmainv
+
+ if self.affine:
+ out += Ey.dot(E_Sigmainv_b)
+ out -= Ex.dot(E_AT_Sigmainv_b)
+ out -= 1./2 * E_bT_Sigmainv_b
+
+ return out
+
+ def get_vlb(self):
+ E_Sigmainv, E_Sigmainv_A, E_AT_Sigmainv_A, E_logdetSigmainv = \
+ mniw_expectedstats(*self._natural_to_standard(self.mf_natural_hypparam))
+ A, B, C, d = self.natural_hypparam - self.mf_natural_hypparam
+ bilinear_term = -1./2 * np.trace(A.dot(E_Sigmainv)) \
+ + np.trace(B.T.dot(E_Sigmainv_A)) \
+ - 1./2 * np.trace(C.dot(E_AT_Sigmainv_A)) \
+ + 1./2 * d * E_logdetSigmainv
+
+ # log normalizer term
+ Z = mniw_log_partitionfunction(*self._natural_to_standard(
+ self.natural_hypparam))
+ Z_mf = mniw_log_partitionfunction(*self._natural_to_standard(
+ self.mf_natural_hypparam))
+
+ return bilinear_term - (Z - Z_mf)
+
+ def resample_from_mf(self):
+ self.A, self.sigma = sample_mniw(
+ *self._natural_to_standard(self.mf_natural_hypparam))
+
+ def _set_params_from_mf(self):
+ nu, S, M, K = self._natural_to_standard(self.mf_natural_hypparam)
+ self.A, self.sigma = M, S / nu
+
+ def _initialize_mean_field(self):
+ if hasattr(self, 'natural_hypparam'):
+ A, Sigma = self.A, self.sigma
+ nu, S, M, K = self._natural_to_standard(self.natural_hypparam)
+ self.mf_natural_hypparam = self._standard_to_natural(
+ nu, nu*Sigma, A, K)
+
+
+class RegressionNonconj(Regression):
+ def __init__(self, M_0, Sigma_0, nu_0, S_0,
+ A=None, sigma=None, affine=False, niter=10):
+ self.A = A
+ self.sigma = sigma
+ self.affine = affine
+
+ self.h_0 = np.linalg.solve(Sigma_0, M_0.ravel()).reshape(M_0.shape)
+ self.J_0 = np.linalg.inv(Sigma_0)
+ self.nu_0 = nu_0
+ self.S_0 = S_0
+
+ self.niter = niter
+
+ if all_none(A,sigma):
+ self.resample() # initialize from prior
+
+ ### Gibbs
+
+ def resample(self,data=[],niter=None):
+ niter = niter if niter else self.niter
+ if getdatasize(data) == 0:
+ self.A = sample_gaussian(J=self.J_0,h=self.h_0.ravel())\
+ .reshape(self.h_0.shape)
+ self.sigma = sample_invwishart(self.S_0,self.nu_0)
+ else:
+ yyT, yxT, xxT, n = self._get_statistics(data)
+ for itr in range(niter):
+ self._resample_A(xxT, yxT, self.sigma)
+ self._resample_sigma(xxT, yxT, yyT, n, self.A)
+
+ def _resample_A(self, xxT, yxT, sigma):
+ sigmainv = np.linalg.inv(sigma)
+ J = self.J_0 + np.kron(sigmainv, xxT)
+ h = self.h_0 + sigmainv.dot(yxT)
+ self.A = sample_gaussian(J=J,h=h.ravel()).reshape(h.shape)
+
+ def _resample_sigma(self, xxT, yxT, yyT, n, A):
+ S = self.S_0 + yyT - yxT.dot(A.T) - A.dot(yxT.T) + A.dot(xxT).dot(A.T)
+ nu = self.nu_0 + n
+ self.sigma = sample_invwishart(S, nu)
+
+
+class ARDRegression(Regression):
+ def __init__(
+ self, a,b,nu_0,S_0,M_0,
+ blocksizes=None,K_0=None,niter=10,**kwargs):
+ blocksizes = np.ones(M_0.shape[1],dtype=np.int64) \
+ if blocksizes is None else blocksizes
+ self.niter = niter
+ self.blocksizes = np.array(blocksizes)
+ self.starts = cumsum(blocksizes,strict=True)
+ self.stops = cumsum(blocksizes,strict=False)
+
+ self.a = np.repeat(a,len(blocksizes))
+ self.b = np.repeat(b,len(blocksizes))
+
+ self.nu_0 = nu_0
+ self.S_0 = S_0
+ self.M_0 = M_0
+
+ if K_0 is None:
+ self.resample_K()
+ else:
+ self.K_0 = K_0
+
+ super(ARDRegression,self).__init__(
+ K_0=self.K_0,nu_0=nu_0,S_0=S_0,M_0=M_0,**kwargs)
+
+ def resample(self,data=[],stats=None):
+ if len(data) > 0 or stats is not None:
+ stats = self._get_statistics(data) if stats is None else stats
+ for itr in range(self.niter):
+ self.A, self.sigma = \
+ sample_mniw(*self._natural_to_standard(
+ self.natural_hypparam + stats))
+
+ mat = self.M_0 - self.A
+ self.resample_K(1./2*np.einsum(
+ 'ij,ij->j',mat,np.linalg.solve(self.sigma,mat)))
+ else:
+ self.resample_K()
+ super(ARDRegression,self).resample()
+
+ def resample_K(self,diag=None):
+ if diag is None:
+ a, b = self.a, self.b
+ else:
+ sums = [diag[start:stop].sum()
+ for start,stop in zip(self.starts,self.stops)]
+ a = self.a + self.D_out*self.blocksizes/2.
+ b = self.b + np.array(sums)
+
+ ks = 1./np.random.gamma(a,scale=1./b)
+ self.K_0 = np.diag(np.repeat(ks,self.blocksizes))
+
+ self.natural_hypparam = self._standard_to_natural(
+ self.nu_0,self.S_0,self.M_0,self.K_0)
+
+ @property
+ def parameters(self):
+ return (self.A, self.sigma, self.K_0)
+
+ @parameters.setter
+ def parameters(self, A_sigma_K_0_tuple1):
+ (A,sigma,K_0) = A_sigma_K_0_tuple1
+ self.A = A
+ self.sigma = sigma
+ self.K_0 = K_0
+
+
+class DiagonalRegression(Regression, MeanFieldSVI):
+ """
+ Special case of the regression class in which the observations
+ have diagonal Gaussian noise and, potentially, missing data.
+ """
+
+ def __init__(self, D_out, D_in, mu_0=None, Sigma_0=None, alpha_0=3.0, beta_0=2.0,
+ A=None, sigmasq=None, niter=1):
+
+ self._D_out = D_out
+ self._D_in = D_in
+ self.A = A
+ self.sigmasq_flat = sigmasq
+ self.affine = False # We do not yet support affine
+
+ mu_0 = np.zeros(D_in) if mu_0 is None else mu_0
+ Sigma_0 = np.eye(D_in) if Sigma_0 is None else Sigma_0
+ assert mu_0.shape == (D_in,)
+ assert Sigma_0.shape == (D_in, D_in)
+ self.h_0 = np.linalg.solve(Sigma_0, mu_0)
+ self.J_0 = np.linalg.inv(Sigma_0)
+ self.alpha_0 = alpha_0
+ self.beta_0 = beta_0
+
+ self.niter = niter
+
+ if any_none(A, sigmasq):
+ self.A = np.zeros((D_out, D_in))
+ self.sigmasq_flat = np.ones((D_out,))
+ self.resample(data=None) # initialize from prior
+
+ # Store the natural parameters and expose the standard versions as properties
+ self.mf_J_A = np.array([self.J_0.copy() for _ in range(D_out)])
+ # Initializing with mean zero is pathological. Break symmetry by starting with sampled A.
+ # self.mf_h_A = np.array([self.h_0.copy() for _ in range(D_out)])
+ self.mf_h_A = np.array([Jd.dot(Ad) for Jd,Ad in zip(self.mf_J_A, self.A)])
+
+ self.mf_alpha = self.alpha_0 * np.ones(D_out)
+ self.mf_beta = self.alpha_0 * self.sigmasq_flat
+
+ # Cache the standard parameters for A as well
+ self._mf_A_cache = {}
+
+ # Store the natural hypparams. These correspond to the suff. stats
+ # (y^2, yxT, xxT, n)
+ # self.natural_hypparam = (2 * self.beta_0, self.h_0, self.J_0, 1.0)
+
+ @property
+ def D_out(self):
+ return self._D_out
+
+ @property
+ def D_in(self):
+ return self._D_in
+
+ @property
+ def sigma(self):
+ return np.diag(self.sigmasq_flat)
+
+ @property
+ def mf_expectations(self):
+ # Look for expectations in the cache
+ if ("mf_E_A" not in self._mf_A_cache) or \
+ ("mf_E_AAT" not in self._mf_A_cache):
+ mf_Sigma_A = \
+ np.array([np.linalg.inv(Jd) for Jd in self.mf_J_A])
+
+ self._mf_A_cache["mf_E_A"] = \
+ np.array([np.dot(Sd, hd)
+ for Sd,hd in zip(mf_Sigma_A, self.mf_h_A)])
+
+ self._mf_A_cache["mf_E_AAT"] = \
+ np.array([Sd + np.outer(md,md)
+ for Sd,md in zip(mf_Sigma_A, self._mf_A_cache["mf_E_A"])])
+
+ mf_E_A = self._mf_A_cache["mf_E_A"]
+ mf_E_AAT = self._mf_A_cache["mf_E_AAT"]
+
+ # Set the invgamma meanfield expectation
+ from scipy.special import digamma
+ mf_E_sigmasq_inv = self.mf_alpha / self.mf_beta
+ mf_E_log_sigmasq = np.log(self.mf_beta) - digamma(self.mf_alpha)
+
+ return mf_E_A, mf_E_AAT, mf_E_sigmasq_inv, mf_E_log_sigmasq
+
+ # TODO: This is a bit ugly... Return stats in the form expected by PyLDS
+ def meanfield_expectedstats(self):
+ mf_E_A, mf_E_AAT, mf_E_sigmasq_inv, mf_E_log_sigmasq = self.mf_expectations
+ E_Sigmainv = np.diag(mf_E_sigmasq_inv)
+ E_Sigmainv_A = mf_E_A * mf_E_sigmasq_inv[:,None]
+ E_AT_Sigmainv_A = np.sum(mf_E_sigmasq_inv[:,None,None] * mf_E_AAT, axis=0)
+ E_logdetSigmainv = -np.sum(mf_E_log_sigmasq)
+ return E_Sigmainv, E_Sigmainv_A, E_AT_Sigmainv_A, E_logdetSigmainv
+
+ def log_likelihood(self, xy, mask=None):
+ if isinstance(xy, tuple):
+ x,y = xy
+ else:
+ x,y = xy[:,:self.D_in], xy[:,self.D_in:]
+ assert y.shape[1] == self.D_out
+
+ if mask is None:
+ mask = np.ones_like(y)
+ else:
+ assert mask.shape == y.shape
+
+ sqerr = -0.5 * (y-x.dot(self.A.T))**2 * mask
+ ll = np.sum(sqerr / self.sigmasq_flat, axis=1)
+
+ # Add normalizer
+ ll += np.sum(-0.5*np.log(2*np.pi*self.sigmasq_flat) * mask, axis=1)
+
+ return ll
+
+ def _get_statistics(self, data, D_out=None, D_in=None, mask=None):
+ D_out = self.D_out if D_out is None else D_out
+ D_in = self.D_in if D_in is None else D_in
+ if data is None:
+ return (np.zeros((D_out,)),
+ np.zeros((D_out, D_in)),
+ np.zeros((D_out, D_in, D_in)),
+ np.zeros((D_out,)))
+
+ # Make sure data is a list
+ if not isinstance(data, list):
+ datas = [data]
+ else:
+ datas = data
+
+ # Make sure mask is also a list if given
+ if mask is not None:
+ if not isinstance(mask, list):
+ masks = [mask]
+ else:
+ masks = mask
+ else:
+ masks = [None] * len(datas)
+
+ # Sum sufficient statistics from each dataset
+ ysq = np.zeros(D_out)
+ yxT = np.zeros((D_out, D_in))
+ xxT = np.zeros((D_out, D_in, D_in))
+ n = np.zeros(D_out)
+
+ for data, mask in zip(datas, masks):
+ # Dandle tuples or hstack-ed arrays
+ if isinstance(data, tuple):
+ x, y = data
+ else:
+ x, y = data[:,:D_in], data[:, D_in:]
+ assert x.shape[1] == D_in
+ assert y.shape[1] == D_out
+
+ if mask is None:
+ mask = np.ones_like(y, dtype=bool)
+
+ ysq += np.sum(y**2 * mask, axis=0)
+ yxT += (y*mask).T.dot(x)
+ xxT += np.array([(x * mask[:,d][:,None]).T.dot(x)
+ for d in range(D_out)])
+ n += np.sum(mask, axis=0)
+ return ysq, yxT, xxT, n
+
+ @staticmethod
+ def _stats_ensure_array(stats):
+ ysq, yxT, xxT, n = stats
+
+ if yxT.ndim != 2:
+ raise Exception("yxT.shape must be (D_out, D_in)")
+ D_out, D_in = yxT.shape
+
+ # If ysq is D_out x D_out, just take the diagonal
+ if ysq.ndim == 1:
+ assert ysq.shape == (D_out,)
+ elif ysq.ndim == 2:
+ assert ysq.shape == (D_out, D_out)
+ ysq = np.diag(ysq)
+ else:
+ raise Exception("ysq.shape must be (D_out,) or (D_out, D_out)")
+
+ # Make sure xxT is D_out x D_in x D_in
+ if xxT.ndim == 2:
+ assert xxT.shape == (D_in, D_in)
+ xxT = np.tile(xxT[None,:,:], (D_out, 1, 1))
+ elif xxT.ndim == 3:
+ assert xxT.shape == (D_out, D_in, D_in)
+ else:
+ raise Exception("xxT.shape must be (D_in, D_in) or (D_out, D_in, D_in)")
+
+ # Make sure n is of shape (D_out,)
+ if np.isscalar(n):
+ n = n * np.ones(D_out)
+ elif n.ndim == 1:
+ assert n.shape == (D_out,)
+ else:
+ raise Exception("n must be a scalar or an array of shape (D_out,)")
+
+ return objarray([ysq, yxT, xxT, n])
+
+ ### Gibbs
+ def resample(self, data, stats=None, mask=None, niter=None):
+ """
+ Introduce a mask that allows for missing data
+ """
+ stats = self._get_statistics(data, mask=mask) if stats is None else stats
+ stats = self._stats_ensure_array(stats)
+
+ niter = niter if niter else self.niter
+ for itr in range(niter):
+ self._resample_A(stats)
+ self._resample_sigma(stats)
+
+ def _resample_A(self, stats):
+
+ _, yxT, xxT, _ = stats
+
+ # Sample each row of W
+ for d in range(self.D_out):
+ # Get sufficient statistics from the data
+ Jd = self.J_0 + xxT[d] / self.sigmasq_flat[d]
+ hd = self.h_0 + yxT[d] / self.sigmasq_flat[d]
+ self.A[d] = sample_gaussian(J=Jd, h=hd)
+
+ def _resample_sigma(self, stats):
+ ysq, yxT, xxT, n = stats
+ AAT = np.array([np.outer(a,a) for a in self.A])
+
+ alpha = self.alpha_0 + n / 2.0
+
+ beta = self.beta_0
+ beta += 0.5 * ysq
+ beta += -1.0 * np.sum(yxT * self.A, axis=1)
+ beta += 0.5 * np.sum(AAT * xxT, axis=(1,2))
+
+ self.sigmasq_flat = np.reshape(sample_invgamma(alpha, beta), (self.D_out,))
+
+ ### Max likelihood
+ def max_likelihood(self,data, weights=None, stats=None, mask=None):
+ if stats is None:
+ stats = self._get_statistics(data, mask)
+ stats = self._stats_ensure_array(stats)
+
+ ysq, yxT, xxT, n = stats
+
+ self.A = np.array([
+ np.linalg.solve(self.J_0 + xxTd, self.h_0 + yxTd)
+ for xxTd, yxTd in zip(xxT, yxT)
+ ])
+
+ alpha = self.alpha_0 + n / 2.0
+ beta = self.beta_0
+ beta += 0.5 * ysq
+ beta += -1.0 * np.sum(yxT * self.A, axis=1)
+ AAT = np.array([np.outer(ad, ad) for ad in self.A])
+ beta += 0.5 * np.sum(AAT * xxT, axis=(1, 2))
+
+ self.sigmasq_flat = beta / (alpha + 1.0)
+ assert np.all(self.sigmasq_flat >= 0)
+
+ ### Mean Field
+ def meanfieldupdate(self, data=None, weights=None, stats=None, mask=None):
+ assert weights is None, "Not supporting weighted data, just masked data."
+ if stats is None:
+ stats = self._get_statistics(data, mask)
+ stats = self._stats_ensure_array(stats)
+
+ self._meanfieldupdate_A(stats)
+ self._meanfieldupdate_sigma(stats)
+
+ # Update A and sigmasq_flat
+ A, _, sigmasq_inv, _ = self.mf_expectations
+ self.A = A.copy()
+ self.sigmasq_flat = 1. / sigmasq_inv
+
+ def _meanfieldupdate_A(self, stats, prob=1.0, stepsize=1.0):
+ E_sigmasq_inv = self.mf_alpha / self.mf_beta
+ _, E_yxT, E_xxT, _ = stats / prob
+
+ # Update statistics each row of A
+ for d in range(self.D_out):
+ Jd = self.J_0 + (E_xxT[d] * E_sigmasq_inv[d])
+ hd = self.h_0 + (E_yxT[d] * E_sigmasq_inv[d])
+
+ # Update the mean field natural parameters
+ self.mf_J_A[d] = update_param(self.mf_J_A[d], Jd, stepsize)
+ self.mf_h_A[d] = update_param(self.mf_h_A[d], hd, stepsize)
+
+ # Clear the cache
+ self._mf_A_cache = {}
+
+ def _meanfieldupdate_sigma(self, stats, prob=1.0, stepsize=1.0):
+ E_ysq, E_yxT, E_xxT, E_n = stats / prob
+ E_A, E_AAT, _, _ = self.mf_expectations
+
+ alpha = self.alpha_0 + E_n / 2.0
+
+ beta = self.beta_0
+ beta += 0.5 * E_ysq
+ beta += -1.0 * np.sum(E_yxT * E_A, axis=1)
+ beta += 0.5 * np.sum(E_AAT * E_xxT, axis=(1,2))
+
+ # Set the invgamma meanfield parameters
+ self.mf_alpha = update_param(self.mf_alpha, alpha, stepsize)
+ self.mf_beta = update_param(self.mf_beta, beta, stepsize)
+
+ def get_vlb(self):
+ # TODO: Implement this!
+ return 0
+
+
+ def expected_log_likelihood(self, xy=None, stats=None, mask=None):
+ if xy is not None:
+ if isinstance(xy, tuple):
+ x, y = xy
+ else:
+ x, y = xy[:, :self.D_in], xy[:, self.D_in:]
+ assert y.shape[1] == self.D_out
+
+ E_ysq = y**2
+ E_yxT = y[:,:,None] * x[:,None,:]
+ E_xxT = x[:,:,None] * x[:,None,:]
+ E_n = np.ones_like(y) if mask is None else mask
+
+ elif stats is not None:
+ E_ysq, E_yxT, E_xxT, E_n = stats
+ T = E_ysq.shape[0]
+ assert E_ysq.shape == (T,self.D_out)
+ assert E_yxT.shape == (T,self.D_out,self.D_in)
+
+ if E_xxT.shape == (T, self.D_in, self.D_in):
+ E_xxT = E_xxT[:, None, :, :]
+ else:
+ assert E_xxT.shape == (T,self.D_out,self.D_in,self.D_in)
+
+ if E_n.shape == (T,):
+ E_n = E_n[:,None]
+ else:
+ assert E_n.shape == (T,self.D_out)
+
+ E_A, E_AAT, E_sigmasq_inv, E_log_sigmasq = self.mf_expectations
+
+ sqerr = -0.5 * E_ysq
+ sqerr += 1.0 * np.sum(E_yxT * E_A, axis=2)
+ sqerr += -0.5 * np.sum(E_xxT * E_AAT, axis=(2,3))
+
+ # Compute expected log likelihood
+ ell = np.sum(sqerr * E_sigmasq_inv, axis=1)
+ ell += np.sum(-0.5 * E_n * (E_log_sigmasq + np.log(2 * np.pi)), axis=1)
+
+ return ell
+
+ def resample_from_mf(self):
+ for d in range(self.D_out):
+ self.A[d] = sample_gaussian(J=self.mf_J_A[d], h=self.mf_h_A[d])
+ self.sigmasq_flat = sample_invgamma(self.mf_alpha, self.mf_beta) * np.ones(self.D_out)
+
+ def _initialize_mean_field(self):
+ A, sigmasq = self.A, self.sigmasq_flat
+
+ # Set mean field params such that A and sigmasq are the mean
+ self.mf_alpha = self.alpha_0
+ self.mf_beta = self.alpha_0 * sigmasq
+
+ self.mf_J_A = np.array([self.J_0.copy() for _ in range(self.D_out)])
+ self.mf_h_A = np.array([Jd.dot(Ad) for Jd, Ad in zip(self.mf_J_A, A)])
+
+ ### SVI
+ def meanfield_sgdstep(self, data, weights, prob, stepsize, stats=None, mask=None):
+ assert weights is None, "Not supporting weighted datapoints (just masked data)"
+ if stats is None:
+ stats = self._get_statistics(data, mask)
+ stats = self._stats_ensure_array(stats)
+
+ self._meanfieldupdate_A(stats, prob=prob, stepsize=stepsize)
+ self._meanfieldupdate_sigma(stats, prob=prob, stepsize=stepsize)
+
+
+class RobustRegression(Regression):
+ """
+ Regression with multivariate-t distributed noise.
+
+ y | x ~ t(Ax + b, \Sigma, \nu)
+
+ where \nu >= 1 is the degrees of freedom.
+
+ This is equivalent to the model,
+
+ \tau ~ Gamma(\nu/2, \nu/2)
+ y | x, \tau ~ N(Ax + b, \Sigma / \tau)
+
+ To perform inference in this model, we will introduce
+ auxiliary variables tau (precisions). With these, we
+ can compute sufficient statistics scaled by \tau and
+ use the standard regression object to
+ update A, b, Sigma | x, y, \tau.
+
+ The degrees of freedom parameter \nu is updated via maximum
+ likelihood using a generalized Newton's method proposed by
+ Tom Minka. We are not using any prior on \nu, but we
+ could experiment with updating \nu under an
+ uninformative prior, e.g. p(\nu) \propto \nu^{-2},
+ which is equivalent to a flat prior on \nu^{-1}.
+ """
+ def __init__(
+ self, nu_0=None,S_0=None, M_0=None, K_0=None, affine=False,
+ A=None, sigma=None, nu=None):
+
+ # Default to a somewhat intermediate value of nu
+ self.nu = self.default_nu = nu if nu is not None else 4.0
+
+ super(RobustRegression, self).__init__(
+ nu_0=nu_0, S_0=S_0, M_0=M_0, K_0=K_0, affine=affine, A=A, sigma=sigma)
+
+ def log_likelihood(self,xy):
+ assert isinstance(xy, (tuple, np.ndarray))
+ sigma, D, nu = self.sigma, self.D_out, self.nu
+ x, y = (xy[:,:-D], xy[:,-D:]) if isinstance(xy,np.ndarray) else xy
+
+ sigma_inv, L = inv_psd(sigma, return_chol=True)
+ r = y - self.predict(x)
+ z = sigma_inv.dot(r.T).T
+
+ out = -0.5 * (nu + D) * np.log(1.0 + (r * z).sum(1) / nu)
+ out += gammaln((nu + D) / 2.0) - gammaln(nu / 2.0) - D / 2.0 * np.log(nu) \
+ - D / 2.0 * np.log(np.pi) - np.log(np.diag(L)).sum()
+
+ return out
+
+ def rvs(self,x=None,size=1,return_xy=True):
+ A, sigma, nu, D = self.A, self.sigma, self.nu, self.D_out
+
+ if self.affine:
+ A, b = A[:,:-1], A[:,-1]
+
+ x = np.random.normal(size=(size, A.shape[1])) if x is None else x
+ N = x.shape[0]
+ mu = self.predict(x)
+
+ # Sample precisions and t-distributed residuals
+ tau = np.random.gamma(nu / 2.0, 2.0 / nu, size=(N,))
+ resid = np.random.randn(N, D).dot(np.linalg.cholesky(sigma).T)
+ resid /= np.sqrt(tau[:, None])
+
+ y = mu + resid
+ return np.hstack((x,y)) if return_xy else y
+
+ def _get_statistics(self, data):
+ raise Exception("RobustRegression needs scaled statistics.")
+
+ def _get_scaled_statistics(self, data, precisions):
+ assert isinstance(data, (list, tuple, np.ndarray))
+ if isinstance(data,list):
+ return sum((self._get_scaled_statistics(d, p) for d, p in zip(data, precisions)),
+ self._empty_statistics())
+
+ elif isinstance(data, tuple):
+ x, y = data
+ bad = np.isnan(x).any(1) | np.isnan(y).any(1)
+ x, y = x[~bad], y[~bad]
+ precisions = precisions[~bad]
+ sqrt_prec = np.sqrt(precisions)
+ n, D = y.shape
+
+ if self.affine:
+ x = np.column_stack((x, np.ones(n)))
+
+ # Scale by the precision
+ # xs = x * sqrt_prec[:, na]
+ # ys = y * sqrt_prec[:, na]
+ xs = x * np.tile(sqrt_prec[:, None], (1, x.shape[1]))
+ ys = y * np.tile(sqrt_prec[:, None], (1, D))
+
+ xxT, yxT, yyT = xs.T.dot(xs), ys.T.dot(xs), ys.T.dot(ys)
+ return np.array([yyT, yxT, xxT, n])
+
+ else:
+ # data passed in like np.hstack((x, y))
+ # x, y = data[:,:-self.D_out], data[:,-self.D_out:]
+ # return self._get_scaled_statistics((x, y), precisions)
+ bad = np.isnan(data).any(1)
+ data = data[~bad]
+ precisions = precisions[~bad]
+ n, D = data.shape[0], self.D_out
+
+ # This tile call is suboptimal but without it we can hit issues
+ # with strided data, as in autoregressive models.
+ scaled_data = data * np.tile(precisions[:,None], (1, data.shape[1]))
+ statmat = scaled_data.T.dot(data)
+
+ xxT, yxT, yyT = \
+ statmat[:-D,:-D], statmat[-D:,:-D], statmat[-D:,-D:]
+
+ if self.affine:
+ xy = scaled_data.sum(0)
+ x, y = xy[:-D], xy[-D:]
+ xxT = blockarray([[xxT, x[:,na]],
+ [x[na,:], np.atleast_2d(precisions.sum())]])
+ yxT = np.hstack((yxT, y[:,na]))
+
+ return np.array([yyT, yxT, xxT, n])
+
+ def resample(self, data=[], stats=None):
+ assert stats is None, \
+ "We only support RobustRegression.resample() with data, not stats."
+
+ # First sample auxiliary variables for each data point
+ tau = self._resample_precision(data)
+
+ # Compute statistics, scaling by tau, and resample as in standard Regression
+ stats = self._get_scaled_statistics(data, tau)
+ super(RobustRegression, self).resample(stats=stats)
+
+ # Resample degrees of freedom \nu
+ self._resample_nu(tau)
+
+ def _resample_precision(self, data):
+ assert isinstance(data, (list, tuple, np.ndarray))
+ if isinstance(data, list):
+ return [self._resample_precision(d) for d in data]
+
+ elif isinstance(data, tuple):
+ x, y = data
+
+ else:
+ x, y = data[:, :-self.D_out], data[:, -self.D_out:]
+
+ assert x.ndim == y.ndim == 2
+ assert x.shape[0] == y.shape[0]
+ assert x.shape[1] == self.D_in - 1 if self.affine else self.D_in
+ assert y.shape[1] == self.D_out
+ N = x.shape[0]
+
+ # Weed out the nan's
+ bad = np.any(np.isnan(x), axis=1) | np.any(np.isnan(y), axis=1)
+
+ # Compute posterior params of gamma distribution
+ a_post = self.nu / 2.0 + self.D_out / 2.0
+
+ r = y - self.predict(x)
+ sigma_inv = inv_psd(self.sigma)
+ z = sigma_inv.dot(r.T).T
+ b_post = self.nu / 2.0 + (r * z).sum(1) / 2.0
+
+ assert np.isscalar(a_post) and b_post.shape == (N,)
+ tau = np.nan * np.ones(N)
+ tau[~bad] = np.random.gamma(a_post, 1./b_post[~bad])
+
+ return tau
+
+ def _resample_nu(self, tau, N_steps=100, prop_std=0.1, alpha=1, beta=1):
+ """
+ Update the degree of freedom parameter with
+ Metropolis-Hastings. Assume a prior nu ~ Ga(alpha, beta)
+ and use a proposal nu' ~ N(nu, prop_std^2). If proposals
+ are negative, reject automatically due to likelihood.
+ """
+ # Convert tau to a list of arrays
+ taus = [tau] if isinstance(tau, np.ndarray) else tau
+
+ N = 0
+ E_tau = 0
+ E_logtau = 0
+ for tau in taus:
+ bad = ~np.isfinite(tau)
+ N += np.sum(~bad)
+ E_tau += np.sum(tau[~bad])
+ E_logtau += np.sum(np.log(tau[~bad]))
+
+ if N > 0:
+ E_tau /= N
+ E_logtau /= N
+
+ # Compute the log prior, likelihood, and posterior
+ lprior = lambda nu: (alpha - 1) * np.log(nu) - alpha * nu
+ ll = lambda nu: N * (nu/2 * np.log(nu/2) - gammaln(nu/2) + (nu/2 - 1) * E_logtau - nu/2 * E_tau)
+ lp = lambda nu: ll(nu) + lprior(nu)
+
+ lp_curr = lp(self.nu)
+ for step in range(N_steps):
+ # Symmetric proposal
+ nu_new = self.nu + prop_std * np.random.randn()
+ if nu_new <1e-3:
+ # Reject if too small
+ continue
+
+ # Accept / reject based on likelihoods
+ lp_new = lp(nu_new)
+ if np.log(np.random.rand()) < lp_new - lp_curr:
+ self.nu = nu_new
+ lp_curr = lp_new
+
+ # Not supporting MLE or mean field for now
+ def max_likelihood(self,data,weights=None,stats=None):
+ raise NotImplementedError
+
+ def meanfieldupdate(self, data=None, weights=None, stats=None):
+ raise NotImplementedError
+
+ def meanfield_sgdstep(self, data, weights, prob, stepsize, stats=None):
+ raise NotImplementedError
+
+ def meanfield_expectedstats(self):
+ raise NotImplementedError
+
+ def expected_log_likelihood(self, xy=None, stats=None):
+ raise NotImplementedError
+
+ def get_vlb(self):
+ raise NotImplementedError
+
+ def resample_from_mf(self):
+ raise NotImplementedError
+
+ def _set_params_from_mf(self):
+ raise NotImplementedError
+
+ def _initialize_mean_field(self):
+ pass
+
+
+class _ARMixin(object):
+ @property
+ def nlags(self):
+ if not self.affine:
+ return self.D_in // self.D_out
+ else:
+ return (self.D_in - 1) // self.D_out
+
+ @property
+ def D(self):
+ return self.D_out
+
+ def predict(self, x):
+ return super(_ARMixin,self).predict(np.atleast_2d(x))
+
+ def rvs(self,lagged_data):
+ return super(_ARMixin,self).rvs(
+ x=np.atleast_2d(lagged_data.ravel()),return_xy=False)
+
+ def _get_statistics(self,data):
+ return super(_ARMixin,self)._get_statistics(
+ data=self._ensure_strided(data))
+
+ def _get_weighted_statistics(self,data,weights):
+ return super(_ARMixin,self)._get_weighted_statistics(
+ data=self._ensure_strided(data),weights=weights)
+
+ def log_likelihood(self,xy):
+ return super(_ARMixin,self).log_likelihood(self._ensure_strided(xy))
+
+ def _ensure_strided(self,data):
+ if isinstance(data,np.ndarray):
+ if data.shape[1] != self.D*(self.nlags+1):
+ data = AR_striding(data,self.nlags)
+ return data
+ else:
+ return [self._ensure_strided(d) for d in data]
+
+
+class AutoRegression(_ARMixin,Regression):
+ pass
+
+
+class ARDAutoRegression(_ARMixin,ARDRegression):
+ def __init__(self,M_0,**kwargs):
+ blocksizes = [M_0.shape[0]]*(M_0.shape[1] // M_0.shape[0]) \
+ + ([1] if M_0.shape[1] % M_0.shape[0] and M_0.shape[0] != 1 else [])
+ super(ARDAutoRegression,self).__init__(
+ M_0=M_0,blocksizes=blocksizes,**kwargs)
+
+
+class RobustAutoRegression(_ARMixin, RobustRegression):
+ pass
diff --git a/build/lib.linux-x86_64-cpython-37/pybasicbayes/distributions/uniform.py b/build/lib.linux-x86_64-cpython-37/pybasicbayes/distributions/uniform.py
new file mode 100644
index 0000000..9104120
--- /dev/null
+++ b/build/lib.linux-x86_64-cpython-37/pybasicbayes/distributions/uniform.py
@@ -0,0 +1,137 @@
+from __future__ import division
+from builtins import map
+from builtins import range
+__all__ = ['UniformOneSided', 'Uniform']
+
+import numpy as np
+
+from pybasicbayes.abstractions import GibbsSampling
+from pybasicbayes.util.stats import sample_pareto
+from pybasicbayes.util.general import any_none
+
+
+class UniformOneSided(GibbsSampling):
+ '''
+ Models a uniform distribution over [low,high] for a parameter high.
+ Low is a fixed hyperparameter (hence "OneSided"). See the Uniform class for
+ the two-sided version.
+
+ Likelihood is x ~ U[low,high]
+ Prior is high ~ Pareto(x_m,alpha) following Wikipedia's notation
+
+ Hyperparameters:
+ x_m, alpha, low
+
+ Parameters:
+ high
+ '''
+ def __init__(self,high=None,x_m=None,alpha=None,low=0.):
+ self.high = high
+
+ self.x_m = x_m
+ self.alpha = alpha
+ self.low = low
+
+ have_hypers = x_m is not None and alpha is not None
+ if high is None and have_hypers:
+ self.resample() # intialize from prior
+
+ @property
+ def params(self):
+ return {'high':self.high}
+
+ @property
+ def hypparams(self):
+ return dict(x_m=self.x_m,alpha=self.alpha,low=self.low)
+
+ def log_likelihood(self,x):
+ x = np.atleast_1d(x)
+ raw = np.where(
+ (self.low <= x) & (x < self.high),
+ -np.log(self.high - self.low),-np.inf)
+ return raw if isinstance(x,np.ndarray) else raw[0]
+
+ def rvs(self,size=[]):
+ return np.random.uniform(low=self.low,high=self.high,size=size)
+
+ def resample(self,data=[]):
+ self.high = sample_pareto(
+ *self._posterior_hypparams(*self._get_statistics(data)))
+ return self
+
+ def _get_statistics(self,data):
+ if isinstance(data,np.ndarray):
+ n = data.shape[0]
+ datamax = data.max()
+ else:
+ n = sum(d.shape[0] for d in data)
+ datamax = \
+ max(d.max() for d in data) if n > 0 else -np.inf
+ return n, datamax
+
+ def _posterior_hypparams(self,n,datamax):
+ return max(datamax,self.x_m), n + self.alpha
+
+
+class Uniform(UniformOneSided):
+ '''
+ Models a uniform distribution over [low,high] for parameters low and high.
+ The prior is non-conjugate (though it's conditionally conjugate over one
+ parameter at a time).
+
+ Likelihood is x ~ U[low,high]
+ Prior is -low ~ Pareto(x_m_low,alpha_low)-2*x_m_low
+ high ~ Pareto(x_m_high,alpha_high)
+
+ Hyperparameters:
+ x_m_low, alpha_low
+ x_m_high, alpha_high
+
+ Parameters:
+ low, high
+ '''
+ def __init__(
+ self,low=None,high=None,
+ x_m_low=None,alpha_low=None,x_m_high=None,alpha_high=None):
+ self.low = low
+ self.high = high
+
+ self.x_m_low = x_m_low
+ self.alpha_low = alpha_low
+ self.x_m_high = x_m_high
+ self.alpha_high = alpha_high
+
+ have_hypers = not any_none(x_m_low,alpha_low,x_m_high,alpha_high)
+ if low is high is None and have_hypers:
+ self.resample() # initialize from prior
+
+ @property
+ def params(self):
+ return dict(low=self.low,high=self.high)
+
+ @property
+ def hypparams(self):
+ return dict(
+ x_m_low=self.x_m_low,alpha_low=self.alpha_low,
+ x_m_high=self.x_m_high,alpha_high=self.alpha_high)
+
+ def resample(self,data=[],niter=5):
+ if len(data) == 0:
+ self.low = -sample_pareto(-self.x_m_low,self.alpha_low)
+ self.high = sample_pareto(self.x_m_high,self.alpha_high)
+ else:
+ for itr in range(niter):
+ # resample high, fixing low
+ self.x_m, self.alpha = self.x_m_high, self.alpha_high
+ super(Uniform,self).resample(data)
+ # tricky: flip data and resample 'high' again
+ self.x_m, self.alpha = -self.x_m_low, self.alpha_low
+ self.low, self.high = self.high, self.low
+ super(Uniform,self).resample(self._flip_data(data))
+ self.low, self.high = self.x_m_low - self.high, self.low
+
+ def _flip_data(self,data):
+ if isinstance(data,np.ndarray):
+ return self.x_m_low - data
+ else:
+ return list(map(self._flip_data,data))
diff --git a/build/lib.linux-x86_64-cpython-37/pybasicbayes/models/__init__.py b/build/lib.linux-x86_64-cpython-37/pybasicbayes/models/__init__.py
new file mode 100644
index 0000000..838c912
--- /dev/null
+++ b/build/lib.linux-x86_64-cpython-37/pybasicbayes/models/__init__.py
@@ -0,0 +1,2 @@
+from .mixture import Labels, CRPLabels, Mixture, MixtureDistribution, CollapsedMixture, CRPMixture
+from .factor_analysis import FactorAnalysis
\ No newline at end of file
diff --git a/build/lib.linux-x86_64-cpython-37/pybasicbayes/models/factor_analysis.py b/build/lib.linux-x86_64-cpython-37/pybasicbayes/models/factor_analysis.py
new file mode 100644
index 0000000..6a8eba4
--- /dev/null
+++ b/build/lib.linux-x86_64-cpython-37/pybasicbayes/models/factor_analysis.py
@@ -0,0 +1,336 @@
+"""
+Probabilistic factor analysis to perform dimensionality reduction on mouse images.
+With the probabilistic approach, we can handle missing data in the images.
+Technically this holds for missing at random data, but we can try it
+out on images where we treat cable pixels as missing, even though they
+won't be random. This should give us a model-based way to fill in pixels,
+and hopefully a more robust way to estimate principle components for modeling.
+"""
+import abc
+import numpy as np
+
+from pybasicbayes.abstractions import Model, \
+ ModelGibbsSampling, ModelMeanField, ModelMeanFieldSVI, ModelEM
+from pybasicbayes.util.stats import sample_gaussian
+from pybasicbayes.util.general import objarray
+
+from pybasicbayes.distributions import DiagonalRegression
+
+from pybasicbayes.util.profiling import line_profiled
+PROFILING = True
+
+class FactorAnalysisStates(object):
+ """
+ Wrapper for the latent states of a factor analysis model
+ """
+ def __init__(self, model, data, mask=None, **kwargs):
+ self.model = model
+ self.X = data
+ if mask is None:
+ mask = np.ones_like(data, dtype=bool)
+ self.mask = mask
+ assert data.shape == mask.shape and mask.dtype == bool
+ assert self.X.shape[1] == self.D_obs
+
+ # Initialize latent states
+ self.N = self.X.shape[0]
+ self.Z = np.random.randn(self.N, self.D_latent)
+
+ @property
+ def D_obs(self):
+ return self.model.D_obs
+
+ @property
+ def D_latent(self):
+ return self.model.D_latent
+
+ @property
+ def W(self):
+ return self.model.W
+
+ @property
+ def mean(self):
+ return self.model.mean
+
+ @property
+ def sigmasq(self):
+ return self.model.sigmasq
+
+ @property
+ def regression(self):
+ return self.model.regression
+
+ def log_likelihood(self):
+ # mu = np.dot(self.Z, self.W.T)
+ # return -0.5 * np.sum(((self.X - mu) * self.mask) ** 2 / self.sigmasq)
+
+ # Compute the marginal likelihood, integrating out z
+ mu_x = self.mean
+ Sigma_x = self.W.dot(self.W.T) + np.diag(self.sigmasq)
+
+ from scipy.stats import multivariate_normal
+ if not np.all(self.mask):
+ # Find the patterns of missing dta
+ missing_patterns = np.unique(self.mask, axis=0)
+
+ # Evaluate the likelihood for each missing pattern
+ lls = np.zeros(self.N)
+ for pat in missing_patterns:
+ inds = np.all(self.mask == pat, axis=1)
+ lls[inds] = \
+ multivariate_normal(mu_x[pat], Sigma_x[np.ix_(pat, pat)])\
+ .logpdf(self.X[np.ix_(inds, pat)])
+
+ else:
+ lls = multivariate_normal(mu_x, Sigma_x).logpdf(self.X)
+
+ return lls
+
+ ## Gibbs
+ def resample(self):
+ W, sigmasq = self.W, self.sigmasq
+ J0 = np.eye(self.D_latent)
+ h0 = np.zeros(self.D_latent)
+
+ # Sample each latent embedding
+ for n in range(self.N):
+ Jobs = self.mask[n] / sigmasq
+ Jpost = J0 + (W * Jobs[:, None]).T.dot(W)
+ hpost = h0 + ((self.X[n] - self.mean) * Jobs).dot(W)
+ self.Z[n] = sample_gaussian(J=Jpost, h=hpost)
+
+ ## Mean field
+ def E_step(self):
+ W = self.W
+ WWT = np.array([np.outer(wd,wd) for wd in W])
+ sigmasq_inv = 1./self.sigmasq
+ self._meanfieldupdate(W, WWT, sigmasq_inv)
+
+ # Copy over the expected states to Z
+ self.Z = self.E_Z
+
+ def meanfieldupdate(self):
+ E_W, E_WWT, E_sigmasq_inv, _ = self.regression.mf_expectations
+ self._meanfieldupdate(E_W, E_WWT, E_sigmasq_inv)
+
+ # Copy over the expected states to Z
+ self.Z = self.E_Z
+
+ def _meanfieldupdate(self, E_W, E_WWT, E_sigmasq_inv):
+ N, D_obs, D_lat = self.N, self.D_obs, self.D_latent
+ E_WWT_vec = E_WWT.reshape(D_obs, -1)
+
+ J0 = np.eye(D_lat)
+ h0 = np.zeros(D_lat)
+
+ # Get expectations for the latent embedding of these datapoints
+ self.E_Z = np.zeros((N, D_lat))
+ self.E_ZZT = np.zeros((N, D_lat, D_lat))
+
+ for n in range(N):
+ Jobs = self.mask[n] * E_sigmasq_inv
+ # Faster than Jpost = J0 + np.sum(E_WWT * Jobs[:,None,None], axis=0)
+ Jpost = J0 + (np.dot(Jobs, E_WWT_vec)).reshape((D_lat, D_lat))
+ hpost = h0 + ((self.X[n] - self.mean) * Jobs).dot(E_W)
+
+ # Get the expectations for this set of indices
+ Sigma_post = np.linalg.inv(Jpost)
+ self.E_Z[n] = Sigma_post.dot(hpost)
+ self.E_ZZT[n] = Sigma_post + np.outer(self.E_Z[n], self.E_Z[n])
+
+ self._set_expected_stats()
+
+ def _set_expected_stats(self):
+ D_lat = self.D_latent
+ Xc = self.X - self.mean
+ E_Xsq = np.sum(Xc**2 * self.mask, axis=0)
+ E_XZT = (Xc * self.mask).T.dot(self.E_Z)
+ E_ZZT_vec = self.E_ZZT.reshape((self.E_ZZT.shape[0], D_lat ** 2))
+ E_ZZT = np.array([np.dot(self.mask[:, d], E_ZZT_vec).reshape((D_lat, D_lat))
+ for d in range(self.D_obs)])
+ n = np.sum(self.mask, axis=0)
+
+ self.E_emission_stats = objarray([E_Xsq, E_XZT, E_ZZT, n])
+
+ def resample_from_mf(self):
+ for n in range(self.N):
+ mu_n = self.E_Z[n]
+ Sigma_n = self.E_ZZT[n] - np.outer(mu_n, mu_n)
+ self.Z[n] = sample_gaussian(mu=mu_n, Sigma=Sigma_n)
+
+ def expected_log_likelihood(self):
+ E_W, E_WWT, E_sigmasq_inv, E_log_sigmasq = self.regression.mf_expectations
+ E_Xsq, E_XZT, E_ZZT, n = self.E_emission_stats
+
+ ll = -0.5 * np.log(2 * np.pi) - 0.5 * np.sum(E_log_sigmasq * self.mask)
+ ll += -0.5 * np.sum(E_Xsq * E_sigmasq_inv)
+ ll += -0.5 * np.sum(-2 * E_XZT * E_W * E_sigmasq_inv[:,None])
+ ll += -0.5 * np.sum(E_WWT * E_ZZT * E_sigmasq_inv[:,None,None])
+ return ll
+
+
+class _FactorAnalysisBase(Model):
+ __metaclass__ = abc.ABCMeta
+ _states_class = FactorAnalysisStates
+
+ def __init__(self, D_obs, D_latent,
+ W=None, sigmasq=None,
+ sigmasq_W_0=1.0, mu_W_0=0.0,
+ alpha_0=3.0, beta_0=2.0):
+
+ self.D_obs, self.D_latent = D_obs, D_latent
+
+ # The weights and variances are encapsulated in a DiagonalRegression class
+ self.regression = \
+ DiagonalRegression(
+ self.D_obs, self.D_latent,
+ mu_0=mu_W_0 * np.ones(self.D_latent),
+ Sigma_0=sigmasq_W_0 * np.eye(self.D_latent),
+ alpha_0=alpha_0, beta_0=beta_0,
+ A=W, sigmasq=sigmasq)
+
+ # Handle the mean separately since DiagonalRegression doesn't support affine :-/
+ self.mean = np.zeros(D_obs)
+
+ self.data_list = []
+
+ @property
+ def W(self):
+ return self.regression.A
+
+ @property
+ def sigmasq(self):
+ return self.regression.sigmasq_flat
+
+ def set_empirical_mean(self):
+ self.mean = np.zeros(self.D_obs)
+ for n in range(self.D_obs):
+ self.mean[n] = np.concatenate([d.X[d.mask[:,n] == 1, n] for d in self.data_list]).mean()
+
+ def add_data(self, data, mask=None, **kwargs):
+ self.data_list.append(self._states_class(self, data, mask=mask, **kwargs))
+ return self.data_list[-1]
+
+ def generate(self, keep=True, N=1, mask=None, **kwargs):
+ # Sample from the factor analysis model
+ W, sigmasq = self.W, self.sigmasq
+ Z = np.random.randn(N, self.D_latent)
+ X = self.mean + np.dot(Z, W.T) + np.sqrt(sigmasq) * np.random.randn(N, self.D_obs)
+
+ data = self._states_class(self, X, mask=mask, **kwargs)
+ data.Z = Z
+ if keep:
+ self.data_list.append(data)
+ return data.X, data.Z
+
+ def _log_likelihoods(self, x, mask=None, **kwargs):
+ self.add_data(x, mask=mask, **kwargs)
+ states = self.data_list.pop()
+ return states.log_likelihood()
+
+ def log_likelihood(self):
+ return sum([d.log_likelihood().sum() for d in self.data_list])
+
+ def log_probability(self):
+ lp = 0
+
+ # Prior
+ # lp += (-self.alpha_0-1) * np.log(self.sigmasq) - self.beta_0 / self.sigmasq
+ lp += -0.5 * np.sum(self.W**2)
+ lp += -0.5 * np.sum(self.Z**2)
+ lp += self.log_likelihood()
+ return lp
+
+
+class _FactorAnalysisGibbs(_FactorAnalysisBase, ModelGibbsSampling):
+ __metaclass__ = abc.ABCMeta
+
+ def resample_model(self):
+ for data in self.data_list:
+ data.resample()
+
+ Zs = np.vstack([d.Z for d in self.data_list])
+ Xs = np.vstack([d.X for d in self.data_list])
+ mask = np.vstack([d.mask for d in self.data_list])
+ self.regression.resample((Zs, Xs), mask=mask)
+
+
+class _FactorAnalysisEM(_FactorAnalysisBase, ModelEM):
+
+ def _null_stats(self):
+ return objarray(
+ [np.zeros(self.D_obs),
+ np.zeros((self.D_obs, self.D_latent)),
+ np.zeros((self.D_obs, self.D_latent, self.D_latent)),
+ np.zeros(self.D_obs)])
+
+ def EM_step(self):
+ for data in self.data_list:
+ data.E_step()
+
+ stats = self._null_stats() + sum([d.E_emission_stats for d in self.data_list])
+ self.regression.max_likelihood(data=None, weights=None, stats=stats)
+ assert np.all(np.isfinite(self.sigmasq ))
+
+
+class _FactorAnalysisMeanField(_FactorAnalysisBase, ModelMeanField, ModelMeanFieldSVI):
+ __metaclass__ = abc.ABCMeta
+
+ def _null_stats(self):
+ return objarray(
+ [np.zeros(self.D_obs),
+ np.zeros((self.D_obs, self.D_latent)),
+ np.zeros((self.D_obs, self.D_latent, self.D_latent)),
+ np.zeros(self.D_obs)])
+
+ def meanfield_coordinate_descent_step(self):
+ for data in self.data_list:
+ data.meanfieldupdate()
+
+ stats = self._null_stats() + sum([d.E_emission_stats for d in self.data_list])
+ self.regression.meanfieldupdate(stats=stats)
+
+ def meanfield_sgdstep(self, minibatch, prob, stepsize, masks=None):
+ assert stepsize > 0 and stepsize <= 1
+
+ states_list = self._get_mb_states_list(minibatch, masks)
+ for s in states_list:
+ s.meanfieldupdate()
+
+ # Compute the sufficient statistics of the latent parameters
+ self.regression.meanfield_sgdstep(
+ data=None, weights=None, prob=prob, stepsize=stepsize,
+ stats=(sum(s.E_emission_stats for s in states_list)))
+
+ # Compute the expected log likelihood for this minibatch
+ return sum([s.expected_log_likelihood() for s in states_list])
+
+ def _get_mb_states_list(self, minibatch, masks):
+ minibatch = minibatch if isinstance(minibatch, list) else [minibatch]
+ masks = [None] * len(minibatch) if masks is None else \
+ (masks if isinstance(masks, list) else [masks])
+
+ def get_states(data, mask):
+ self.add_data(data, mask=mask)
+ return self.data_list.pop()
+
+ return [get_states(data, mask) for data, mask in zip(minibatch, masks)]
+
+ def resample_from_mf(self):
+ for data in self.data_list:
+ data.resample_from_mf()
+ self.regression.resample_from_mf()
+
+ def expected_log_likelihood(self):
+ ell = 0
+ for data in self.data_list:
+ ell += data.expected_log_likelihood()
+ return ell
+
+ def initialize_meanfield(self):
+ self.regression._initialize_mean_field()
+
+
+class FactorAnalysis(_FactorAnalysisGibbs, _FactorAnalysisEM, _FactorAnalysisMeanField):
+ pass
+
diff --git a/build/lib.linux-x86_64-cpython-37/pybasicbayes/models/mixture.py b/build/lib.linux-x86_64-cpython-37/pybasicbayes/models/mixture.py
new file mode 100644
index 0000000..55292c6
--- /dev/null
+++ b/build/lib.linux-x86_64-cpython-37/pybasicbayes/models/mixture.py
@@ -0,0 +1,841 @@
+from __future__ import division
+from __future__ import absolute_import
+from builtins import zip
+from builtins import range
+from builtins import object
+import numpy as np
+from functools import reduce
+from future.utils import with_metaclass
+na = np.newaxis
+import scipy.special as special
+import abc, copy
+from warnings import warn
+from scipy.special import logsumexp
+
+from pybasicbayes.abstractions import ModelGibbsSampling, ModelMeanField, ModelEM
+from pybasicbayes.abstractions import Distribution, GibbsSampling, MeanField, Collapsed, \
+ MeanFieldSVI, MaxLikelihood, ModelParallelTempering
+from pybasicbayes.distributions import Categorical, CategoricalAndConcentration
+from pybasicbayes.util.stats import getdatasize, sample_discrete_from_log, sample_discrete
+
+
+#############################
+# internal labels classes #
+#############################
+
+class Labels(object):
+ def __init__(self,model,data=None,N=None,z=None,
+ initialize_from_prior=True):
+ assert data is not None or (N is not None and z is None)
+
+ self.model = model
+
+ if data is None:
+ self._generate(N)
+ else:
+ self.data = data
+
+ if z is not None:
+ self.z = z
+ elif initialize_from_prior:
+ self._generate(len(data))
+ else:
+ self.resample()
+
+ def _generate(self,N):
+ self.z = self.weights.rvs(N)
+
+ @property
+ def N(self):
+ return len(self.z)
+
+ @property
+ def components(self):
+ return self.model.components
+
+ @property
+ def weights(self):
+ return self.model.weights
+
+ def log_likelihood(self):
+ if not hasattr(self,'_normalizer') or self._normalizer is None:
+ scores = self._compute_scores()
+ self._normalizer = logsumexp(scores[~np.isnan(self.data).any(1)],axis=1).sum()
+ return self._normalizer
+
+ def _compute_scores(self):
+ data, K = self.data, len(self.components)
+ scores = np.empty((data.shape[0],K))
+ for idx, c in enumerate(self.components):
+ scores[:,idx] = c.log_likelihood(data)
+ scores += self.weights.log_likelihood(np.arange(K))
+ scores[np.isnan(data).any(1)] = 0. # missing data
+ return scores
+
+ def clear_caches(self):
+ self._normalizer = None
+
+ ### Gibbs sampling
+
+ def resample(self):
+ scores = self._compute_scores()
+ self.z, lognorms = sample_discrete_from_log(scores,axis=1,return_lognorms=True)
+ self._normalizer = lognorms[~np.isnan(self.data).any(1)].sum()
+
+ def copy_sample(self):
+ new = copy.copy(self)
+ new.z = self.z.copy()
+ return new
+
+ ### Mean Field
+
+ def meanfieldupdate(self):
+ data, N, K = self.data, self.data.shape[0], len(self.components)
+
+ # update, see Eq. 10.67 in Bishop
+ component_scores = np.empty((N,K))
+ for idx, c in enumerate(self.components):
+ component_scores[:,idx] = c.expected_log_likelihood(data)
+ component_scores = np.nan_to_num(component_scores)
+
+ logpitilde = self.weights.expected_log_likelihood(np.arange(len(self.components)))
+ logr = logpitilde + component_scores
+
+ self.r = np.exp(logr - logr.max(1)[:,na])
+ self.r /= self.r.sum(1)[:,na]
+
+ # for plotting
+ self.z = self.r.argmax(1)
+
+ def get_vlb(self):
+ # return avg energy plus entropy, our contribution to the mean field
+ # variational lower bound
+ errs = np.seterr(invalid='ignore',divide='ignore')
+ prod = self.r*np.log(self.r)
+ prod[np.isnan(prod)] = 0. # 0 * -inf = 0.
+ np.seterr(**errs)
+
+ logpitilde = self.weights.expected_log_likelihood(np.arange(len(self.components)))
+
+ q_entropy = -prod.sum()
+ p_avgengy = (self.r*logpitilde).sum()
+
+ return p_avgengy + q_entropy
+
+ ### EM
+
+ def E_step(self):
+ data, N, K = self.data, self.data.shape[0], len(self.components)
+
+ self.expectations = np.empty((N,K))
+ for idx, c in enumerate(self.components):
+ self.expectations[:,idx] = c.log_likelihood(data)
+ self.expectations = np.nan_to_num(self.expectations)
+
+ self.expectations += self.weights.log_likelihood(np.arange(K))
+
+ self.expectations -= self.expectations.max(1)[:,na]
+ np.exp(self.expectations,out=self.expectations)
+ self.expectations /= self.expectations.sum(1)[:,na]
+
+ self.z = self.expectations.argmax(1)
+
+
+class CRPLabels(object):
+ def __init__(self,model,alpha_0,obs_distn,data=None,N=None):
+ assert (data is not None) ^ (N is not None)
+ self.alpha_0 = alpha_0
+ self.obs_distn = obs_distn
+ self.model = model
+
+ if data is None:
+ # generating
+ self._generate(N)
+ else:
+ self.data = data
+ self._generate(data.shape[0])
+ self.resample() # one resampling step
+
+ def _generate(self,N):
+ # run a CRP forwards
+ alpha_0 = self.alpha_0
+ self.z = np.zeros(N,dtype=np.int32)
+ for n in range(N):
+ self.z[n] = sample_discrete(np.concatenate((np.bincount(self.z[:n]),(alpha_0,))))
+
+ def resample(self):
+ al, o = np.log(self.alpha_0), self.obs_distn
+ self.z = ma.masked_array(self.z,mask=np.zeros(self.z.shape))
+ model = self.model
+
+ for n in np.random.permutation(self.data.shape[0]):
+ # mask out n
+ self.z.mask[n] = True
+
+ # form the scores and sample them
+ ks = list(model._get_occupied())
+ scores = np.array([
+ np.log(model._get_counts(k))+ o.log_predictive(self.data[n],model._get_data_withlabel(k)) \
+ for k in ks] + [al + o.log_marginal_likelihood(self.data[n])])
+
+ idx = sample_discrete_from_log(scores)
+ if idx == scores.shape[0]-1:
+ self.z[n] = self._new_label(ks)
+ else:
+ self.z[n] = ks[idx]
+
+ # sample
+ # note: the mask gets fixed by assigning into the array
+ self.z[n] = sample_discrete_from_log(np.array(scores))
+
+ def _new_label(self,ks):
+ # return a label that isn't already used...
+ newlabel = np.random.randint(low=0,high=5*max(ks))
+ while newlabel in ks:
+ newlabel = np.random.randint(low=0,high=5*max(ks))
+ return newlabel
+
+
+ def _get_counts(self,k):
+ return np.sum(self.z == k)
+
+ def _get_data_withlabel(self,k):
+ return self.data[self.z == k]
+
+ def _get_occupied(self):
+ if ma.is_masked(self.z):
+ return set(self.z[~self.z.mask])
+ else:
+ return set(self.z)
+
+
+###################
+# model classes #
+###################
+
+class Mixture(ModelGibbsSampling, ModelMeanField, ModelEM, ModelParallelTempering):
+ '''
+ This class is for mixtures of other distributions.
+ '''
+ _labels_class = Labels
+
+ def __init__(self,components,alpha_0=None,a_0=None,b_0=None,weights=None,weights_obj=None):
+ assert len(components) > 0
+ assert (alpha_0 is not None) ^ (a_0 is not None and b_0 is not None) \
+ ^ (weights_obj is not None)
+
+ self.components = components
+
+ if alpha_0 is not None:
+ self.weights = Categorical(alpha_0=alpha_0,K=len(components),weights=weights)
+ elif weights_obj is not None:
+ self.weights = weights_obj
+ else:
+ self.weights = CategoricalAndConcentration(
+ a_0=a_0,b_0=b_0,K=len(components),weights=weights)
+
+ self.labels_list = []
+
+ def add_data(self,data,**kwargs):
+ self.labels_list.append(self._labels_class(data=np.asarray(data),model=self,**kwargs))
+ return self.labels_list[-1]
+
+ @property
+ def N(self):
+ return len(self.components)
+
+ def generate(self,N,keep=True):
+ templabels = self._labels_class(model=self,N=N)
+
+ out = np.empty(self.components[0].rvs(N).shape)
+ counts = np.bincount(templabels.z,minlength=self.N)
+ for idx,(c,count) in enumerate(zip(self.components,counts)):
+ out[templabels.z == idx,...] = c.rvs(count)
+
+ perm = np.random.permutation(N)
+ out = out[perm]
+ templabels.z = templabels.z[perm]
+
+ if keep:
+ templabels.data = out
+ self.labels_list.append(templabels)
+
+ return out, templabels.z
+
+ def _clear_caches(self):
+ for l in self.labels_list:
+ l.clear_caches()
+
+ def _log_likelihoods(self,x):
+ # NOTE: nans propagate as nans
+ x = np.asarray(x)
+ K = len(self.components)
+ vals = np.empty((x.shape[0],K))
+ for idx, c in enumerate(self.components):
+ vals[:,idx] = c.log_likelihood(x)
+ vals += self.weights.log_likelihood(np.arange(K))
+ return logsumexp(vals,axis=1)
+
+ def log_likelihood(self,x=None):
+ if x is None:
+ return sum(l.log_likelihood() for l in self.labels_list)
+ else:
+ assert isinstance(x,(np.ndarray,list))
+ if isinstance(x,list):
+ return sum(self.log_likelihood(d) for d in x)
+ else:
+ self.add_data(x)
+ return self.labels_list.pop().log_likelihood()
+
+ ### parallel tempering
+
+ @property
+ def temperature(self):
+ return self._temperature if hasattr(self,'_temperature') else 1.
+
+ @temperature.setter
+ def temperature(self,T):
+ self._temperature = T
+
+ @property
+ def energy(self):
+ energy = 0.
+ for l in self.labels_list:
+ for label, datum in zip(l.z,l.data):
+ energy += self.components[label].energy(datum)
+ return energy
+
+ def swap_sample_with(self,other):
+ self.components, other.components = other.components, self.components
+ self.weights, other.weights = other.weights, self.weights
+
+ for l1, l2 in zip(self.labels_list,other.labels_list):
+ l1.z, l2.z = l2.z, l1.z
+
+ ### Gibbs sampling
+
+ def resample_model(self,num_procs=0,components_jobs=0):
+ self.resample_components(num_procs=components_jobs)
+ self.resample_weights()
+ self.resample_labels(num_procs=num_procs)
+
+ def resample_weights(self):
+ self.weights.resample([l.z for l in self.labels_list])
+ self._clear_caches()
+
+ def resample_components(self,num_procs=0):
+ if num_procs == 0:
+ for idx, c in enumerate(self.components):
+ c.resample(data=[l.data[l.z == idx] for l in self.labels_list])
+ else:
+ self._resample_components_joblib(num_procs)
+ self._clear_caches()
+
+ def resample_labels(self,num_procs=0):
+ if num_procs == 0:
+ for l in self.labels_list:
+ l.resample()
+ else:
+ self._resample_labels_joblib(num_procs)
+
+ def copy_sample(self):
+ new = copy.copy(self)
+ new.components = [c.copy_sample() for c in self.components]
+ new.weights = self.weights.copy_sample()
+ new.labels_list = [l.copy_sample() for l in self.labels_list]
+ for l in new.labels_list:
+ l.model = new
+ return new
+
+ def _resample_components_joblib(self,num_procs):
+ from joblib import Parallel, delayed
+ from . import parallel_mixture
+
+ parallel_mixture.model = self
+ parallel_mixture.labels_list = self.labels_list
+
+ if len(self.components) > 0:
+ params = Parallel(n_jobs=num_procs,backend='multiprocessing')\
+ (delayed(parallel_mixture._get_sampled_component_params)(idx)
+ for idx in range(len(self.components)))
+
+ for c, p in zip(self.components,params):
+ c.parameters = p
+
+ def _resample_labels_joblib(self,num_procs):
+ from joblib import Parallel, delayed
+ from . import parallel_mixture
+
+ if len(self.labels_list) > 0:
+ parallel_mixture.model = self
+
+ raw = Parallel(n_jobs=num_procs,backend='multiprocessing')\
+ (delayed(parallel_mixture._get_sampled_labels)(idx)
+ for idx in range(len(self.labels_list)))
+
+ for l, (z,normalizer) in zip(self.labels_list,raw):
+ l.z, l._normalizer = z, normalizer
+
+
+ ### Mean Field
+
+ def meanfield_coordinate_descent_step(self):
+ assert all(isinstance(c,MeanField) for c in self.components), \
+ 'Components must implement MeanField'
+ assert len(self.labels_list) > 0, 'Must have data to run MeanField'
+
+ self._meanfield_update_sweep()
+ return self._vlb()
+
+ def _meanfield_update_sweep(self):
+ # NOTE: to interleave mean field steps with Gibbs sampling steps, label
+ # updates need to come first, otherwise the sampled updates will be
+ # ignored and the model will essentially stay where it was the last time
+ # mean field updates were run
+ # TODO fix that, seed with sample from variational distribution
+ self.meanfield_update_labels()
+ self.meanfield_update_parameters()
+
+ def meanfield_update_labels(self):
+ for l in self.labels_list:
+ l.meanfieldupdate()
+
+ def meanfield_update_parameters(self):
+ self.meanfield_update_components()
+ self.meanfield_update_weights()
+
+ def meanfield_update_weights(self):
+ self.weights.meanfieldupdate(None,[l.r for l in self.labels_list])
+ self._clear_caches()
+
+ def meanfield_update_components(self):
+ for idx, c in enumerate(self.components):
+ c.meanfieldupdate([l.data for l in self.labels_list],
+ [l.r[:,idx] for l in self.labels_list])
+ self._clear_caches()
+
+ def _vlb(self):
+ vlb = 0.
+ vlb += sum(l.get_vlb() for l in self.labels_list)
+ vlb += self.weights.get_vlb()
+ vlb += sum(c.get_vlb() for c in self.components)
+ for l in self.labels_list:
+ vlb += np.sum([r.dot(c.expected_log_likelihood(l.data))
+ for c,r in zip(self.components, l.r.T)])
+
+ # add in symmetry factor (if we're actually symmetric)
+ if len(set(type(c) for c in self.components)) == 1:
+ vlb += special.gammaln(len(self.components)+1)
+
+ return vlb
+
+ ### SVI
+
+ def meanfield_sgdstep(self,minibatch,prob,stepsize,**kwargs):
+ minibatch = minibatch if isinstance(minibatch,list) else [minibatch]
+ mb_labels_list = []
+ for data in minibatch:
+ self.add_data(data,z=np.empty(data.shape[0]),**kwargs) # NOTE: dummy
+ mb_labels_list.append(self.labels_list.pop())
+
+ for l in mb_labels_list:
+ l.meanfieldupdate()
+
+ self._meanfield_sgdstep_parameters(mb_labels_list,prob,stepsize)
+
+ def _meanfield_sgdstep_parameters(self,mb_labels_list,prob,stepsize):
+ self._meanfield_sgdstep_components(mb_labels_list,prob,stepsize)
+ self._meanfield_sgdstep_weights(mb_labels_list,prob,stepsize)
+
+ def _meanfield_sgdstep_components(self,mb_labels_list,prob,stepsize):
+ for idx, c in enumerate(self.components):
+ c.meanfield_sgdstep(
+ [l.data for l in mb_labels_list],
+ [l.r[:,idx] for l in mb_labels_list],
+ prob,stepsize)
+
+ def _meanfield_sgdstep_weights(self,mb_labels_list,prob,stepsize):
+ self.weights.meanfield_sgdstep(
+ None,[l.r for l in mb_labels_list],
+ prob,stepsize)
+
+ ### EM
+
+ def EM_step(self):
+ # assert all(isinstance(c,MaxLikelihood) for c in self.components), \
+ # 'Components must implement MaxLikelihood'
+ assert len(self.labels_list) > 0, 'Must have data to run EM'
+
+ ## E step
+ for l in self.labels_list:
+ l.E_step()
+
+ ## M step
+ # component parameters
+ for idx, c in enumerate(self.components):
+ c.max_likelihood([l.data for l in self.labels_list],
+ [l.expectations[:,idx] for l in self.labels_list])
+
+ # mixture weights
+ self.weights.max_likelihood(None,
+ [l.expectations for l in self.labels_list])
+
+ @property
+ def num_parameters(self):
+ # NOTE: scikit.learn's gmm.py doesn't count the weights in the number of
+ # parameters, but I don't know why they wouldn't. Some convention?
+ return sum(c.num_parameters for c in self.components) + self.weights.num_parameters
+
+ def BIC(self,data=None):
+ '''
+ BIC on the passed data.
+ If passed data is None (default), calculates BIC on the model's assigned data.
+ '''
+ # NOTE: in principle this method computes the BIC only after finding the
+ # maximum likelihood parameters (or, of course, an EM fixed-point as an
+ # approximation!)
+ if data is None:
+ assert len(self.labels_list) > 0, \
+ "If not passing in data, the class must already have it. Use the method add_data()"
+ return -2*sum(self.log_likelihood(l.data) for l in self.labels_list) + \
+ self.num_parameters * np.log(sum(l.data.shape[0] for l in self.labels_list))
+ else:
+ return -2*self.log_likelihood(data) + self.num_parameters * np.log(data.shape[0])
+
+ def AIC(self):
+ # NOTE: in principle this method computes the AIC only after finding the
+ # maximum likelihood parameters (or, of course, an EM fixed-point as an
+ # approximation!)
+ assert len(self.labels_list) > 0, 'Must have data to get AIC'
+ return 2*self.num_parameters - 2*sum(self.log_likelihood(l.data) for l in self.labels_list)
+
+ ### Misc.
+
+ @property
+ def used_labels(self):
+ if len(self.labels_list) > 0:
+ label_usages = sum(np.bincount(l.z,minlength=self.N) for l in self.labels_list)
+ used_labels, = np.where(label_usages > 0)
+ else:
+ used_labels = np.argsort(self.weights.weights)[-1:-11:-1]
+ return used_labels
+
+ def plot(self,color=None,legend=False,alpha=None,update=False,draw=True):
+ import matplotlib.pyplot as plt
+ from matplotlib import cm
+ artists = []
+
+ ### get colors
+ cmap = cm.get_cmap()
+ if color is None:
+ label_colors = dict((idx,cmap(v))
+ for idx, v in enumerate(np.linspace(0,1,self.N,endpoint=True)))
+ else:
+ label_colors = dict((idx,color) for idx in range(self.N))
+
+ ### plot data scatter
+ for l in self.labels_list:
+ colorseq = [label_colors[label] for label in l.z]
+ if update and hasattr(l,'_data_scatter'):
+ l._data_scatter.set_offsets(l.data[:,:2])
+ l._data_scatter.set_color(colorseq)
+ else:
+ l._data_scatter = plt.scatter(l.data[:,0],l.data[:,1],c=colorseq,s=5)
+ artists.append(l._data_scatter)
+
+ ### plot parameters
+ axis = plt.axis()
+ for label, (c, w) in enumerate(zip(self.components,self.weights.weights)):
+ artists.extend(
+ c.plot(
+ color=label_colors[label],
+ label='%d' % label,
+ alpha=min(0.25,1.-(1.-w)**2)/0.25 if alpha is None else alpha,
+ update=update,draw=False))
+ plt.axis(axis)
+
+ ### add legend
+ if legend and color is None:
+ plt.legend(
+ [plt.Rectangle((0,0),1,1,fc=c)
+ for i,c in label_colors.items() if i in used_labels],
+ [i for i in label_colors if i in used_labels],
+ loc='best', ncol=2)
+
+ if draw: plt.draw()
+ return artists
+
+
+ def to_json_dict(self):
+ assert len(self.labels_list) == 1
+ data = self.labels_list[0].data
+ z = self.labels_list[0].z
+ assert data.ndim == 2 and data.shape[1] == 2
+
+ return {
+ 'points':[{'x':x,'y':y,'label':int(label)} for x,y,label in zip(data[:,0],data[:,1],z)],
+ 'ellipses':[dict(list(c.to_json_dict().items()) + [('label',i)])
+ for i,c in enumerate(self.components) if i in z]
+ }
+
+ def predictive_likelihoods(self,test_data,forecast_horizons):
+ likes = self._log_likelihoods(test_data)
+ return [likes[k:] for k in forecast_horizons]
+
+ def block_predictive_likelihoods(self,test_data,blocklens):
+ csums = np.cumsum(self._log_likelihoods(test_data))
+ outs = []
+ for k in blocklens:
+ outs.append(csums[k:] - csums[:-k])
+ return outs
+
+
+class MixtureDistribution(Mixture, GibbsSampling, MeanField, MeanFieldSVI, Distribution):
+ '''
+ This makes a Mixture act like a Distribution for use in other models
+ '''
+
+ def __init__(self,niter=1,**kwargs):
+ self.niter = niter
+ super(MixtureDistribution,self).__init__(**kwargs)
+
+ @property
+ def params(self):
+ return dict(weights=self.weights.params,components=[c.params for c in self.components])
+
+ @property
+ def hypparams(self):
+ return dict(weights=self.weights.hypparams,components=[c.hypparams for c in self.components])
+
+ def energy(self,data):
+ # TODO TODO this function is horrible
+ assert data.ndim == 1
+
+ if np.isnan(data).any():
+ return 0.
+
+ from .util.stats import sample_discrete
+ likes = np.array([c.log_likelihood(data) for c in self.components]).reshape((-1,))
+ likes += np.log(self.weights.weights)
+ label = sample_discrete(np.exp(likes - likes.max()))
+
+ return self.components[label].energy(data)
+
+ def log_likelihood(self,x):
+ return self._log_likelihoods(x)
+
+ def resample(self,data):
+ # doesn't keep a reference to the data like a model would
+ assert isinstance(data,list) or isinstance(data,np.ndarray)
+
+ if getdatasize(data) > 0:
+ if not isinstance(data,np.ndarray):
+ data = np.concatenate(data)
+
+ self.add_data(data,initialize_from_prior=False)
+
+ for itr in range(self.niter):
+ self.resample_model()
+
+ self.labels_list.pop()
+ else:
+ self.resample_model()
+
+ def max_likelihood(self,data,weights=None):
+ if weights is not None:
+ raise NotImplementedError
+ assert isinstance(data,list) or isinstance(data,np.ndarray)
+ if isinstance(data,list):
+ data = np.concatenate(data)
+
+ if getdatasize(data) > 0:
+ self.add_data(data)
+ self.EM_fit()
+ self.labels_list = []
+
+ def get_vlb(self):
+ from warnings import warn
+ warn('Pretty sure this is missing a term, VLB is wrong but updates are fine') # TODO
+ vlb = 0.
+ # vlb += self._labels_vlb # TODO this part is wrong! we need weights passed in again
+ vlb += self.weights.get_vlb()
+ vlb += sum(c.get_vlb() for c in self.components)
+ return vlb
+
+ def expected_log_likelihood(self,x):
+ lognorm = logsumexp(self.weights._alpha_mf)
+ return sum(np.exp(a - lognorm) * c.expected_log_likelihood(x)
+ for a, c in zip(self.weights._alpha_mf, self.components))
+
+ def meanfieldupdate(self,data,weights,**kwargs):
+ # NOTE: difference from parent's method is the inclusion of weights
+ if not isinstance(data,(list,tuple)):
+ data = [data]
+ weights = [weights]
+ old_labels = self.labels_list
+ self.labels_list = []
+
+ for d in data:
+ self.add_data(d,z=np.empty(d.shape[0])) # NOTE: dummy
+
+ self.meanfield_update_labels()
+ for l, w in zip(self.labels_list,weights):
+ l.r *= w[:,na] # here's where the weights are used
+ self.meanfield_update_parameters()
+
+ # self._labels_vlb = sum(l.get_vlb() for l in self.labels_list) # TODO hack
+
+ self.labels_list = old_labels
+
+ def meanfield_sgdstep(self,minibatch,weights,prob,stepsize):
+ # NOTE: difference from parent's method is the inclusion of weights
+ if not isinstance(minibatch,list):
+ minibatch = [minibatch]
+ weights = [weights]
+ mb_labels_list = []
+ for data in minibatch:
+ self.add_data(data,z=np.empty(data.shape[0])) # NOTE: dummy
+ mb_labels_list.append(self.labels_list.pop())
+
+ for l, w in zip(mb_labels_list,weights):
+ l.meanfieldupdate()
+ l.r *= w[:,na] # here's where weights are used
+
+ self._meanfield_sgdstep_parameters(mb_labels_list,prob,stepsize)
+
+ def plot(self,data=[],color='b',label='',plot_params=True,indices=None):
+ # TODO handle indices for 1D
+ if not isinstance(data,list):
+ data = [data]
+ for d in data:
+ self.add_data(d)
+
+ for l in self.labels_list:
+ l.E_step() # sets l.z to MAP estimates
+ for label, o in enumerate(self.components):
+ if label in l.z:
+ o.plot(color=color,label=label,
+ data=l.data[l.z == label] if l.data is not None else None)
+
+ for d in data:
+ self.labels_list.pop()
+
+
+class CollapsedMixture(with_metaclass(abc.ABCMeta, ModelGibbsSampling)):
+ def _get_counts(self,k):
+ return sum(l._get_counts(k) for l in self.labels_list)
+
+ def _get_data_withlabel(self,k):
+ return [l._get_data_withlabel(k) for l in self.labels_list]
+
+ def _get_occupied(self):
+ return reduce(set.union,(l._get_occupied() for l in self.labels_list),set([]))
+
+ def plot(self):
+ import matplotlib.pyplot as plt
+ from matplotlib import cm
+ plt.figure()
+ cmap = cm.get_cmap()
+ used_labels = self._get_occupied()
+ num_labels = len(used_labels)
+
+ label_colors = {}
+ for idx,label in enumerate(used_labels):
+ label_colors[label] = idx/(num_labels-1. if num_labels > 1 else 1.)
+
+ for subfigidx,l in enumerate(self.labels_list):
+ plt.subplot(len(self.labels_list),1,1+subfigidx)
+ # TODO assuming data is 2D
+ for label in used_labels:
+ if label in l.z:
+ plt.plot(l.data[l.z==label,0],l.data[l.z==label,1],
+ color=cmap(label_colors[label]),ls='None',marker='x')
+
+
+class CRPMixture(CollapsedMixture):
+ _labels_class = CRPLabels
+
+ def __init__(self,alpha_0,obs_distn):
+ assert isinstance(obs_distn,Collapsed)
+ self.obs_distn = obs_distn
+ self.alpha_0 = alpha_0
+
+ self.labels_list = []
+
+ def add_data(self,data):
+ assert len(self.labels_list) == 0
+ self.labels_list.append(self._labels_class(model=self,data=np.asarray(data),
+ alpha_0=self.alpha_0,obs_distn=self.obs_distn))
+ return self.labels_list[-1]
+
+ def resample_model(self):
+ for l in self.labels_list:
+ l.resample()
+
+ def generate(self,N,keep=True):
+ warn('not fully implemented')
+ # TODO only works if there's no other data in the model; o/w need to add
+ # existing data to obs resample. should be an easy update.
+ # templabels needs to pay attention to its own counts as well as model
+ # counts
+ assert len(self.labels_list) == 0
+
+ templabels = self._labels_class(model=self,alpha_0=self.alpha_0,obs_distn=self.obs_distn,N=N)
+
+ counts = np.bincount(templabels.z)
+ out = np.empty(self.obs_distn.rvs(N).shape)
+ for idx, count in enumerate(counts):
+ self.obs_distn.resample()
+ out[templabels.z == idx,...] = self.obs_distn.rvs(count)
+
+ perm = np.random.permutation(N)
+ out = out[perm]
+ templabels.z = templabels.z[perm]
+
+ if keep:
+ templabels.data = out
+ self.labels_list.append(templabels)
+
+ return out, templabels.z
+
+ def log_likelihood(self,x, K_extra=1):
+ """
+ Estimate the log likelihood with samples from
+ the model. Draw k_extra components which were not populated by
+ the current model in order to create a truncated approximate
+ mixture model.
+ """
+ x = np.asarray(x)
+ ks = self._get_occupied()
+ K = len(ks)
+ K_total = K + K_extra
+
+ # Sample observation distributions given current labels
+ obs_distns = []
+ for k in range(K):
+ o = copy.deepcopy(self.obs_distn)
+ o.resample(data=self._get_data_withlabel(k))
+ obs_distns.append(o)
+
+ # Sample extra observation distributions from prior
+ for k in range(K_extra):
+ o = copy.deepcopy(self.obs_distn)
+ o.resample()
+ obs_distns.append(o)
+
+ # Sample a set of weights
+ weights = Categorical(alpha_0=self.alpha_0,
+ K=K_total,
+ weights=None)
+
+ assert len(self.labels_list) == 1
+ weights.resample(data=self.labels_list[0].z)
+
+ # Now compute the log likelihood
+ vals = np.empty((x.shape[0],K_total))
+ for k in range(K_total):
+ vals[:,k] = obs_distns[k].log_likelihood(x)
+
+ vals += weights.log_likelihood(np.arange(K_total))
+ assert not np.isnan(vals).any()
+ return logsumexp(vals,axis=1).sum()
diff --git a/build/lib.linux-x86_64-cpython-37/pybasicbayes/models/parallel_mixture.py b/build/lib.linux-x86_64-cpython-37/pybasicbayes/models/parallel_mixture.py
new file mode 100644
index 0000000..8607ecd
--- /dev/null
+++ b/build/lib.linux-x86_64-cpython-37/pybasicbayes/models/parallel_mixture.py
@@ -0,0 +1,15 @@
+from __future__ import division
+import numpy as np
+
+model = None
+labels_list = None
+
+def _get_sampled_labels(idx):
+ model.add_data(model.labels_list[idx].data,initialize_from_prior=False)
+ l = model.labels_list.pop()
+ return l.z, l._normalizer
+
+def _get_sampled_component_params(idx):
+ model.components[idx].resample([l.data[l.z == idx] for l in labels_list])
+ return model.components[idx].parameters
+
diff --git a/build/lib.linux-x86_64-cpython-37/pybasicbayes/testing/__init__.py b/build/lib.linux-x86_64-cpython-37/pybasicbayes/testing/__init__.py
new file mode 100644
index 0000000..e69de29
diff --git a/build/lib.linux-x86_64-cpython-37/pybasicbayes/testing/mixins.py b/build/lib.linux-x86_64-cpython-37/pybasicbayes/testing/mixins.py
new file mode 100644
index 0000000..1f4d22c
--- /dev/null
+++ b/build/lib.linux-x86_64-cpython-37/pybasicbayes/testing/mixins.py
@@ -0,0 +1,262 @@
+from __future__ import division
+from builtins import zip
+from builtins import range
+from builtins import object
+import numpy as np
+import abc, os
+
+from nose.plugins.attrib import attr
+
+import pybasicbayes
+from pybasicbayes.util import testing
+from future.utils import with_metaclass
+
+class DistributionTester(with_metaclass(abc.ABCMeta, object)):
+ @abc.abstractproperty
+ def distribution_class(self):
+ pass
+
+ @abc.abstractproperty
+ def hyperparameter_settings(self):
+ pass
+
+class BasicTester(DistributionTester):
+ @property
+ def basic_data_size(self):
+ return 1000
+
+ def loglike_lists_tests(self):
+ for setting_idx, hypparam_dict in enumerate(self.hyperparameter_settings):
+ yield self.check_loglike_lists, setting_idx, hypparam_dict
+
+ def check_loglike_lists(self,setting_idx,hypparam_dict):
+ dist = self.distribution_class(**hypparam_dict)
+ data = dist.rvs(size=self.basic_data_size)
+
+ l1 = dist.log_likelihood(data).sum()
+ l2 = sum(dist.log_likelihood(d) for d in np.array_split(data,self.basic_data_size))
+
+ assert np.isclose(l1,l2)
+
+ def stats_lists_tests(self):
+ for setting_idx, hypparam_dict in enumerate(self.hyperparameter_settings):
+ yield self.check_stats_lists, setting_idx, hypparam_dict
+
+ def check_stats_lists(self,setting_idx,hypparam_dict):
+ dist = self.distribution_class(**hypparam_dict)
+ data = dist.rvs(size=self.basic_data_size)
+
+ if hasattr(dist,'_get_statistics'):
+ s1 = dist._get_statistics(data)
+ s2 = dist._get_statistics([d for d in np.array_split(data,self.basic_data_size)])
+
+ self._check_stats(s1,s2)
+
+ def _check_stats(self,s1,s2):
+ if isinstance(s1,np.ndarray):
+ if s1.dtype == np.object:
+ assert all(np.allclose(t1,t2) for t1, t2 in zip(s1,s2))
+ else:
+ assert np.allclose(s1,s2)
+ elif isinstance(s1,tuple):
+ assert all(np.allclose(ss1,ss2) for ss1,ss2 in zip(s1,s2))
+
+ def missing_data_tests(self):
+ for setting_idx, hypparam_dict in enumerate(self.hyperparameter_settings):
+ yield self.check_missing_data_stats, setting_idx, hypparam_dict
+
+ def check_missing_data_stats(self,setting_idx,hypparam_dict):
+ dist = self.distribution_class(**hypparam_dict)
+ data = dist.rvs(size=self.basic_data_size)
+
+ if isinstance(data,np.ndarray):
+ data[np.random.randint(2,size=data.shape[0]) == 1] = np.nan
+
+ s1 = dist._get_statistics(data)
+ s2 = dist._get_statistics(data[~np.isnan(data).any(1)])
+
+ self._check_stats(s1,s2)
+
+class BigDataGibbsTester(with_metaclass(abc.ABCMeta, DistributionTester)):
+ @abc.abstractmethod
+ def params_close(self,distn1,distn2):
+ pass
+
+ @property
+ def big_data_size(self):
+ return 20000
+
+ @property
+ def big_data_repeats_per_setting(self):
+ return 1
+
+ @property
+ def big_data_hyperparameter_settings(self):
+ return self.hyperparameter_settings
+
+ @attr('random')
+ def big_data_Gibbs_tests(self):
+ for setting_idx, hypparam_dict in enumerate(self.big_data_hyperparameter_settings):
+ for i in range(self.big_data_repeats_per_setting):
+ yield self.check_big_data_Gibbs, setting_idx, hypparam_dict
+
+ def check_big_data_Gibbs(self,setting_idx,hypparam_dict):
+ d1 = self.distribution_class(**hypparam_dict)
+ d2 = self.distribution_class(**hypparam_dict)
+
+ data = d1.rvs(size=self.big_data_size)
+ d2.resample(data)
+
+ assert self.params_close(d1,d2)
+
+class MaxLikelihoodTester(with_metaclass(abc.ABCMeta, DistributionTester)):
+ @abc.abstractmethod
+ def params_close(self,distn1,distn2):
+ pass
+
+
+ @property
+ def big_data_size(self):
+ return 20000
+
+ @property
+ def big_data_repeats_per_setting(self):
+ return 1
+
+ @property
+ def big_data_hyperparameter_settings(self):
+ return self.hyperparameter_settings
+
+
+ def maxlike_tests(self):
+ for setting_idx, hypparam_dict in enumerate(self.big_data_hyperparameter_settings):
+ for i in range(self.big_data_repeats_per_setting):
+ yield self.check_maxlike, setting_idx, hypparam_dict
+
+ def check_maxlike(self,setting_idx,hypparam_dict):
+ d1 = self.distribution_class(**hypparam_dict)
+ d2 = self.distribution_class(**hypparam_dict)
+
+ data = d1.rvs(size=self.big_data_size)
+ d2.max_likelihood(data)
+
+ assert self.params_close(d1,d2)
+
+class GewekeGibbsTester(with_metaclass(abc.ABCMeta, DistributionTester)):
+ @abc.abstractmethod
+ def geweke_statistics(self,distn,data):
+ pass
+
+
+ @property
+ def geweke_nsamples(self):
+ return 30000
+
+ @property
+ def geweke_data_size(self):
+ return 1 # NOTE: more data usually means slower mixing
+
+ @property
+ def geweke_ntrials(self):
+ return 3
+
+ @property
+ def geweke_pval(self):
+ return 0.05
+
+ @property
+ def geweke_hyperparameter_settings(self):
+ return self.hyperparameter_settings
+
+ def geweke_numerical_slice(self,distn,setting_idx):
+ return slice(None)
+
+ @property
+ def resample_kwargs(self):
+ return {}
+
+ @property
+ def geweke_resample_kwargs(self):
+ return self.resample_kwargs
+
+ @property
+ def geweke_num_statistic_fails_to_tolerate(self):
+ return 1
+
+
+ @attr('slow', 'random')
+ def geweke_tests(self):
+ for setting_idx, hypparam_dict in enumerate(self.geweke_hyperparameter_settings):
+ yield self.check_geweke, setting_idx, hypparam_dict
+
+ def geweke_figure_filepath(self,setting_idx):
+ return os.path.join(os.path.dirname(__file__),'figures',
+ self.__class__.__name__,'setting_%d.pdf' % setting_idx)
+
+ def check_geweke(self,setting_idx,hypparam_dict):
+ import os
+ from matplotlib import pyplot as plt
+ plt.ioff()
+ fig = plt.figure()
+ figpath = self.geweke_figure_filepath(setting_idx)
+ mkdir(os.path.dirname(figpath))
+
+ nsamples, data_size, ntrials = self.geweke_nsamples, \
+ self.geweke_data_size, self.geweke_ntrials
+
+ d = self.distribution_class(**hypparam_dict)
+ sample_dim = np.atleast_1d(self.geweke_statistics(d,d.rvs(size=10))).shape[0]
+
+ num_statistic_fails = 0
+ for trial in range(ntrials):
+ # collect forward-generated statistics
+ forward_statistics = np.squeeze(np.empty((nsamples,sample_dim)))
+ for i in range(nsamples):
+ d = self.distribution_class(**hypparam_dict)
+ data = d.rvs(size=data_size)
+ forward_statistics[i] = self.geweke_statistics(d,data)
+
+ # collect gibbs-generated statistics
+ gibbs_statistics = np.squeeze(np.empty((nsamples,sample_dim)))
+ d = self.distribution_class(**hypparam_dict)
+ data = d.rvs(size=data_size)
+ for i in range(nsamples):
+ d.resample(data,**self.geweke_resample_kwargs)
+ data = d.rvs(size=data_size)
+ gibbs_statistics[i] = self.geweke_statistics(d,data)
+
+ testing.populations_eq_quantile_plot(forward_statistics,gibbs_statistics,fig=fig)
+ try:
+ sl = self.geweke_numerical_slice(d,setting_idx)
+ testing.assert_populations_eq_moments(
+ forward_statistics[...,sl],gibbs_statistics[...,sl],
+ pval=self.geweke_pval)
+ except AssertionError:
+ datapath = os.path.join(os.path.dirname(__file__),'figures',
+ self.__class__.__name__,'setting_%d_trial_%d.npz' % (setting_idx,trial))
+ np.savez(datapath,fwd=forward_statistics,gibbs=gibbs_statistics)
+ example_violating_means = forward_statistics.mean(0), gibbs_statistics.mean(0)
+ num_statistic_fails += 1
+
+ plt.savefig(figpath)
+
+ assert num_statistic_fails <= self.geweke_num_statistic_fails_to_tolerate, \
+ 'Geweke MAY have failed, check FIGURES in %s (e.g. %s vs %s)' \
+ % ((os.path.dirname(figpath),) + example_violating_means)
+
+
+##########
+# misc #
+##########
+
+def mkdir(path):
+ # from
+ # http://stackoverflow.com/questions/600268/mkdir-p-functionality-in-python
+ import errno
+ try:
+ os.makedirs(path)
+ except OSError as exc:
+ if exc.errno == errno.EEXIST and os.path.isdir(path):
+ pass
+ else: raise
+
diff --git a/build/lib.linux-x86_64-cpython-37/pybasicbayes/util/__init__.py b/build/lib.linux-x86_64-cpython-37/pybasicbayes/util/__init__.py
new file mode 100644
index 0000000..ed6fb6d
--- /dev/null
+++ b/build/lib.linux-x86_64-cpython-37/pybasicbayes/util/__init__.py
@@ -0,0 +1,3 @@
+from __future__ import absolute_import
+__all__ = ['general','plot','stats','text']
+from . import general, plot, stats, text
diff --git a/build/lib.linux-x86_64-cpython-37/pybasicbayes/util/cstats.cpython-37m-x86_64-linux-gnu.so b/build/lib.linux-x86_64-cpython-37/pybasicbayes/util/cstats.cpython-37m-x86_64-linux-gnu.so
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diff --git a/build/lib.linux-x86_64-cpython-37/pybasicbayes/util/cyutil.py b/build/lib.linux-x86_64-cpython-37/pybasicbayes/util/cyutil.py
new file mode 100644
index 0000000..d17086d
--- /dev/null
+++ b/build/lib.linux-x86_64-cpython-37/pybasicbayes/util/cyutil.py
@@ -0,0 +1,112 @@
+from builtins import map
+from builtins import str
+import Cython.Build
+from Cython.Build.Dependencies import *
+
+# NOTE: mostly a copy of cython's create_extension_list except for the lines
+# surrounded by "begin matt added" / "end matt added"
+def create_extension_list(patterns, exclude=[], ctx=None, aliases=None, quiet=False, language=None,
+ exclude_failures=False):
+ if not isinstance(patterns, (list, tuple)):
+ patterns = [patterns]
+ explicit_modules = set([m.name for m in patterns if isinstance(m, Extension)])
+ seen = set()
+ deps = create_dependency_tree(ctx, quiet=quiet)
+ to_exclude = set()
+ if not isinstance(exclude, list):
+ exclude = [exclude]
+ for pattern in exclude:
+ to_exclude.update(list(map(os.path.abspath, extended_iglob(pattern))))
+
+ module_list = []
+ for pattern in patterns:
+ if isinstance(pattern, str):
+ filepattern = pattern
+ template = None
+ name = '*'
+ base = None
+ exn_type = Extension
+ ext_language = language
+ elif isinstance(pattern, Extension):
+ for filepattern in pattern.sources:
+ if os.path.splitext(filepattern)[1] in ('.py', '.pyx'):
+ break
+ else:
+ # ignore non-cython modules
+ module_list.append(pattern)
+ continue
+ template = pattern
+ name = template.name
+ base = DistutilsInfo(exn=template)
+ exn_type = template.__class__
+ ext_language = None # do not override whatever the Extension says
+ else:
+ raise TypeError(pattern)
+
+ for file in extended_iglob(filepattern):
+ if os.path.abspath(file) in to_exclude:
+ continue
+ pkg = deps.package(file)
+ if '*' in name:
+ module_name = deps.fully_qualified_name(file)
+ if module_name in explicit_modules:
+ continue
+ else:
+ module_name = name
+
+ if module_name not in seen:
+ try:
+ kwds = deps.distutils_info(file, aliases, base).values
+ except Exception:
+ if exclude_failures:
+ continue
+ raise
+ if base is not None:
+ for key, value in list(base.values.items()):
+ if key not in kwds:
+ kwds[key] = value
+
+ sources = [file]
+ if template is not None:
+ sources += [m for m in template.sources if m != filepattern]
+ if 'sources' in kwds:
+ # allow users to add .c files etc.
+ for source in kwds['sources']:
+ source = encode_filename_in_py2(source)
+ if source not in sources:
+ sources.append(source)
+ del kwds['sources']
+ if 'depends' in kwds:
+ depends = resolve_depends(kwds['depends'], (kwds.get('include_dirs') or []) + [find_root_package_dir(file)])
+ if template is not None:
+ # Always include everything from the template.
+ depends = list(set(template.depends).union(set(depends)))
+ kwds['depends'] = depends
+
+ if ext_language and 'language' not in kwds:
+ kwds['language'] = ext_language
+
+ # NOTE: begin matt added
+ if 'name' in kwds:
+ module_name = str(kwds['name'])
+ del kwds['name']
+ else:
+ module_name = os.path.splitext(file)[0].replace('/','.')
+ # NOTE: end matt added
+ module_list.append(exn_type(
+ name=module_name,
+ sources=sources,
+ **kwds))
+ m = module_list[-1]
+ seen.add(name)
+ return module_list
+
+true_cythonize = Cython.Build.cythonize
+true_create_extension_list = Cython.Build.Dependencies.create_extension_list
+
+def cythonize(*args,**kwargs):
+ Cython.Build.Dependencies.create_extension_list = create_extension_list
+ out = true_cythonize(*args,**kwargs)
+ Cython.Build.Dependencies.create_extension_list = true_create_extension_list
+ return out
+
diff --git a/build/lib.linux-x86_64-cpython-37/pybasicbayes/util/general.py b/build/lib.linux-x86_64-cpython-37/pybasicbayes/util/general.py
new file mode 100644
index 0000000..4a7c8ef
--- /dev/null
+++ b/build/lib.linux-x86_64-cpython-37/pybasicbayes/util/general.py
@@ -0,0 +1,328 @@
+from __future__ import division
+from future import standard_library
+standard_library.install_aliases()
+from builtins import next
+from builtins import zip
+from builtins import range
+import sys
+import numpy as np
+from numpy.lib.stride_tricks import as_strided as ast
+import scipy.linalg
+import scipy.linalg.lapack as lapack
+import copy, collections, os, shutil, hashlib
+from contextlib import closing
+from itertools import chain, count
+from functools import reduce
+from urllib.request import urlopen # py2.7 covered by standard_library.install_aliases()
+
+
+def blockarray(*args,**kwargs):
+ return np.array(np.bmat(*args,**kwargs),copy=False)
+
+def interleave(*iterables):
+ return list(chain.from_iterable(zip(*iterables)))
+
+def joindicts(dicts):
+ # stuff on right clobbers stuff on left
+ return reduce(lambda x,y: dict(x,**y), dicts, {})
+
+def one_vs_all(stuff):
+ stuffset = set(stuff)
+ for thing in stuff:
+ yield thing, stuffset - set([thing])
+
+def rle(stateseq):
+ pos, = np.where(np.diff(stateseq) != 0)
+ pos = np.concatenate(([0],pos+1,[len(stateseq)]))
+ return stateseq[pos[:-1]], np.diff(pos)
+
+def irle(vals,lens):
+ out = np.empty(np.sum(lens))
+ for v,l,start in zip(vals,lens,np.concatenate(((0,),np.cumsum(lens)[:-1]))):
+ out[start:start+l] = v
+ return out
+
+def ibincount(counts):
+ 'returns an array a such that counts = np.bincount(a)'
+ return np.repeat(np.arange(counts.shape[0]),counts)
+
+def cumsum(v,strict=False):
+ if not strict:
+ return np.cumsum(v,axis=0)
+ else:
+ out = np.zeros_like(v)
+ out[1:] = np.cumsum(v[:-1],axis=0)
+ return out
+
+def rcumsum(v,strict=False):
+ if not strict:
+ return np.cumsum(v[::-1],axis=0)[::-1]
+ else:
+ out = np.zeros_like(v)
+ out[:-1] = np.cumsum(v[-1:0:-1],axis=0)[::-1]
+ return out
+
+def delta_like(v,i):
+ out = np.zeros_like(v)
+ out[i] = 1
+ return out
+
+def deepcopy(obj):
+ return copy.deepcopy(obj)
+
+def nice_indices(arr):
+ '''
+ takes an array like [1,1,5,5,5,999,1,1]
+ and maps to something like [0,0,1,1,1,2,0,0]
+ modifies original in place as well as returns a ref
+ '''
+ # surprisingly, this is slower for very small (and very large) inputs:
+ # u,f,i = np.unique(arr,return_index=True,return_inverse=True)
+ # arr[:] = np.arange(u.shape[0])[np.argsort(f)][i]
+ ids = collections.defaultdict(count().__next__)
+ for idx,x in enumerate(arr):
+ arr[idx] = ids[x]
+ return arr
+
+def ndargmax(arr):
+ return np.unravel_index(np.argmax(np.ravel(arr)),arr.shape)
+
+def match_by_overlap(a,b):
+ assert a.ndim == b.ndim == 1 and a.shape[0] == b.shape[0]
+ ais, bjs = list(set(a)), list(set(b))
+ scores = np.zeros((len(ais),len(bjs)))
+ for i,ai in enumerate(ais):
+ for j,bj in enumerate(bjs):
+ scores[i,j] = np.dot(np.array(a==ai,dtype=np.float),b==bj)
+
+ flip = len(bjs) > len(ais)
+
+ if flip:
+ ais, bjs = bjs, ais
+ scores = scores.T
+
+ matching = []
+ while scores.size > 0:
+ i,j = ndargmax(scores)
+ matching.append((ais[i],bjs[j]))
+ scores = np.delete(np.delete(scores,i,0),j,1)
+ ais = np.delete(ais,i)
+ bjs = np.delete(bjs,j)
+
+ return matching if not flip else [(x,y) for y,x in matching]
+
+def hamming_error(a,b):
+ return (a!=b).sum()
+
+def scoreatpercentile(data,per,axis=0):
+ 'like the function in scipy.stats but with an axis argument and works on arrays'
+ a = np.sort(data,axis=axis)
+ idx = per/100. * (data.shape[axis]-1)
+
+ if (idx % 1 == 0):
+ return a[[slice(None) if ii != axis else idx for ii in range(a.ndim)]]
+ else:
+ lowerweight = 1-(idx % 1)
+ upperweight = (idx % 1)
+ idx = int(np.floor(idx))
+ return lowerweight * a[[slice(None) if ii != axis else idx for ii in range(a.ndim)]] \
+ + upperweight * a[[slice(None) if ii != axis else idx+1 for ii in range(a.ndim)]]
+
+def stateseq_hamming_error(sampledstates,truestates):
+ sampledstates = np.array(sampledstates,ndmin=2).copy()
+
+ errors = np.zeros(sampledstates.shape[0])
+ for idx,s in enumerate(sampledstates):
+ # match labels by maximum overlap
+ matching = match_by_overlap(s,truestates)
+ s2 = s.copy()
+ for i,j in matching:
+ s2[s==i] = j
+ errors[idx] = hamming_error(s2,truestates)
+
+ return errors if errors.shape[0] > 1 else errors[0]
+
+def _sieve(stream):
+ # just for fun; doesn't work over a few hundred
+ val = next(stream)
+ yield val
+ for x in [x for x in _sieve(stream) if x % val != 0]:
+ yield x
+
+def primes():
+ return _sieve(count(2))
+
+def top_eigenvector(A,niter=1000,force_iteration=False):
+ '''
+ assuming the LEFT invariant subspace of A corresponding to the LEFT
+ eigenvalue of largest modulus has geometric multiplicity of 1 (trivial
+ Jordan block), returns the vector at the intersection of that eigenspace and
+ the simplex
+
+ A should probably be a ROW-stochastic matrix
+
+ probably uses power iteration
+ '''
+ n = A.shape[0]
+ np.seterr(invalid='raise',divide='raise')
+ if n <= 25 and not force_iteration:
+ x = np.repeat(1./n,n)
+ x = np.linalg.matrix_power(A.T,niter).dot(x)
+ x /= x.sum()
+ return x
+ else:
+ x1 = np.repeat(1./n,n)
+ x2 = x1.copy()
+ for itr in range(niter):
+ np.dot(A.T,x1,out=x2)
+ x2 /= x2.sum()
+ x1,x2 = x2,x1
+ if np.linalg.norm(x1-x2) < 1e-8:
+ break
+ return x1
+
+def engine_global_namespace(f):
+ # see IPython.parallel.util.interactive; it's copied here so as to avoid
+ # extra imports/dependences elsewhere, and to provide a slightly clearer
+ # name
+ f.__module__ = '__main__'
+ return f
+
+def block_view(a,block_shape):
+ shape = (a.shape[0]/block_shape[0],a.shape[1]/block_shape[1]) + block_shape
+ strides = (a.strides[0]*block_shape[0],a.strides[1]*block_shape[1]) + a.strides
+ return ast(a,shape=shape,strides=strides)
+
+def AR_striding(data,nlags):
+ data = np.asarray(data)
+ if not data.flags.c_contiguous:
+ data = data.copy(order='C')
+ if data.ndim == 1:
+ data = np.reshape(data,(-1,1))
+ sz = data.dtype.itemsize
+ return ast(
+ data,
+ shape=(data.shape[0]-nlags,data.shape[1]*(nlags+1)),
+ strides=(data.shape[1]*sz,sz))
+
+def count_transitions(stateseq,minlength=None):
+ if minlength is None:
+ minlength = stateseq.max() + 1
+ out = np.zeros((minlength,minlength),dtype=np.int32)
+ for a,b in zip(stateseq[:-1],stateseq[1:]):
+ out[a,b] += 1
+ return out
+
+### SGD
+
+def sgd_steps(tau,kappa):
+ assert 0.5 < kappa <= 1 and tau >= 0
+ for t in count(1):
+ yield (t+tau)**(-kappa)
+
+def hold_out(datalist,frac):
+ N = len(datalist)
+ perm = np.random.permutation(N)
+ split = int(np.ceil(frac * N))
+ return [datalist[i] for i in perm[split:]], [datalist[i] for i in perm[:split]]
+
+def sgd_passes(tau,kappa,datalist,minibatchsize=1,npasses=1):
+ N = len(datalist)
+
+ for superitr in range(npasses):
+ if minibatchsize == 1:
+ perm = np.random.permutation(N)
+ for idx, rho_t in zip(perm,sgd_steps(tau,kappa)):
+ yield datalist[idx], rho_t
+ else:
+ minibatch_indices = np.array_split(np.random.permutation(N),N/minibatchsize)
+ for indices, rho_t in zip(minibatch_indices,sgd_steps(tau,kappa)):
+ yield [datalist[idx] for idx in indices], rho_t
+
+def sgd_sampling(tau,kappa,datalist,minibatchsize=1):
+ N = len(datalist)
+ if minibatchsize == 1:
+ for rho_t in sgd_steps(tau,kappa):
+ minibatch_index = np.random.choice(N)
+ yield datalist[minibatch_index], rho_t
+ else:
+ for rho_t in sgd_steps(tau,kappa):
+ minibatch_indices = np.random.choice(N,size=minibatchsize,replace=False)
+ yield [datalist[idx] for idx in minibatch_indices], rho_t
+
+# TODO should probably eliminate this function
+def minibatchsize(lst):
+ return float(sum(d.shape[0] for d in lst))
+
+### misc
+
+def random_subset(lst,sz):
+ perm = np.random.permutation(len(lst))
+ return [lst[perm[idx]] for idx in range(sz)]
+
+def get_file(remote_url,local_path):
+ if not os.path.isfile(local_path):
+ with closing(urlopen(remote_url)) as remotefile:
+ with open(local_path,'wb') as localfile:
+ shutil.copyfileobj(remotefile,localfile)
+
+def list_split(lst,num):
+ assert num > 0
+ return [lst[start::num] for start in range(num)]
+
+def ndarrayhash(v):
+ assert isinstance(v,np.ndarray)
+ return hashlib.sha1(v).hexdigest()
+
+### numerical linear algebra
+
+def inv_psd(A, return_chol=False):
+ L = np.linalg.cholesky(A)
+ Ainv = lapack.dpotri(L, lower=True)[0]
+ copy_lower_to_upper(Ainv)
+ # if not np.allclose(Ainv, np.linalg.inv(A), rtol=1e-5, atol=1e-5):
+ # import ipdb; ipdb.set_trace()
+ if return_chol:
+ return Ainv, L
+ else:
+ return Ainv
+
+def solve_psd(A,b,chol=None,lower=True,overwrite_b=False,overwrite_A=False):
+ if chol is None:
+ return lapack.dposv(A,b,overwrite_b=overwrite_b,overwrite_a=overwrite_A)[1]
+ else:
+ return lapack.dpotrs(chol,b,lower,overwrite_b)[0]
+
+def copy_lower_to_upper(A):
+ A += np.tril(A,k=-1).T
+
+
+# NOTE: existing numpy object array construction acts a bit weird, e.g.
+# np.array([randn(3,4),randn(3,5)]) vs np.array([randn(3,4),randn(5,3)])
+# this wrapper class is just meant to ensure that when ndarrays of objects are
+# constructed the construction doesn't "recurse" as in the first example
+class ObjArray(np.ndarray):
+ def __new__(cls,lst):
+ if isinstance(lst,(np.ndarray,float,int)):
+ return lst
+ else:
+ return np.ndarray.__new__(cls,len(lst),dtype=np.object)
+
+ def __init__(self,lst):
+ if not isinstance(lst,(np.ndarray,float,int)):
+ for i, elt in enumerate(lst):
+ self[i] = self.__class__(elt)
+
+# Here's an alternative to ObjArray: just construct an obj array from a list
+def objarray(lst):
+ a = np.empty(len(lst), dtype=object)
+ for i,o in enumerate(lst):
+ a[i] = o
+ return a
+
+def all_none(*args):
+ return all(_ is None for _ in args)
+
+def any_none(*args):
+ return any(_ is None for _ in args)
+
diff --git a/build/lib.linux-x86_64-cpython-37/pybasicbayes/util/plot.py b/build/lib.linux-x86_64-cpython-37/pybasicbayes/util/plot.py
new file mode 100644
index 0000000..1bb6e77
--- /dev/null
+++ b/build/lib.linux-x86_64-cpython-37/pybasicbayes/util/plot.py
@@ -0,0 +1,68 @@
+from __future__ import division
+from builtins import range
+import numpy as np
+from matplotlib import pyplot as plt
+
+def plot_gaussian_2D(mu, lmbda, color='b', centermarker=True,label='',alpha=1.,ax=None,artists=None):
+ '''
+ Plots mean and cov ellipsoid into current axes. Must be 2D. lmbda is a covariance matrix.
+ '''
+ assert len(mu) == 2
+ ax = ax if ax else plt.gca()
+
+ # TODO if update alpha=0. and our previous alpha is 0., we don't need to
+ # dirty the artist
+
+ t = np.hstack([np.arange(0,2*np.pi,0.01),0])
+ circle = np.vstack([np.sin(t),np.cos(t)])
+ ellipse = np.dot(np.linalg.cholesky(lmbda),circle)
+
+ if artists is None:
+ point = ax.scatter([mu[0]],[mu[1]],marker='D',color=color,s=4,alpha=alpha) \
+ if centermarker else None
+ line, = ax.plot(ellipse[0,:] + mu[0], ellipse[1,:] + mu[1],linestyle='-',
+ linewidth=2,color=color,label=label,alpha=alpha)
+ else:
+ line, point = artists
+ if centermarker:
+ point.set_offsets(np.atleast_2d(mu))
+ point.set_alpha(alpha)
+ point.set_color(color)
+ line.set_xdata(ellipse[0,:] + mu[0])
+ line.set_ydata(ellipse[1,:] + mu[1])
+ line.set_alpha(alpha)
+ line.set_color(color)
+
+ return (line, point) if point else (line,)
+
+
+def plot_gaussian_projection(mu, lmbda, vecs, **kwargs):
+ '''
+ Plots a ndim gaussian projected onto 2D vecs, where vecs is a matrix whose two columns
+ are the subset of some orthonomral basis (e.g. from PCA on samples).
+ '''
+ return plot_gaussian_2D(project_data(mu,vecs),project_ellipsoid(lmbda,vecs),**kwargs)
+
+
+def pca_project_data(data,num_components=2):
+ # convenience combination of the next two functions
+ return project_data(data,pca(data,num_components=num_components))
+
+
+def pca(data,num_components=2):
+ U,s,Vh = np.linalg.svd(data - np.mean(data,axis=0))
+ return Vh.T[:,:num_components]
+
+
+def project_data(data,vecs):
+ return np.dot(data,vecs.T)
+
+
+def project_ellipsoid(ellipsoid,vecs):
+ # vecs is a matrix whose columns are a subset of an orthonormal basis
+ # ellipsoid is a pos def matrix
+ return np.dot(vecs,np.dot(ellipsoid,vecs.T))
+
+
+def subplot_gridsize(num):
+ return sorted(min([(x,int(np.ceil(num/x))) for x in range(1,int(np.floor(np.sqrt(num)))+1)],key=sum))
diff --git a/build/lib.linux-x86_64-cpython-37/pybasicbayes/util/profiling.py b/build/lib.linux-x86_64-cpython-37/pybasicbayes/util/profiling.py
new file mode 100644
index 0000000..6666b17
--- /dev/null
+++ b/build/lib.linux-x86_64-cpython-37/pybasicbayes/util/profiling.py
@@ -0,0 +1,53 @@
+from __future__ import division
+from __future__ import print_function
+from future import standard_library
+standard_library.install_aliases()
+import numpy as np
+import sys, io, inspect, os, functools, time, collections
+
+### use @timed for really basic timing
+
+_timings = collections.defaultdict(list)
+
+def timed(func):
+ @functools.wraps(func)
+ def wrapped(*args,**kwargs):
+ tic = time.time()
+ out = func(*args,**kwargs)
+ _timings[func].append(time.time() - tic)
+ return out
+ return wrapped
+
+def show_timings(stream=None):
+ if stream is None:
+ stream = sys.stdout
+ if len(_timings) > 0:
+ results = [(inspect.getsourcefile(f),f.__name__,
+ len(vals),np.sum(vals),np.mean(vals),np.std(vals))
+ for f, vals in _timings.items()]
+ filename_lens = max(len(filename) for filename, _, _, _, _, _ in results)
+ name_lens = max(len(name) for _, name, _, _, _, _ in results)
+
+ fmt = '{:>%d} {:>%d} {:>10} {:>10} {:>10} {:>10}' % (filename_lens, name_lens)
+ print(fmt.format('file','name','ncalls','tottime','avg time','std dev'), file=stream)
+
+ fmt = '{:>%d} {:>%d} {:>10} {:>10.3} {:>10.3} {:>10.3}' % (filename_lens, name_lens)
+ print('\n'.join(fmt.format(*tup) for tup in sorted(results)), file=stream)
+
+### use @line_profiled for a thin wrapper around line_profiler
+
+try:
+ import line_profiler
+ _prof = line_profiler.LineProfiler()
+
+ def line_profiled(func):
+ mod = inspect.getmodule(func)
+ if 'PROFILING' in os.environ or (hasattr(mod,'PROFILING') and mod.PROFILING):
+ return _prof(func)
+ return func
+
+ def show_line_stats(stream=None):
+ _prof.print_stats(stream=stream)
+except ImportError:
+ line_profiled = lambda x: x
+
diff --git a/build/lib.linux-x86_64-cpython-37/pybasicbayes/util/stats.py b/build/lib.linux-x86_64-cpython-37/pybasicbayes/util/stats.py
new file mode 100644
index 0000000..7a133d4
--- /dev/null
+++ b/build/lib.linux-x86_64-cpython-37/pybasicbayes/util/stats.py
@@ -0,0 +1,365 @@
+from __future__ import division
+from __future__ import absolute_import
+from builtins import range
+import numpy as np
+from numpy.random import random
+na = np.newaxis
+import scipy.stats as stats
+import scipy.special as special
+import scipy.linalg
+from scipy.special import logsumexp
+from numpy.core.umath_tests import inner1d
+
+from .general import any_none, blockarray
+
+### data abstraction
+
+# the data type is ndarrays OR lists of ndarrays
+# type Data = ndarray | [ndarray]
+
+def atleast_2d(data):
+ # NOTE: can't use np.atleast_2d because if it's 1D we want axis 1 to be the
+ # singleton and axis 0 to be the sequence index
+ if data.ndim == 1:
+ return data.reshape((-1,1))
+ return data
+
+def mask_data(data):
+ return np.ma.masked_array(
+ np.nan_to_num(data),np.isnan(data),fill_value=0.,hard_mask=True)
+
+def gi(data):
+ out = (np.isnan(atleast_2d(data)).sum(1) == 0).ravel()
+ return out if len(out) != 0 else None
+
+def getdatasize(data):
+ if isinstance(data,np.ma.masked_array):
+ return data.shape[0] - data.mask.reshape((data.shape[0],-1))[:,0].sum()
+ elif isinstance(data,np.ndarray):
+ if len(data) == 0:
+ return 0
+ return data[gi(data)].shape[0]
+ elif isinstance(data,list):
+ return sum(getdatasize(d) for d in data)
+ else:
+ # handle unboxed case for convenience
+ assert isinstance(data,int) or isinstance(data,float)
+ return 1
+
+def getdatadimension(data):
+ if isinstance(data,np.ndarray):
+ assert data.ndim > 1
+ return data.shape[1]
+ elif isinstance(data,list):
+ assert len(data) > 0
+ return getdatadimension(data[0])
+ else:
+ # handle unboxed case for convenience
+ assert isinstance(data,int) or isinstance(data,float)
+ return 1
+
+def combinedata(datas):
+ ret = []
+ for data in datas:
+ if isinstance(data,np.ma.masked_array):
+ ret.append(np.ma.compress_rows(data))
+ if isinstance(data,np.ndarray):
+ ret.append(data)
+ elif isinstance(data,list):
+ ret.extend(combinedata(data))
+ else:
+ # handle unboxed case for convenience
+ assert isinstance(data,int) or isinstance(data,float)
+ ret.append(np.atleast_1d(data))
+ return ret
+
+def flattendata(data):
+ # data is either an array (possibly a maskedarray) or a list of arrays
+ if isinstance(data,np.ndarray):
+ return data
+ elif isinstance(data,list) or isinstance(data,tuple):
+ if any(isinstance(d,np.ma.MaskedArray) for d in data):
+ return np.concatenate([np.ma.compress_rows(d) for d in data])
+ else:
+ return np.concatenate(data)
+ else:
+ # handle unboxed case for convenience
+ assert isinstance(data,int) or isinstance(data,float)
+ return np.atleast_1d(data)
+
+### misc
+def update_param(oldv, newv, stepsize):
+ return oldv * (1 - stepsize) + newv * stepsize
+
+
+def cov(a):
+ # return np.cov(a,rowvar=0,bias=1)
+ mu = a.mean(0)
+ if isinstance(a,np.ma.MaskedArray):
+ return np.ma.dot(a.T,a)/a.count(0)[0] - np.ma.outer(mu,mu)
+ else:
+ return a.T.dot(a)/a.shape[0] - np.outer(mu,mu)
+
+def normal_cdf(x, mu=0.0, sigma=1.0):
+ z = (x - mu) / sigma
+ return 0.5 * special.erfc(-z / np.sqrt(2))
+
+
+### Sampling functions
+
+def sample_gaussian(mu=None,Sigma=None,J=None,h=None):
+ mean_params = mu is not None and Sigma is not None
+ info_params = J is not None and h is not None
+ assert mean_params or info_params
+
+ if not any_none(mu,Sigma):
+ return np.random.multivariate_normal(mu,Sigma)
+ else:
+ from scipy.linalg.lapack import dpotrs
+ L = np.linalg.cholesky(J)
+ x = np.random.randn(h.shape[0])
+ return scipy.linalg.solve_triangular(L,x,lower=True,trans='T') \
+ + dpotrs(L,h,lower=True)[0]
+
+def sample_truncated_gaussian(mu=0, sigma=1, lb=-np.Inf, ub=np.Inf):
+ """
+ Sample a truncated normal with the specified params. This
+ is not the most stable way but it works as long as the
+ truncation region is not too far from the mean.
+ """
+ # Broadcast arrays to be of the same shape
+ mu, sigma, lb, ub = np.broadcast_arrays(mu, sigma, lb, ub)
+ shp = mu.shape
+ if np.allclose(sigma, 0.0):
+ return mu
+
+ cdflb = normal_cdf(lb, mu, sigma)
+ cdfub = normal_cdf(ub, mu, sigma)
+
+ # Sample uniformly from the CDF
+ cdfsamples = cdflb + np.random.rand(*shp) * (cdfub-cdflb)
+
+ # Clip the CDF samples so that we can invert them
+ cdfsamples = np.clip(cdfsamples, 1e-15, 1-1e-15)
+ zs = -np.sqrt(2) * special.erfcinv(2 * cdfsamples)
+
+ # Transform the standard normal samples
+ xs = sigma * zs + mu
+ xs = np.clip(xs, lb, ub)
+
+ return xs
+
+def sample_discrete(distn,size=[],dtype=np.int32):
+ 'samples from a one-dimensional finite pmf'
+ distn = np.atleast_1d(distn)
+ assert (distn >=0).all() and distn.ndim == 1
+ if (0 == distn).all():
+ return np.random.randint(distn.shape[0],size=size)
+ cumvals = np.cumsum(distn)
+ return np.sum(np.array(random(size))[...,na] * cumvals[-1] > cumvals, axis=-1,dtype=dtype)
+
+def sample_discrete_from_log(p_log,return_lognorms=False,axis=0,dtype=np.int32):
+ 'samples log probability array along specified axis'
+ lognorms = logsumexp(p_log,axis=axis)
+ cumvals = np.exp(p_log - np.expand_dims(lognorms,axis)).cumsum(axis)
+ thesize = np.array(p_log.shape)
+ thesize[axis] = 1
+ randvals = random(size=thesize) * \
+ np.reshape(cumvals[[slice(None) if i is not axis else -1
+ for i in range(p_log.ndim)]],thesize)
+ samples = np.sum(randvals > cumvals,axis=axis,dtype=dtype)
+ if return_lognorms:
+ return samples, lognorms
+ else:
+ return samples
+
+def sample_markov(T,trans_matrix,init_state_distn):
+ out = np.empty(T,dtype=np.int32)
+ out[0] = sample_discrete(init_state_distn)
+ for t in range(1,T):
+ out[t] = sample_discrete(trans_matrix[out[t-1]])
+ return out
+
+def sample_invgamma(alpha, beta):
+ return 1./np.random.gamma(alpha, 1./beta)
+
+def niw_expectedstats(nu, S, m, kappa):
+ D = m.shape[0]
+
+ # TODO speed this up with cholesky of S
+ E_J = nu * np.linalg.inv(S)
+ E_h = nu * np.linalg.solve(S,m)
+ E_muJmuT = D/kappa + m.dot(E_h)
+ E_logdetSigmainv = special.digamma((nu-np.arange(D))/2.).sum() \
+ + D*np.log(2.) - np.linalg.slogdet(S)[1]
+
+ return E_J, E_h, E_muJmuT, E_logdetSigmainv
+
+
+def sample_niw(mu,lmbda,kappa,nu):
+ '''
+ Returns a sample from the normal/inverse-wishart distribution, conjugate
+ prior for (simultaneously) unknown mean and unknown covariance in a
+ Gaussian likelihood model. Returns covariance.
+ '''
+ # code is based on Matlab's method
+ # reference: p. 87 in Gelman's Bayesian Data Analysis
+ assert nu > lmbda.shape[0] and kappa > 0
+
+ # first sample Sigma ~ IW(lmbda,nu)
+ lmbda = sample_invwishart(lmbda,nu)
+ # then sample mu | Lambda ~ N(mu, Lambda/kappa)
+ mu = np.random.multivariate_normal(mu,lmbda / kappa)
+
+ return mu, lmbda
+
+def sample_invwishart(S,nu):
+ # TODO make a version that returns the cholesky
+ # TODO allow passing in chol/cholinv of matrix parameter lmbda
+ # TODO lowmem! memoize! dchud (eigen?)
+ n = S.shape[0]
+ chol = np.linalg.cholesky(S)
+
+ if (nu <= 81+n) and (nu == np.round(nu)):
+ x = np.random.randn(int(nu),n)
+ else:
+ x = np.diag(np.sqrt(np.atleast_1d(stats.chi2.rvs(nu-np.arange(n)))))
+ x[np.triu_indices_from(x,1)] = np.random.randn(n*(n-1)//2)
+ R = np.linalg.qr(x,'r')
+ T = scipy.linalg.solve_triangular(R.T,chol.T,lower=True).T
+ return np.dot(T,T.T)
+
+def sample_wishart(sigma, nu):
+ n = sigma.shape[0]
+ chol = np.linalg.cholesky(sigma)
+
+ # use matlab's heuristic for choosing between the two different sampling schemes
+ if (nu <= 81+n) and (nu == round(nu)):
+ # direct
+ X = np.dot(chol,np.random.normal(size=(n,nu)))
+ else:
+ A = np.diag(np.sqrt(np.random.chisquare(nu - np.arange(n))))
+ A[np.tri(n,k=-1,dtype=bool)] = np.random.normal(size=(n*(n-1)/2.))
+ X = np.dot(chol,A)
+
+ return np.dot(X,X.T)
+
+def sample_mn(M, U=None, Uinv=None, V=None, Vinv=None):
+ assert (U is None) ^ (Uinv is None)
+ assert (V is None) ^ (Vinv is None)
+
+ G = np.random.normal(size=M.shape)
+
+ if U is not None:
+ G = np.dot(np.linalg.cholesky(U),G)
+ else:
+ G = np.linalg.solve(np.linalg.cholesky(Uinv).T,G)
+
+ if V is not None:
+ G = np.dot(G,np.linalg.cholesky(V).T)
+ else:
+ G = np.linalg.solve(np.linalg.cholesky(Vinv).T,G.T).T
+
+ return M + G
+
+def sample_mniw(nu, S, M, K=None, Kinv=None):
+ assert (K is None) ^ (Kinv is None)
+ Sigma = sample_invwishart(S,nu)
+ if K is not None:
+ return sample_mn(M=M,U=Sigma,V=K), Sigma
+ else:
+ return sample_mn(M=M,U=Sigma,Vinv=Kinv), Sigma
+
+def mniw_expectedstats(nu, S, M, K=None, Kinv=None):
+ # NOTE: could speed this up with chol factorizing S, not re-solving
+ assert (K is None) ^ (Kinv is None)
+ m = M.shape[0]
+ K = K if K is not None else np.linalg.inv(Kinv)
+
+ E_Sigmainv = nu*np.linalg.inv(S)
+ E_Sigmainv_A = nu*np.linalg.solve(S,M)
+ E_AT_Sigmainv_A = m*K + nu*M.T.dot(np.linalg.solve(S,M))
+ E_logdetSigmainv = special.digamma((nu-np.arange(m))/2.).sum() \
+ + m*np.log(2) - np.linalg.slogdet(S)[1]
+
+ return E_Sigmainv, E_Sigmainv_A, E_AT_Sigmainv_A, E_logdetSigmainv
+
+def mniw_log_partitionfunction(nu, S, M, K):
+ n = M.shape[0]
+ return n*nu/2*np.log(2) + special.multigammaln(nu/2., n) \
+ - nu/2*np.linalg.slogdet(S)[1] - n/2*np.linalg.slogdet(K)[1]
+
+def sample_pareto(x_m,alpha):
+ return x_m + np.random.pareto(alpha)
+
+def sample_crp_tablecounts(concentration,customers,colweights):
+ m = np.zeros_like(customers)
+ tot = customers.sum()
+ randseq = np.random.random(tot)
+
+ starts = np.empty_like(customers)
+ starts[0,0] = 0
+ starts.flat[1:] = np.cumsum(np.ravel(customers)[:customers.size-1])
+
+ for (i,j), n in np.ndenumerate(customers):
+ w = colweights[j]
+ for k in range(n):
+ m[i,j] += randseq[starts[i,j]+k] \
+ < (concentration * w) / (k + concentration * w)
+
+ return m
+
+### Entropy
+def invwishart_entropy(sigma,nu,chol=None):
+ D = sigma.shape[0]
+ chol = np.linalg.cholesky(sigma) if chol is None else chol
+ Elogdetlmbda = special.digamma((nu-np.arange(D))/2).sum() + D*np.log(2) - 2*np.log(chol.diagonal()).sum()
+ return invwishart_log_partitionfunction(sigma,nu,chol)-(nu-D-1)/2*Elogdetlmbda + nu*D/2
+
+def invwishart_log_partitionfunction(sigma,nu,chol=None):
+ # In Bishop B.79 notation, this is -log B(W, nu), where W = sigma^{-1}
+ D = sigma.shape[0]
+ chol = np.linalg.cholesky(sigma) if chol is None else chol
+ return -1*(nu*np.log(chol.diagonal()).sum() - (nu*D/2*np.log(2) + D*(D-1)/4*np.log(np.pi) \
+ + special.gammaln((nu-np.arange(D))/2).sum()))
+
+### Predictive
+
+def multivariate_t_loglik(y,nu,mu,lmbda):
+ # returns the log value
+ d = len(mu)
+ yc = np.array(y-mu,ndmin=2)
+ L = np.linalg.cholesky(lmbda)
+ ys = scipy.linalg.solve_triangular(L,yc.T,overwrite_b=True,lower=True)
+ return scipy.special.gammaln((nu+d)/2.) - scipy.special.gammaln(nu/2.) \
+ - (d/2.)*np.log(nu*np.pi) - np.log(L.diagonal()).sum() \
+ - (nu+d)/2.*np.log1p(1./nu*inner1d(ys.T,ys.T))
+
+def beta_predictive(priorcounts,newcounts):
+ prior_nsuc, prior_nfail = priorcounts
+ nsuc, nfail = newcounts
+
+ numer = scipy.special.gammaln(np.array([nsuc+prior_nsuc,
+ nfail+prior_nfail, prior_nsuc+prior_nfail])).sum()
+ denom = scipy.special.gammaln(np.array([prior_nsuc, prior_nfail,
+ prior_nsuc+prior_nfail+nsuc+nfail])).sum()
+ return numer - denom
+
+### Statistical tests
+
+def two_sample_t_statistic(pop1, pop2):
+ pop1, pop2 = (flattendata(p) for p in (pop1, pop2))
+ t = (pop1.mean(0) - pop2.mean(0)) / np.sqrt(pop1.var(0)/pop1.shape[0] + pop2.var(0)/pop2.shape[0])
+ p = 2*stats.t.sf(np.abs(t),np.minimum(pop1.shape[0],pop2.shape[0]))
+ return t,p
+
+def f_statistic(pop1, pop2): # TODO test
+ pop1, pop2 = (flattendata(p) for p in (pop1, pop2))
+ var1, var2 = pop1.var(0), pop2.var(0)
+ n1, n2 = np.where(var1 >= var2, pop1.shape[0], pop2.shape[0]), \
+ np.where(var1 >= var2, pop2.shape[0], pop1.shape[0])
+ var1, var2 = np.maximum(var1,var2), np.minimum(var1,var2)
+ f = var1 / var2
+ p = stats.f.sf(f,n1,n2)
+ return f,p
+
diff --git a/build/lib.linux-x86_64-cpython-37/pybasicbayes/util/testing.py b/build/lib.linux-x86_64-cpython-37/pybasicbayes/util/testing.py
new file mode 100644
index 0000000..73f7725
--- /dev/null
+++ b/build/lib.linux-x86_64-cpython-37/pybasicbayes/util/testing.py
@@ -0,0 +1,99 @@
+from __future__ import division
+from __future__ import absolute_import
+from builtins import zip
+import numpy as np
+from numpy import newaxis as na
+
+from . import stats, general
+
+#########################
+# statistical testing #
+#########################
+
+### graphical
+
+def populations_eq_quantile_plot(pop1, pop2, fig=None, percentilecutoff=5):
+ import matplotlib.pyplot as plt
+
+ pop1, pop2 = stats.flattendata(pop1), stats.flattendata(pop2)
+ assert pop1.ndim == pop2.ndim == 1 or \
+ (pop1.ndim == pop2.ndim == 2 and pop1.shape[1] == pop2.shape[1]), \
+ 'populations must have consistent dimensions'
+ D = pop1.shape[1] if pop1.ndim == 2 else 1
+
+ # we want to have the same number of samples
+ n1, n2 = pop1.shape[0], pop2.shape[0]
+ if n1 != n2:
+ # subsample, since interpolation is dangerous
+ if n1 < n2:
+ pop1, pop2 = pop2, pop1
+ np.random.shuffle(pop1)
+ pop1 = pop1[:pop2.shape[0]]
+
+ def plot_1d_scaled_quantiles(p1,p2,plot_midline=True):
+
+ # scaled quantiles so that multiple calls line up
+ p1.sort(), p2.sort() # NOTE: destructive! but that's cool
+ xmin,xmax = general.scoreatpercentile(p1,percentilecutoff), \
+ general.scoreatpercentile(p1,100-percentilecutoff)
+ ymin,ymax = general.scoreatpercentile(p2,percentilecutoff), \
+ general.scoreatpercentile(p2,100-percentilecutoff)
+ plt.plot((p1-xmin)/(xmax-xmin),(p2-ymin)/(ymax-ymin))
+
+ if plot_midline:
+ plt.plot((0,1),(0,1),'k--')
+ plt.axis((0,1,0,1))
+
+ if D == 1:
+ if fig is None:
+ plt.figure()
+ plot_1d_scaled_quantiles(pop1,pop2)
+ else:
+ if fig is None:
+ fig = plt.figure()
+
+ if not hasattr(fig,'_quantile_test_projs'):
+ firsttime = True
+ randprojs = np.random.randn(D,D)
+ randprojs /= np.sqrt(np.sum(randprojs**2,axis=1))[:,na]
+ projs = np.vstack((np.eye(D),randprojs))
+ fig._quantile_test_projs = projs
+ else:
+ firsttime = False
+ projs = fig._quantile_test_projs
+
+ ims1, ims2 = pop1.dot(projs.T), pop2.dot(projs.T)
+ for i, (im1, im2) in enumerate(zip(ims1.T,ims2.T)):
+ plt.subplot(2,D,i+1)
+ plot_1d_scaled_quantiles(im1,im2,plot_midline=firsttime)
+
+### numerical
+
+# NOTE: a random numerical test should be repeated at the OUTERMOST loop (with
+# exception catching) to see if its failures exceed the number expected
+# according to the specified pvalue (tests could be repeated via sample
+# bootstrapping inside the test, but that doesn't work reliably and random tests
+# should have no problem generating new randomness!)
+
+def assert_populations_eq(pop1, pop2):
+ assert_populations_eq_moments(pop1,pop2) and \
+ assert_populations_eq_komolgorofsmirnov(pop1,pop2)
+
+def assert_populations_eq_moments(pop1, pop2, **kwargs):
+ # just first two moments implemented; others are hard to estimate anyway!
+ assert_populations_eq_means(pop1,pop2,**kwargs) and \
+ assert_populations_eq_variances(pop1,pop2,**kwargs)
+
+def assert_populations_eq_means(pop1, pop2, pval=0.05, msg=None):
+ _,p = stats.two_sample_t_statistic(pop1,pop2)
+ if np.any(p < pval):
+ raise AssertionError(msg or "population means might be different at %0.3f" % pval)
+
+def assert_populations_eq_variances(pop1, pop2, pval=0.05, msg=None):
+ _,p = stats.f_statistic(pop1, pop2)
+ if np.any(p < pval):
+ raise AssertionError(msg or "population variances might be different at %0.3f" % pval)
+
+def assert_populations_eq_komolgorofsmirnov(pop1, pop2, msg=None):
+ raise NotImplementedError # TODO
+
diff --git a/build/lib.linux-x86_64-cpython-37/pybasicbayes/util/text.py b/build/lib.linux-x86_64-cpython-37/pybasicbayes/util/text.py
new file mode 100644
index 0000000..dcddd4a
--- /dev/null
+++ b/build/lib.linux-x86_64-cpython-37/pybasicbayes/util/text.py
@@ -0,0 +1,59 @@
+from __future__ import print_function
+from builtins import range
+import numpy as np
+import sys, time
+
+# time.clock() is cpu time of current process
+# time.time() is wall time
+
+# TODO there are probably better progress bar libraries I could use
+
+round = (lambda x: lambda y: int(x(y)))(round)
+
+# NOTE: datetime.timedelta.__str__ doesn't allow formatting the number of digits
+def sec2str(seconds):
+ hours, rem = divmod(seconds,3600)
+ minutes, seconds = divmod(rem,60)
+ if hours > 0:
+ return '%02d:%02d:%02d' % (hours,minutes,round(seconds))
+ elif minutes > 0:
+ return '%02d:%02d' % (minutes,round(seconds))
+ else:
+ return '%0.2f' % seconds
+
+def progprint_xrange(*args,**kwargs):
+ xr = range(*args)
+ return progprint(xr,total=len(xr),**kwargs)
+
+def progprint(iterator,total=None,perline=25,show_times=True):
+ times = []
+ idx = 0
+ if total is not None:
+ numdigits = len('%d' % total)
+ for thing in iterator:
+ prev_time = time.time()
+ yield thing
+ times.append(time.time() - prev_time)
+ sys.stdout.write('.')
+ if (idx+1) % perline == 0:
+ if show_times:
+ avgtime = np.mean(times)
+ if total is not None:
+ eta = sec2str(avgtime*(total-(idx+1)))
+ sys.stdout.write((
+ ' [ %%%dd/%%%dd, %%7.2fsec avg, ETA %%s ]\n'
+ % (numdigits,numdigits)) % (idx+1,total,avgtime,eta))
+ else:
+ sys.stdout.write(' [ %d done, %7.2fsec avg ]\n' % (idx+1,avgtime))
+ else:
+ if total is not None:
+ sys.stdout.write((' [ %%%dd/%%%dd ]\n' % (numdigits,numdigits) ) % (idx+1,total))
+ else:
+ sys.stdout.write(' [ %d ]\n' % (idx+1))
+ idx += 1
+ sys.stdout.flush()
+ print('')
+ if show_times and len(times) > 0:
+ total = sec2str(seconds=np.sum(times))
+ print('%7.2fsec avg, %s total\n' % (np.mean(times),total))
+
diff --git a/build/temp.linux-x86_64-cpython-37/pybasicbayes/util/cstats.o b/build/temp.linux-x86_64-cpython-37/pybasicbayes/util/cstats.o
new file mode 100644
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diff --git a/pybasicbayes.egg-info/PKG-INFO b/pybasicbayes.egg-info/PKG-INFO
new file mode 100644
index 0000000..ca4f4de
--- /dev/null
+++ b/pybasicbayes.egg-info/PKG-INFO
@@ -0,0 +1,12 @@
+Metadata-Version: 2.1
+Name: pybasicbayes
+Version: 0.2.4
+Summary: Basic utilities for Bayesian inference
+Home-page: http://github.com/mattjj/pybasicbayes
+Author: Matthew James Johnson
+Author-email: mattjj@csail.mit.edu
+Keywords: bayesian,inference,mcmc,variational inference,mean field,vb
+Platform: ALL
+Classifier: Intended Audience :: Science/Research
+Classifier: Programming Language :: Python
+License-File: LICENSE-MIT
diff --git a/pybasicbayes.egg-info/SOURCES.txt b/pybasicbayes.egg-info/SOURCES.txt
new file mode 100644
index 0000000..5d6133d
--- /dev/null
+++ b/pybasicbayes.egg-info/SOURCES.txt
@@ -0,0 +1,40 @@
+LICENSE-MIT
+MANIFEST.in
+README.md
+setup.py
+pybasicbayes/__init__.py
+pybasicbayes/abstractions.py
+pybasicbayes.egg-info/PKG-INFO
+pybasicbayes.egg-info/SOURCES.txt
+pybasicbayes.egg-info/dependency_links.txt
+pybasicbayes.egg-info/requires.txt
+pybasicbayes.egg-info/top_level.txt
+pybasicbayes/distributions/__init__.py
+pybasicbayes/distributions/binomial.py
+pybasicbayes/distributions/dynamic_glm.py
+pybasicbayes/distributions/dynamic_multinomial.py
+pybasicbayes/distributions/dynamic_multinomial_in_progress.py
+pybasicbayes/distributions/gaussian.py
+pybasicbayes/distributions/geometric.py
+pybasicbayes/distributions/meta.py
+pybasicbayes/distributions/multinomial.py
+pybasicbayes/distributions/negativebinomial.py
+pybasicbayes/distributions/poisson.py
+pybasicbayes/distributions/regression.py
+pybasicbayes/distributions/uniform.py
+pybasicbayes/models/__init__.py
+pybasicbayes/models/factor_analysis.py
+pybasicbayes/models/mixture.py
+pybasicbayes/models/parallel_mixture.py
+pybasicbayes/testing/__init__.py
+pybasicbayes/testing/mixins.py
+pybasicbayes/util/__init__.py
+pybasicbayes/util/cstats.c
+pybasicbayes/util/cstats.pyx
+pybasicbayes/util/cyutil.py
+pybasicbayes/util/general.py
+pybasicbayes/util/plot.py
+pybasicbayes/util/profiling.py
+pybasicbayes/util/stats.py
+pybasicbayes/util/testing.py
+pybasicbayes/util/text.py
\ No newline at end of file
diff --git a/pybasicbayes.egg-info/dependency_links.txt b/pybasicbayes.egg-info/dependency_links.txt
new file mode 100644
index 0000000..8b13789
--- /dev/null
+++ b/pybasicbayes.egg-info/dependency_links.txt
@@ -0,0 +1 @@
+
diff --git a/pybasicbayes.egg-info/requires.txt b/pybasicbayes.egg-info/requires.txt
new file mode 100644
index 0000000..282c018
--- /dev/null
+++ b/pybasicbayes.egg-info/requires.txt
@@ -0,0 +1,5 @@
+numpy
+scipy
+matplotlib
+nose
+future
diff --git a/pybasicbayes.egg-info/top_level.txt b/pybasicbayes.egg-info/top_level.txt
new file mode 100644
index 0000000..c3d0605
--- /dev/null
+++ b/pybasicbayes.egg-info/top_level.txt
@@ -0,0 +1 @@
+pybasicbayes
diff --git a/pybasicbayes/distributions/multinomial.py b/pybasicbayes/distributions/multinomial.py
index 477675b..f779c84 100644
--- a/pybasicbayes/distributions/multinomial.py
+++ b/pybasicbayes/distributions/multinomial.py
@@ -111,12 +111,12 @@ class Categorical(GibbsSampling, MeanField, MeanFieldSVI, MaxLikelihood, MAP):
self.weights = np.random.dirichlet(self.alphav_0 + counts)
except ZeroDivisionError as e:
# print("ZeroDivisionError {}".format(e))
- self.weights = np.random.dirichlet(self.alphav_0 + 0.01 + counts)
+ self.weights = np.random.dirichlet(self.alphav_0 + 0.03 + counts)
except ValueError as e:
# print("ValueError {}".format(e))
- self.weights = np.random.dirichlet(self.alphav_0 + 0.01 + counts)
+ self.weights = np.random.dirichlet(self.alphav_0 + 0.03 + counts)
if np.isnan(self.weights).any():
- self.weights = np.random.dirichlet(self.alphav_0 + 0.01 + counts)
+ self.weights = np.random.dirichlet(self.alphav_0 + 0.03 + counts)
np.clip(self.weights, np.spacing(1.), np.inf, out=self.weights)
# NOTE: next line is so we can use Gibbs sampling to initialize mean field
self._alpha_mf = self.weights * self.alphav_0.sum()
--
GitLab