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# Hidden Markov Models
#
# Author: Ron Weiss <ronweiss@gmail.com>
#         Shiqiao Du <lucidfrontier.45@gmail.com>
# API changes: Jaques Grobler <jaquesgrobler@gmail.com>
# Modifications to create of the HMMLearn module: Gael Varoquaux
# More API changes: Sergei Lebedev <superbobry@gmail.com>"""
The :mod:`hmmlearn.hmm` module implements hidden Markov models.
"""import numpy as np
from scipy.special import logsumexp
from sklearn import cluster
from sklearn.utils import check_random_statefrom . import _utils
from .stats import log_multivariate_normal_density
from .base import _BaseHMM
from .utils import iter_from_X_lengths, normalize, fill_covars__all__ = ["GMMHMM", "GaussianHMM", "MultinomialHMM"]COVARIANCE_TYPES = frozenset(("spherical", "diag", "full", "tied"))class GaussianHMM(_BaseHMM):r"""Hidden Markov Model with Gaussian emissions.Parameters----------n_components : intNumber of states.covariance_type : string, optionalString describing the type of covariance parameters touse.  Must be one of* "spherical" --- each state uses a single variance value thatapplies to all features.* "diag" --- each state uses a diagonal covariance matrix.* "full" --- each state uses a full (i.e. unrestricted)covariance matrix.* "tied" --- all states use **the same** full covariance matrix.Defaults to "diag".min_covar : float, optionalFloor on the diagonal of the covariance matrix to preventoverfitting. Defaults to 1e-3.startprob_prior : array, shape (n_components, ), optionalParameters of the Dirichlet prior distribution for:attr:`startprob_`.transmat_prior : array, shape (n_components, n_components), optionalParameters of the Dirichlet prior distribution for each rowof the transition probabilities :attr:`transmat_`.means_prior, means_weight : array, shape (n_components, ), optionalMean and precision of the Normal prior distribtion for:attr:`means_`.covars_prior, covars_weight : array, shape (n_components, ), optionalParameters of the prior distribution for the covariance matrix:attr:`covars_`.If :attr:`covariance_type` is "spherical" or "diag" the prior isthe inverse gamma distribution, otherwise --- the inverse Wishartdistribution.algorithm : string, optionalDecoder algorithm. Must be one of "viterbi" or`"map".Defaults to "viterbi".random_state: RandomState or an int seed, optionalA random number generator instance.n_iter : int, optionalMaximum number of iterations to perform.tol : float, optionalConvergence threshold. EM will stop if the gain in log-likelihoodis below this value.verbose : bool, optionalWhen ``True`` per-iteration convergence reports are printedto :data:`sys.stderr`. You can diagnose convergence via the:attr:`monitor_` attribute.params : string, optionalControls which parameters are updated in the trainingprocess.  Can contain any combination of 's' for startprob,'t' for transmat, 'm' for means and 'c' for covars. Defaultsto all parameters.init_params : string, optionalControls which parameters are initialized prior totraining.  Can contain any combination of 's' forstartprob, 't' for transmat, 'm' for means and 'c' for covars.Defaults to all parameters.Attributes----------n_features : intDimensionality of the Gaussian emissions.monitor\_ : ConvergenceMonitorMonitor object used to check the convergence of EM.transmat\_ : array, shape (n_components, n_components)Matrix of transition probabilities between states.startprob\_ : array, shape (n_components, )Initial state occupation distribution.means\_ : array, shape (n_components, n_features)Mean parameters for each state.covars\_ : arrayCovariance parameters for each state.The shape depends on :attr:`covariance_type`::(n_components, )                        if "spherical",(n_features, n_features)                if "tied",(n_components, n_features)              if "diag",(n_components, n_features, n_features)  if "full"Examples-------->>> from hmmlearn.hmm import GaussianHMM>>> GaussianHMM(n_components=2)...                             #doctest: +ELLIPSIS +NORMALIZE_WHITESPACEGaussianHMM(algorithm='viterbi',..."""def __init__(self, n_components=1, covariance_type='diag',min_covar=1e-3,startprob_prior=1.0, transmat_prior=1.0,means_prior=0, means_weight=0,covars_prior=1e-2, covars_weight=1,algorithm="viterbi", random_state=None,n_iter=10, tol=1e-2, verbose=False,params="stmc", init_params="stmc"):_BaseHMM.__init__(self, n_components,startprob_prior=startprob_prior,transmat_prior=transmat_prior, algorithm=algorithm,random_state=random_state, n_iter=n_iter,tol=tol, params=params, verbose=verbose,init_params=init_params)self.covariance_type = covariance_typeself.min_covar = min_covarself.means_prior = means_priorself.means_weight = means_weightself.covars_prior = covars_priorself.covars_weight = covars_weight@propertydef covars_(self):"""Return covars as a full matrix."""return fill_covars(self._covars_, self.covariance_type,self.n_components, self.n_features)@covars_.setterdef covars_(self, covars):self._covars_ = np.asarray(covars).copy()def _check(self):super(GaussianHMM, self)._check()self.means_ = np.asarray(self.means_)self.n_features = self.means_.shape[1]if self.covariance_type not in COVARIANCE_TYPES:raise ValueError('covariance_type must be one of {0}'.format(COVARIANCE_TYPES))_utils._validate_covars(self._covars_, self.covariance_type,self.n_components)def _init(self, X, lengths=None):super(GaussianHMM, self)._init(X, lengths=lengths)_, n_features = X.shapeif hasattr(self, 'n_features') and self.n_features != n_features:raise ValueError('Unexpected number of dimensions, got %s but ''expected %s' % (n_features, self.n_features))self.n_features = n_featuresif 'm' in self.init_params or not hasattr(self, "means_"):kmeans = cluster.KMeans(n_clusters=self.n_components,random_state=self.random_state)kmeans.fit(X)self.means_ = kmeans.cluster_centers_if 'c' in self.init_params or not hasattr(self, "covars_"):cv = np.cov(X.T) + self.min_covar * np.eye(X.shape[1])if not cv.shape:cv.shape = (1, 1)self._covars_ = \_utils.distribute_covar_matrix_to_match_covariance_type(cv, self.covariance_type, self.n_components).copy()def _compute_log_likelihood(self, X):return log_multivariate_normal_density(X, self.means_, self._covars_, self.covariance_type)def _generate_sample_from_state(self, state, random_state=None):random_state = check_random_state(random_state)return random_state.multivariate_normal(self.means_[state], self.covars_[state])def _initialize_sufficient_statistics(self):stats = super(GaussianHMM, self)._initialize_sufficient_statistics()stats['post'] = np.zeros(self.n_components)stats['obs'] = np.zeros((self.n_components, self.n_features))stats['obs**2'] = np.zeros((self.n_components, self.n_features))if self.covariance_type in ('tied', 'full'):stats['obs*obs.T'] = np.zeros((self.n_components, self.n_features,self.n_features))return statsdef _accumulate_sufficient_statistics(self, stats, obs, framelogprob,posteriors, fwdlattice, bwdlattice):super(GaussianHMM, self)._accumulate_sufficient_statistics(stats, obs, framelogprob, posteriors, fwdlattice, bwdlattice)if 'm' in self.params or 'c' in self.params:stats['post'] += posteriors.sum(axis=0)stats['obs'] += np.dot(posteriors.T, obs)if 'c' in self.params:if self.covariance_type in ('spherical', 'diag'):stats['obs**2'] += np.dot(posteriors.T, obs ** 2)elif self.covariance_type in ('tied', 'full'):# posteriors: (nt, nc); obs: (nt, nf); obs: (nt, nf)# -> (nc, nf, nf)stats['obs*obs.T'] += np.einsum('ij,ik,il->jkl', posteriors, obs, obs)def _do_mstep(self, stats):super(GaussianHMM, self)._do_mstep(stats)means_prior = self.means_priormeans_weight = self.means_weight# TODO: find a proper reference for estimates for different#       covariance models.# Based on Huang, Acero, Hon, "Spoken Language Processing",# p. 443 - 445denom = stats['post'][:, np.newaxis]if 'm' in self.params:self.means_ = ((means_weight * means_prior + stats['obs'])/ (means_weight + denom))if 'c' in self.params:covars_prior = self.covars_priorcovars_weight = self.covars_weightmeandiff = self.means_ - means_priorif self.covariance_type in ('spherical', 'diag'):cv_num = (means_weight * meandiff**2+ stats['obs**2']- 2 * self.means_ * stats['obs']+ self.means_**2 * denom)cv_den = max(covars_weight - 1, 0) + denomself._covars_ = \(covars_prior + cv_num) / np.maximum(cv_den, 1e-5)if self.covariance_type == 'spherical':self._covars_ = np.tile(self._covars_.mean(1)[:, np.newaxis],(1, self._covars_.shape[1]))elif self.covariance_type in ('tied', 'full'):cv_num = np.empty((self.n_components, self.n_features,self.n_features))for c in range(self.n_components):obsmean = np.outer(stats['obs'][c], self.means_[c])cv_num[c] = (means_weight * np.outer(meandiff[c],meandiff[c])+ stats['obs*obs.T'][c]- obsmean - obsmean.T+ np.outer(self.means_[c], self.means_[c])* stats['post'][c])cvweight = max(covars_weight - self.n_features, 0)if self.covariance_type == 'tied':self._covars_ = ((covars_prior + cv_num.sum(axis=0)) /(cvweight + stats['post'].sum()))elif self.covariance_type == 'full':self._covars_ = ((covars_prior + cv_num) /(cvweight + stats['post'][:, None, None]))class MultinomialHMM(_BaseHMM):r"""Hidden Markov Model with multinomial (discrete) emissionsParameters----------n_components : intNumber of states.startprob_prior : array, shape (n_components, ), optionalParameters of the Dirichlet prior distribution for:attr:`startprob_`.transmat_prior : array, shape (n_components, n_components), optionalParameters of the Dirichlet prior distribution for each rowof the transition probabilities :attr:`transmat_`.algorithm : string, optionalDecoder algorithm. Must be one of "viterbi" or "map".Defaults to "viterbi".random_state: RandomState or an int seed, optionalA random number generator instance.n_iter : int, optionalMaximum number of iterations to perform.tol : float, optionalConvergence threshold. EM will stop if the gain in log-likelihoodis below this value.verbose : bool, optionalWhen ``True`` per-iteration convergence reports are printedto :data:`sys.stderr`. You can diagnose convergence via the:attr:`monitor_` attribute.params : string, optionalControls which parameters are updated in the trainingprocess.  Can contain any combination of 's' for startprob,'t' for transmat, 'e' for emissionprob.Defaults to all parameters.init_params : string, optionalControls which parameters are initialized prior totraining.  Can contain any combination of 's' forstartprob, 't' for transmat, 'e' for emissionprob.Defaults to all parameters.Attributes----------n_features : intNumber of possible symbols emitted by the model (in the samples).monitor\_ : ConvergenceMonitorMonitor object used to check the convergence of EM.transmat\_ : array, shape (n_components, n_components)Matrix of transition probabilities between states.startprob\_ : array, shape (n_components, )Initial state occupation distribution.emissionprob\_ : array, shape (n_components, n_features)Probability of emitting a given symbol when in each state.Examples-------->>> from hmmlearn.hmm import MultinomialHMM>>> MultinomialHMM(n_components=2)...                             #doctest: +ELLIPSIS +NORMALIZE_WHITESPACEMultinomialHMM(algorithm='viterbi',..."""# TODO: accept the prior on emissionprob_ for consistency.def __init__(self, n_components=1,startprob_prior=1.0, transmat_prior=1.0,algorithm="viterbi", random_state=None,n_iter=10, tol=1e-2, verbose=False,params="ste", init_params="ste"):_BaseHMM.__init__(self, n_components,startprob_prior=startprob_prior,transmat_prior=transmat_prior,algorithm=algorithm,random_state=random_state,n_iter=n_iter, tol=tol, verbose=verbose,params=params, init_params=init_params)def _init(self, X, lengths=None):if not self._check_input_symbols(X):raise ValueError("expected a sample from ""a Multinomial distribution.")super(MultinomialHMM, self)._init(X, lengths=lengths)self.random_state = check_random_state(self.random_state)if 'e' in self.init_params:if not hasattr(self, "n_features"):symbols = set()for i, j in iter_from_X_lengths(X, lengths):symbols |= set(X[i:j].flatten())self.n_features = len(symbols)self.emissionprob_ = self.random_state \.rand(self.n_components, self.n_features)normalize(self.emissionprob_, axis=1)def _check(self):super(MultinomialHMM, self)._check()self.emissionprob_ = np.atleast_2d(self.emissionprob_)n_features = getattr(self, "n_features", self.emissionprob_.shape[1])if self.emissionprob_.shape != (self.n_components, n_features):raise ValueError("emissionprob_ must have shape (n_components, n_features)")else:self.n_features = n_featuresdef _compute_log_likelihood(self, X):return np.log(self.emissionprob_)[:, np.concatenate(X)].Tdef _generate_sample_from_state(self, state, random_state=None):cdf = np.cumsum(self.emissionprob_[state, :])random_state = check_random_state(random_state)return [(cdf > random_state.rand()).argmax()]def _initialize_sufficient_statistics(self):stats = super(MultinomialHMM, self)._initialize_sufficient_statistics()stats['obs'] = np.zeros((self.n_components, self.n_features))return statsdef _accumulate_sufficient_statistics(self, stats, X, framelogprob,posteriors, fwdlattice, bwdlattice):super(MultinomialHMM, self)._accumulate_sufficient_statistics(stats, X, framelogprob, posteriors, fwdlattice, bwdlattice)if 'e' in self.params:for t, symbol in enumerate(np.concatenate(X)):stats['obs'][:, symbol] += posteriors[t]def _do_mstep(self, stats):super(MultinomialHMM, self)._do_mstep(stats)if 'e' in self.params:self.emissionprob_ = (stats['obs']/ stats['obs'].sum(axis=1)[:, np.newaxis])def _check_input_symbols(self, X):"""Check if ``X`` is a sample from a Multinomial distribution.That is ``X`` should be an array of non-negative integers fromrange ``[min(X), max(X)]``, such that each integer from the rangeoccurs in ``X`` at least once.For example ``[0, 0, 2, 1, 3, 1, 1]`` is a valid sample from aMultinomial distribution, while ``[0, 0, 3, 5, 10]`` is not."""symbols = np.concatenate(X)if (len(symbols) == 1 or          # not enough datasymbols.dtype.kind != 'i' or  # not an integer(symbols < 0).any()):         # contains negative integersreturn Falsesymbols.sort()return np.all(np.diff(symbols) <= 1)class GMMHMM(_BaseHMM):r"""Hidden Markov Model with Gaussian mixture emissions.Parameters----------n_components : intNumber of states in the model.n_mix : intNumber of states in the GMM.covariance_type : string, optionalString describing the type of covariance parameters touse.  Must be one of* "spherical" --- each state uses a single variance value thatapplies to all features.* "diag" --- each state uses a diagonal covariance matrix.* "full" --- each state uses a full (i.e. unrestricted)covariance matrix.* "tied" --- all states use **the same** full covariance matrix.Defaults to "diag".min_covar : float, optionalFloor on the diagonal of the covariance matrix to preventoverfitting. Defaults to 1e-3.startprob_prior : array, shape (n_components, ), optionalParameters of the Dirichlet prior distribution for:attr:`startprob_`.transmat_prior : array, shape (n_components, n_components), optionalParameters of the Dirichlet prior distribution for each rowof the transition probabilities :attr:`transmat_`.weights_prior : array, shape (n_mix, ), optionalParameters of the Dirichlet prior distribution for:attr:`weights_`.means_prior, means_weight : array, shape (n_mix, ), optionalMean and precision of the Normal prior distribtion for:attr:`means_`.covars_prior, covars_weight : array, shape (n_mix, ), optionalParameters of the prior distribution for the covariance matrix:attr:`covars_`.If :attr:`covariance_type` is "spherical" or "diag" the prior isthe inverse gamma distribution, otherwise --- the inverse Wishartdistribution.algorithm : string, optionalDecoder algorithm. Must be one of "viterbi" or "map".Defaults to "viterbi".random_state: RandomState or an int seed, optionalA random number generator instance.n_iter : int, optionalMaximum number of iterations to perform.tol : float, optionalConvergence threshold. EM will stop if the gain in log-likelihoodis below this value.verbose : bool, optionalWhen ``True`` per-iteration convergence reports are printedto :data:`sys.stderr`. You can diagnose convergence via the:attr:`monitor_` attribute.init_params : string, optionalControls which parameters are initialized prior to training. Cancontain any combination of 's' for startprob, 't' for transmat, 'm'for means, 'c' for covars, and 'w' for GMM mixing weights.Defaults to all parameters.params : string, optionalControls which parameters are updated in the training process.  Cancontain any combination of 's' for startprob, 't' for transmat, 'm' formeans, and 'c' for covars, and 'w' for GMM mixing weights.Defaults to all parameters.Attributes----------monitor\_ : ConvergenceMonitorMonitor object used to check the convergence of EM.startprob\_ : array, shape (n_components, )Initial state occupation distribution.transmat\_ : array, shape (n_components, n_components)Matrix of transition probabilities between states.weights\_ : array, shape (n_components, n_mix)Mixture weights for each state.means\_ : array, shape (n_components, n_mix)Mean parameters for each mixture component in each state.covars\_ : arrayCovariance parameters for each mixture components in each state.The shape depends on :attr:`covariance_type`::(n_components, n_mix)                          if "spherical",(n_components, n_features, n_features)         if "tied",(n_components, n_mix, n_features)              if "diag",(n_components, n_mix, n_features, n_features)  if "full""""def __init__(self, n_components=1, n_mix=1,min_covar=1e-3, startprob_prior=1.0, transmat_prior=1.0,weights_prior=1.0, means_prior=0.0, means_weight=0.0,covars_prior=None, covars_weight=None,algorithm="viterbi", covariance_type="diag",random_state=None, n_iter=10, tol=1e-2,verbose=False, params="stmcw",init_params="stmcw"):_BaseHMM.__init__(self, n_components,startprob_prior=startprob_prior,transmat_prior=transmat_prior,algorithm=algorithm, random_state=random_state,n_iter=n_iter, tol=tol, verbose=verbose,params=params, init_params=init_params)self.covariance_type = covariance_typeself.min_covar = min_covarself.n_mix = n_mixself.weights_prior = weights_priorself.means_prior = means_priorself.means_weight = means_weightself.covars_prior = covars_priorself.covars_weight = covars_weightdef _init(self, X, lengths=None):super(GMMHMM, self)._init(X, lengths=lengths)_n_samples, self.n_features = X.shape# Default values for covariance prior parametersself._init_covar_priors()self._fix_priors_shape()main_kmeans = cluster.KMeans(n_clusters=self.n_components,random_state=self.random_state)labels = main_kmeans.fit_predict(X)kmeanses = []for label in range(self.n_components):kmeans = cluster.KMeans(n_clusters=self.n_mix,random_state=self.random_state)kmeans.fit(X[np.where(labels == label)])kmeanses.append(kmeans)if 'w' in self.init_params or not hasattr(self, "weights_"):self.weights_ = (np.ones((self.n_components, self.n_mix)) /(np.ones((self.n_components, 1)) * self.n_mix))if 'm' in self.init_params or not hasattr(self, "means_"):self.means_ = np.zeros((self.n_components, self.n_mix,self.n_features))for i, kmeans in enumerate(kmeanses):self.means_[i] = kmeans.cluster_centers_if 'c' in self.init_params or not hasattr(self, "covars_"):cv = np.cov(X.T) + self.min_covar * np.eye(self.n_features)if not cv.shape:cv.shape = (1, 1)if self.covariance_type == 'tied':self.covars_ = np.zeros((self.n_components,self.n_features, self.n_features))self.covars_[:] = cvelif self.covariance_type == 'full':self.covars_ = np.zeros((self.n_components, self.n_mix,self.n_features, self.n_features))self.covars_[:] = cvelif self.covariance_type == 'diag':self.covars_ = np.zeros((self.n_components, self.n_mix,self.n_features))self.covars_[:] = np.diag(cv)elif self.covariance_type == 'spherical':self.covars_ = np.zeros((self.n_components, self.n_mix))self.covars_[:] = cv.mean()def _init_covar_priors(self):if self.covariance_type == "full":if self.covars_prior is None:self.covars_prior = 0.0if self.covars_weight is None:self.covars_weight = -(1.0 + self.n_features + 1.0)elif self.covariance_type == "tied":if self.covars_prior is None:self.covars_prior = 0.0if self.covars_weight is None:self.covars_weight = -(self.n_mix + self.n_features + 1.0)elif self.covariance_type == "diag":if self.covars_prior is None:self.covars_prior = -1.5if self.covars_weight is None:self.covars_weight = 0.0elif self.covariance_type == "spherical":if self.covars_prior is None:self.covars_prior = -(self.n_mix + 2.0) / 2.0if self.covars_weight is None:self.covars_weight = 0.0def _fix_priors_shape(self):# If priors are numbers, this function will make them into a# matrix of proper shapeself.weights_prior = np.broadcast_to(self.weights_prior, (self.n_components, self.n_mix)).copy()self.means_prior = np.broadcast_to(self.means_prior,(self.n_components, self.n_mix, self.n_features)).copy()self.means_weight = np.broadcast_to(self.means_weight,(self.n_components, self.n_mix)).copy()if self.covariance_type == "full":self.covars_prior = np.broadcast_to(self.covars_prior,(self.n_components, self.n_mix,self.n_features, self.n_features)).copy()self.covars_weight = np.broadcast_to(self.covars_weight, (self.n_components, self.n_mix)).copy()elif self.covariance_type == "tied":self.covars_prior = np.broadcast_to(self.covars_prior,(self.n_components, self.n_features, self.n_features)).copy()self.covars_weight = np.broadcast_to(self.covars_weight, self.n_components).copy()elif self.covariance_type == "diag":self.covars_prior = np.broadcast_to(self.covars_prior,(self.n_components, self.n_mix, self.n_features)).copy()self.covars_weight = np.broadcast_to(self.covars_weight,(self.n_components, self.n_mix, self.n_features)).copy()elif self.covariance_type == "spherical":self.covars_prior = np.broadcast_to(self.covars_prior, (self.n_components, self.n_mix)).copy()self.covars_weight = np.broadcast_to(self.covars_weight, (self.n_components, self.n_mix)).copy()def _check(self):super(GMMHMM, self)._check()if not hasattr(self, "n_features"):self.n_features = self.means_.shape[2]self._init_covar_priors()self._fix_priors_shape()# Checking covariance typeif self.covariance_type not in COVARIANCE_TYPES:raise ValueError("covariance_type must be one of {0}".format(COVARIANCE_TYPES))self.weights_ = np.array(self.weights_)# Checking mixture weights' shapeif self.weights_.shape != (self.n_components, self.n_mix):raise ValueError("mixture weights must have shape ""(n_components, n_mix), ""actual shape: {0}".format(self.weights_.shape))# Checking mixture weights' mathematical correctnessif not np.allclose(np.sum(self.weights_, axis=1),np.ones(self.n_components)):raise ValueError("mixture weights must sum up to 1")# Checking means' shapeself.means_ = np.array(self.means_)if self.means_.shape != (self.n_components, self.n_mix,self.n_features):raise ValueError("mixture means must have shape ""(n_components, n_mix, n_features), ""actual shape: {0}".format(self.means_.shape))# Checking covariances' shapeself.covars_ = np.array(self.covars_)covars_shape = self.covars_.shapeneeded_shapes = {"spherical": (self.n_components, self.n_mix),"tied": (self.n_components, self.n_features, self.n_features),"diag": (self.n_components, self.n_mix, self.n_features),"full": (self.n_components, self.n_mix,self.n_features, self.n_features)}needed_shape = needed_shapes[self.covariance_type]if covars_shape != needed_shape:raise ValueError("{!r} mixture covars must have shape {0}, ""actual shape: {1}".format(self.covariance_type,needed_shape, covars_shape))# Checking covariances' mathematical correctnessfrom scipy import linalgif (self.covariance_type == "spherical" orself.covariance_type == "diag"):if np.any(self.covars_ <= 0):raise ValueError("{!r} mixture covars must be non-negative".format(self.covariance_type))elif self.covariance_type == "tied":for i, covar in enumerate(self.covars_):if (not np.allclose(covar, covar.T) ornp.any(linalg.eigvalsh(covar) <= 0)):raise ValueError("'tied' mixture covars must be ""symmetric, positive-definite")elif self.covariance_type == "full":for i, mix_covars in enumerate(self.covars_):for j, covar in enumerate(mix_covars):if (not np.allclose(covar, covar.T) ornp.any(linalg.eigvalsh(covar) <= 0)):raise ValueError("'full' covariance matrix of ""mixture {0} of component {1} must be ""symmetric, positive-definite".format(j, i))def _generate_sample_from_state(self, state, random_state=None):if random_state is None:random_state = self.random_staterandom_state = check_random_state(random_state)cur_weights = self.weights_[state]i_gauss = random_state.choice(self.n_mix, p=cur_weights)if self.covariance_type == 'tied':# self.covars_.shape == (n_components, n_features, n_features)# shouldn't that be (n_mix, ...)?covs = self.covars_else:covs = self.covars_[:, i_gauss]covs = fill_covars(covs, self.covariance_type,self.n_components, self.n_features)return random_state.multivariate_normal(self.means_[state, i_gauss], covs[state])def _compute_log_weighted_gaussian_densities(self, X, i_comp):cur_means = self.means_[i_comp]cur_covs = self.covars_[i_comp]if self.covariance_type == 'spherical':cur_covs = cur_covs[:, np.newaxis]log_cur_weights = np.log(self.weights_[i_comp])return log_multivariate_normal_density(X, cur_means, cur_covs, self.covariance_type) + log_cur_weightsdef _compute_log_likelihood(self, X):n_samples, _ = X.shaperes = np.zeros((n_samples, self.n_components))for i in range(self.n_components):log_denses = self._compute_log_weighted_gaussian_densities(X, i)with np.errstate(under="ignore"):res[:, i] = logsumexp(log_denses, axis=1)return resdef _initialize_sufficient_statistics(self):stats = super(GMMHMM, self)._initialize_sufficient_statistics()stats['n_samples'] = 0stats['post_comp_mix'] = Nonestats['post_mix_sum'] = np.zeros((self.n_components, self.n_mix))stats['post_sum'] = np.zeros(self.n_components)stats['samples'] = Nonestats['centered'] = Nonereturn statsdef _accumulate_sufficient_statistics(self, stats, X, framelogprob,post_comp, fwdlattice, bwdlattice):# TODO: support multiple framessuper(GMMHMM, self)._accumulate_sufficient_statistics(stats, X, framelogprob, post_comp, fwdlattice, bwdlattice)n_samples, _ = X.shapestats['n_samples'] = n_samplesstats['samples'] = Xprob_mix = np.zeros((n_samples, self.n_components, self.n_mix))for p in range(self.n_components):log_denses = self._compute_log_weighted_gaussian_densities(X, p)with np.errstate(under="ignore"):prob_mix[:, p, :] = np.exp(log_denses) + np.finfo(np.float).epsprob_mix_sum = np.sum(prob_mix, axis=2)post_mix = prob_mix / prob_mix_sum[:, :, np.newaxis]post_comp_mix = post_comp[:, :, np.newaxis] * post_mixstats['post_comp_mix'] = post_comp_mixstats['post_mix_sum'] = np.sum(post_comp_mix, axis=0)stats['post_sum'] = np.sum(post_comp, axis=0)stats['centered'] = X[:, np.newaxis, np.newaxis, :] - self.means_def _do_mstep(self, stats):super(GMMHMM, self)._do_mstep(stats)n_samples = stats['n_samples']n_features = self.n_features# Maximizing weightsalphas_minus_one = self.weights_prior - 1new_weights_numer = stats['post_mix_sum'] + alphas_minus_onenew_weights_denom = (stats['post_sum'] + np.sum(alphas_minus_one, axis=1))[:, np.newaxis]new_weights = new_weights_numer / new_weights_denom# Maximizing meanslambdas, mus = self.means_weight, self.means_priornew_means_numer = np.einsum('ijk,il->jkl',stats['post_comp_mix'], stats['samples']) + lambdas[:, :, np.newaxis] * musnew_means_denom = (stats['post_mix_sum'] + lambdas)[:, :, np.newaxis]new_means = new_means_numer / new_means_denom# Maximizing covariancescentered_means = self.means_ - musif self.covariance_type == 'full':centered = stats['centered'].reshape((n_samples, self.n_components, self.n_mix, self.n_features, 1))centered_t = stats['centered'].reshape((n_samples, self.n_components, self.n_mix, 1, self.n_features))centered_dots = centered * centered_tpsis_t = np.transpose(self.covars_prior, axes=(0, 1, 3, 2))nus = self.covars_weightcentr_means_resh = centered_means.reshape((self.n_components, self.n_mix, self.n_features, 1))centr_means_resh_t = centered_means.reshape((self.n_components, self.n_mix, 1, self.n_features))centered_means_dots = centr_means_resh * centr_means_resh_tnew_cov_numer = np.einsum('ijk,ijklm->jklm',stats['post_comp_mix'], centered_dots) + psis_t + (lambdas[:, :, np.newaxis, np.newaxis] *centered_means_dots)new_cov_denom = (stats['post_mix_sum'] + 1 + nus + self.n_features + 1)[:, :, np.newaxis, np.newaxis]new_cov = new_cov_numer / new_cov_denomelif self.covariance_type == 'diag':centered2 = stats['centered'] ** 2centered_means2 = centered_means ** 2alphas = self.covars_priorbetas = self.covars_weightnew_cov_numer = np.einsum('ijk,ijkl->jkl',stats['post_comp_mix'], centered2) + lambdas[:, :, np.newaxis] * centered_means2 + 2 * betasnew_cov_denom = (stats['post_mix_sum'][:, :, np.newaxis] + 1 + 2 * (alphas + 1))new_cov = new_cov_numer / new_cov_denomelif self.covariance_type == 'spherical':centered_norm2 = np.sum(stats['centered'] ** 2, axis=-1)alphas = self.covars_priorbetas = self.covars_weightcentered_means_norm2 = np.sum(centered_means ** 2, axis=-1)new_cov_numer = np.einsum('ijk,ijk->jk',stats['post_comp_mix'], centered_norm2) + lambdas * centered_means_norm2 + 2 * betasnew_cov_denom = (n_features * stats['post_mix_sum'] + n_features +2 * (alphas + 1))new_cov = new_cov_numer / new_cov_denomelif self.covariance_type == 'tied':centered = stats['centered'].reshape((n_samples, self.n_components, self.n_mix, self.n_features, 1))centered_t = stats['centered'].reshape((n_samples, self.n_components, self.n_mix, 1, self.n_features))centered_dots = centered * centered_tpsis_t = np.transpose(self.covars_prior, axes=(0, 2, 1))nus = self.covars_weightcentr_means_resh = centered_means.reshape((self.n_components, self.n_mix, self.n_features, 1))centr_means_resh_t = centered_means.reshape((self.n_components, self.n_mix, 1, self.n_features))centered_means_dots = centr_means_resh * centr_means_resh_tlambdas_cmdots_prod_sum = np.einsum('ij,ijkl->ikl',lambdas, centered_means_dots)new_cov_numer = np.einsum('ijk,ijklm->jlm',stats['post_comp_mix'], centered_dots) + lambdas_cmdots_prod_sum + psis_tnew_cov_denom = (stats['post_sum'] + self.n_mix + nus + self.n_features + 1)[:, np.newaxis, np.newaxis]new_cov = new_cov_numer / new_cov_denom# Assigning new values to class membersself.weights_ = new_weightsself.means_ = new_meansself.covars_ = new_cov
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