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#
# Author: Ron Weiss <ronweiss@gmail.com>
# and Shiqiao Du <lucidfrontier.45@gmail.com>
"""
The :mod:`sklearn.hmm` module implements hidden Markov models.
**Warning:** :mod:`sklearn.hmm` is orphaned, undocumented and has known
numerical stability issues. If nobody volunteers to write documentation and
make it more stable, this module will be removed in version 0.11.
"""
import string
import numpy as np
from .utils import check_random_state
from .utils.extmath import logsumexp
from .base import BaseEstimator
from .mixture import (
GMM, log_multivariate_normal_density, sample_gaussian,
distribute_covar_matrix_to_match_covariance_type, _validate_covars)
from . import cluster
from .utils import deprecated
from . import _hmmc
ZEROLOGPROB = -1e200
EPS = np.finfo(float).eps
NEGINF = -np.inf
decoder_algorithms = ("viterbi", "map")
def normalize(A, axis=None):
""" Normalize the input array so that it sums to 1.
Parameters
----------
A: array, shape (n_samples, n_features)
Non-normalized input data
axis: int
dimension along which normalization is performed
Returns
-------
normalized_A: array, shape (n_samples, n_features)
A with values normalized (summing to 1) along the prescribed axis
WARNING: Modifies inplace the array
"""
A += EPS
Asum = A.sum(axis)
if axis and A.ndim > 1:
# Make sure we don't divide by zero.
Asum[Asum == 0] = 1
shape = list(A.shape)
shape[axis] = 1
Asum.shape = shape
return A / Asum
class _BaseHMM(BaseEstimator):
"""Hidden Markov Model base class.
Representation of a hidden Markov model probability distribution.
This class allows for easy evaluation of, sampling from, and
maximum-likelihood estimation of the parameters of a HMM.
See the instance documentation for details specific to a
particular object.
Attributes
----------
n_components : int
Number of states in the model.
transmat : array, shape (`n_components`, `n_components`)
Matrix of transition probabilities between states.
startprob : array, shape ('n_components`,)
Initial state occupation distribution.
transmat_prior : array, shape (`n_components`, `n_components`)
Matrix of prior transition probabilities between states.
startprob_prior : array, shape ('n_components`,)
Initial state occupation prior distribution.
algorithm : string, one of the decoder_algorithms
decoder algorithm
random_state: RandomState or an int seed (0 by default)
A random number generator instance
See Also
--------
GMM : Gaussian mixture model
"""
# This class implements the public interface to all HMMs that
# derive from it, including all of the machinery for the
# forward-backward and Viterbi algorithms. Subclasses need only
# implement _generate_sample_from_state(), _compute_log_likelihood(),
# _init(), _initialize_sufficient_statistics(),
# _accumulate_sufficient_statistics(), and _do_mstep(), all of
# which depend on the specific emission distribution.
#
# Subclasses will probably also want to implement properties for
# the emission distribution parameters to expose them publically.
def __init__(self, n_components=1, startprob=None, transmat=None,
startprob_prior=None, transmat_prior=None,
algorithm="viterbi", random_state=None):
self.n_components = n_components
if startprob is None:
startprob = np.tile(1.0 / n_components, n_components)
self.startprob_ = startprob
if startprob_prior is None:
startprob_prior = 1.0
self.startprob_prior = startprob_prior
if transmat is None:
transmat = np.tile(1.0 / n_components,
(n_components, n_components))
self.transmat_ = transmat
if transmat_prior is None:
transmat_prior = 1.0
self.transmat_prior = transmat_prior
if algorithm in decoder_algorithms:
self._algorithm = algorithm
else:
self._algorithm = "viterbi"
self.random_state = random_state
def eval(self, obs):
"""Compute the log probability under the model and compute posteriors
Implements rank and beam pruning in the forward-backward
algorithm to speed up inference in large models.
Parameters
----------
obs : array_like, shape (n, n_features)
Sequence of n_features-dimensional data points. Each row
corresponds to a single point in the sequence.
Returns
-------
logprob : float
Log likelihood of the sequence `obs`
posteriors: array_like, shape (n, n_components)
Posterior probabilities of each state for each
observation
See Also
--------
score : Compute the log probability under the model
decode : Find most likely state sequence corresponding to a `obs`
"""
obs = np.asarray(obs)
framelogprob = self._compute_log_likelihood(obs)
logprob, fwdlattice = self._do_forward_pass(framelogprob)
bwdlattice = self._do_backward_pass(framelogprob)
gamma = fwdlattice + bwdlattice
# gamma is guaranteed to be correctly normalized by logprob at
# all frames, unless we do approximate inference using pruning.
# So, we will normalize each frame explicitly in case we
# pruned too aggressively.
posteriors = np.exp(gamma.T - logsumexp(gamma, axis=1)).T
posteriors += np.finfo(np.float32).eps
posteriors /= np.sum(posteriors, axis=1).reshape((-1, 1))
return logprob, posteriors
def score(self, obs):
"""Compute the log probability under the model.
Parameters
----------
obs : array_like, shape (n, n_features)
Sequence of n_features-dimensional data points. Each row
corresponds to a single data point.
Returns
-------
logprob : float
Log likelihood of the `obs`
See Also
--------
eval : Compute the log probability under the model and posteriors
decode : Find most likely state sequence corresponding to a `obs`
"""
obs = np.asarray(obs)
framelogprob = self._compute_log_likelihood(obs)
logprob, _ = self._do_forward_pass(framelogprob)
return logprob
def _decode_viterbi(self, obs):
"""Find most likely state sequence corresponding to `obs`.
Uses the Viterbi algorithm.
Parameters
----------
obs : array_like, shape (n, n_features)
List of n_features-dimensional data points. Each row
corresponds to a single data point.
Returns
-------
viterbi_logprob : float
Log probability of the maximum likelihood path through the HMM
state_sequence : array_like, shape (n,)
Index of the most likely states for each observation
See Also
--------
eval : Compute the log probability under the model and posteriors
score : Compute the log probability under the model
"""
obs = np.asarray(obs)
framelogprob = self._compute_log_likelihood(obs)
viterbi_logprob, state_sequence = self._do_viterbi_pass(framelogprob)
return viterbi_logprob, state_sequence
def _decode_map(self, obs):
"""Find most likely state sequence corresponding to `obs`.
Uses the maximum a posteriori estimation.
Parameters
----------
obs : array_like, shape (n, n_features)
List of n_features-dimensional data points. Each row
corresponds to a single data point.
Returns
-------
map_logprob : float
Log probability of the maximum likelihood path through the HMM
state_sequence : array_like, shape (n,)
Index of the most likely states for each observation
See Also
--------
eval : Compute the log probability under the model and posteriors
score : Compute the log probability under the model
"""
_, posteriors = self.eval(obs)
state_sequence = np.argmax(posteriors, axis=1)
map_logprob = np.max(posteriors, axis=1).sum()
return map_logprob, state_sequence
def decode(self, obs, algorithm="viterbi"):
"""Find most likely state sequence corresponding to `obs`.
Uses the selected algorithm for decoding.
Parameters
----------
obs : array_like, shape (n, n_features)
List of n_features-dimensional data points. Each row
corresponds to a single data point.
algorithm : string, one of the `decoder_algorithms`
decoder algorithm to be used
Returns
-------
logprob : float
Log probability of the maximum likelihood path through the HMM
state_sequence : array_like, shape (n,)
Index of the most likely states for each observation
See Also
--------
eval : Compute the log probability under the model and posteriors
score : Compute the log probability under the model
"""
if self._algorithm in decoder_algorithms:
algorithm = self._algorithm
elif algorithm in decoder_algorithms:
algorithm = algorithm
decoder = {"viterbi": self._decode_viterbi,
"map": self._decode_map}
logprob, state_sequence = decoder[algorithm](obs)
return logprob, state_sequence
def predict(self, obs, algorithm="viterbi"):
"""Find most likely state sequence corresponding to `obs`.
Parameters
----------
obs : array_like, shape (n, n_features)
List of n_features-dimensional data points. Each row
corresponds to a single data point.
Returns
-------
state_sequence : array_like, shape (n,)
Index of the most likely states for each observation
"""
_, state_sequence = self.decode(obs, algorithm)
return state_sequence
def predict_proba(self, obs):
"""Compute the posterior probability for each state in the model
Parameters
----------
obs : array_like, shape (n, n_features)
List of n_features-dimensional data points. Each row
corresponds to a single data point.
Returns
-------
T : array-like, shape (n, n_components)
Returns the probability of the sample for each state in the model.
"""
_, posteriors = self.eval(obs)
return posteriors
def sample(self, n=1, random_state=None):
"""Generate random samples from the model.
Parameters
----------
n : int
Number of samples to generate.
random_state: RandomState or an int seed (0 by default)
A random number generator instance. If None is given, the
object's random_state is used
Returns
-------
(obs, hidden_states)
obs : array_like, length `n` List of samples
hidden_states : array_like, length `n` List of hidden states
"""
if random_state is None:
random_state = self.random_state
random_state = check_random_state(random_state)
startprob_pdf = self.startprob_
startprob_cdf = np.cumsum(startprob_pdf)
transmat_pdf = self.transmat_
transmat_cdf = np.cumsum(transmat_pdf, 1)
# Initial state.
rand = random_state.rand()
currstate = (startprob_cdf > rand).argmax()
hidden_states = [currstate]
obs = [self._generate_sample_from_state(
currstate, random_state=random_state)]
for _ in xrange(n - 1):
rand = random_state.rand()
currstate = (transmat_cdf[currstate] > rand).argmax()
hidden_states.append(currstate)
obs.append(self._generate_sample_from_state(
currstate, random_state=random_state))
return np.array(obs), np.array(hidden_states, dtype=int)
@deprecated("rvs is deprecated in 0.11 will be removed in 0.13:"
+ " use sample instead")
def rvs(self, n=1, random_state=None):
return self.sample(n, random_state)
def fit(self, obs, n_iter=10, thresh=1e-2, params=string.ascii_letters,
init_params=string.ascii_letters, **kwargs):
"""Estimate model parameters.
An initialization step is performed before entering the EM
algorithm. If you want to avoid this step, set the keyword
argument init_params to the empty string ''. Likewise, if you
would like just to do an initialization, call this method with
n_iter=0.
Parameters
----------
obs : list
List of array-like observation sequences (shape (n_i, n_features)).
n_iter : int, optional
Number of iterations to perform.
thresh : float, optional
Convergence threshold.
params : string, optional
Controls which parameters are updated in the training
process. Can contain any combination of 's' for startprob,
't' for transmat, 'm' for means, and 'c' for covars, etc.
Defaults to all parameters.
init_params : string, optional
Controls which parameters are initialized prior to
training. Can contain any combination of 's' for
startprob, 't' for transmat, 'm' for means, and 'c' for
covars, etc. Defaults to all parameters.
Notes
-----
In general, `logprob` should be non-decreasing unless
aggressive pruning is used. Decreasing `logprob` is generally
a sign of overfitting (e.g. a covariance parameter getting too
small). You can fix this by getting more training data, or
decreasing `covars_prior`.
"""
self._init(obs, init_params)
logprob = []
for i in xrange(n_iter):
# Expectation step
stats = self._initialize_sufficient_statistics()
curr_logprob = 0
for seq in obs:
framelogprob = self._compute_log_likelihood(seq)
lpr, fwdlattice = self._do_forward_pass(framelogprob)
bwdlattice = self._do_backward_pass(framelogprob)
gamma = fwdlattice + bwdlattice
posteriors = np.exp(gamma.T - logsumexp(gamma, axis=1)).T
curr_logprob += lpr
self._accumulate_sufficient_statistics(
stats, seq, framelogprob, posteriors, fwdlattice,
bwdlattice, params)
logprob.append(curr_logprob)
# Check for convergence.
if i > 0 and abs(logprob[-1] - logprob[-2]) < thresh:
break
# Maximization step
self._do_mstep(stats, params)
return self
def _get_algorithm(self):
"decoder algorithm"
return self._algorithm
def _set_algorithm(self, algorithm):
if algorithm not in decoder_algorithms:
raise ValueError("algorithm must be one of the decoder_algorithms")
self._algorithm = algorithm
algorithm = property(_get_algorithm, _set_algorithm)
def _get_startprob(self):
"""Mixing startprob for each state."""
return np.exp(self._log_startprob)
def _set_startprob(self, startprob):
if len(startprob) != self.n_components:
raise ValueError('startprob must have length n_components')
if not np.allclose(np.sum(startprob), 1.0):
raise ValueError('startprob must sum to 1.0')
self._log_startprob = np.log(np.asarray(startprob).copy())
startprob_ = property(_get_startprob, _set_startprob)
def _get_transmat(self):
"""Matrix of transition probabilities."""
return np.exp(self._log_transmat)
def _set_transmat(self, transmat):
if (np.asarray(transmat).shape
!= (self.n_components, self.n_components)):
raise ValueError('transmat must have shape ' +
'(n_components, n_components)')
if not np.all(np.allclose(np.sum(transmat, axis=1), 1.0)):
raise ValueError('Rows of transmat must sum to 1.0')
self._log_transmat = np.log(np.asarray(transmat).copy())
underflow_idx = np.isnan(self._log_transmat)
self._log_transmat[underflow_idx] = NEGINF
transmat_ = property(_get_transmat, _set_transmat)
def _do_viterbi_pass(self, framelogprob):
n_observations, n_components = framelogprob.shape
state_sequence, logprob = _hmmc._viterbi(
n_observations, n_components, self._log_startprob,
self._log_transmat, framelogprob)
return logprob, state_sequence
def _do_forward_pass(self, framelogprob):
n_observations, n_components = framelogprob.shape
fwdlattice = np.zeros((n_observations, n_components))
_hmmc._forward(n_observations, n_components, self._log_startprob,
self._log_transmat, framelogprob, fwdlattice)
fwdlattice[fwdlattice <= ZEROLOGPROB] = NEGINF
return logsumexp(fwdlattice[-1]), fwdlattice
def _do_backward_pass(self, framelogprob):
n_observations, n_components = framelogprob.shape
bwdlattice = np.zeros((n_observations, n_components))
_hmmc._backward(n_observations, n_components,
self._log_startprob, self._log_transmat,
framelogprob, bwdlattice)
bwdlattice[bwdlattice <= ZEROLOGPROB] = NEGINF
return bwdlattice
def _compute_log_likelihood(self, obs):
pass
def _generate_sample_from_state(self, state, random_state=None):
pass
def _init(self, obs, params):
if 's' in params:
self.startprob_[:] = 1.0 / self.n_components
if 't' in params:
self.transmat_[:] = 1.0 / self.n_components
# Methods used by self.fit()
def _initialize_sufficient_statistics(self):
stats = {'nobs': 0,
'start': np.zeros(self.n_components),
'trans': np.zeros((self.n_components, self.n_components))}
return stats
def _accumulate_sufficient_statistics(self, stats, seq, framelogprob,
posteriors, fwdlattice, bwdlattice,
params):
stats['nobs'] += 1
if 's' in params:
stats['start'] += posteriors[0]
if 't' in params:
if _hmmc:
n_observations, n_components = framelogprob.shape
lneta = np.zeros((n_observations - 1,
n_components, n_components))
lnP = logsumexp(fwdlattice[-1])
_hmmc._compute_lneta(n_observations, n_components,
fwdlattice, self._log_transmat, bwdlattice,
framelogprob, lnP, lneta)
stats["trans"] += np.exp(logsumexp(lneta, 0))
else:
for t in xrange(len(framelogprob)):
zeta = (fwdlattice[t - 1][:, np.newaxis]
+ self._log_transmat + framelogprob[t]
+ bwdlattice[t])
stats['trans'] += np.exp(zeta - logsumexp(zeta))
def _do_mstep(self, stats, params):
# Based on Huang, Acero, Hon, "Spoken Language Processing",
# p. 443 - 445
if 's' in params:
self.startprob_ = normalize(
np.maximum(self.startprob_prior - 1.0 + stats['start'], 1e-20))
if 't' in params:
self.transmat_ = normalize(
np.maximum(self.transmat_prior - 1.0 + stats['trans'], 1e-20),
axis=1)
class GaussianHMM(_BaseHMM):
"""Hidden Markov Model with Gaussian emissions
Representation of a hidden Markov model probability distribution.
This class allows for easy evaluation of, sampling from, and
maximum-likelihood estimation of the parameters of a HMM.
Parameters
----------
n_components : int
Number of states.
_covariance_type : string
String describing the type of covariance parameters to
use. Must be one of 'spherical', 'tied', 'diag', 'full'.
Defaults to 'diag'.
Attributes
----------
covariance_type : string
String describing the type of covariance parameters used by
the model. Must be one of 'spherical', 'tied', 'diag', 'full'.
n_features : int
Dimensionality of the Gaussian emissions.
n_components : int
Number of states in the model.
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 : array
Covariance parameters for each state. The shape depends on
`_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'
random_state: RandomState or an int seed (0 by default)
A random number generator instance
Examples
--------
>>> from sklearn.hmm import GaussianHMM
>>> GaussianHMM(n_components=2)
... #doctest: +ELLIPSIS +NORMALIZE_WHITESPACE
GaussianHMM(algorithm='viterbi', covariance_type='diag', covars_prior=0.01,
covars_weight=1, means_prior=None, means_weight=0, n_components=2,
random_state=None, startprob=None, startprob_prior=1.0, transmat=None,
transmat_prior=1.0)
See Also
--------
GMM : Gaussian mixture model
"""
def __init__(self, n_components=1, covariance_type='diag', startprob=None,
transmat=None, startprob_prior=None, transmat_prior=None,
algorithm="viterbi", means_prior=None, means_weight=0,
covars_prior=1e-2, covars_weight=1,
random_state=None):
_BaseHMM.__init__(self, n_components, startprob, transmat,
startprob_prior=startprob_prior,
transmat_prior=transmat_prior,
algorithm=algorithm,
random_state=random_state)
self._covariance_type = covariance_type
if not covariance_type in ['spherical', 'tied', 'diag', 'full']:
raise ValueError('bad covariance_type')
self.means_prior = means_prior
self.means_weight = means_weight
self.covars_prior = covars_prior
self.covars_weight = covars_weight
# Read-only properties.
@property
def covariance_type(self):
"""Covariance type of the model.
Must be one of 'spherical', 'tied', 'diag', 'full'.
"""
return self._covariance_type
def _get_means(self):
"""Mean parameters for each state."""
return self._means_
def _set_means(self, means):
means = np.asarray(means)
if hasattr(self, 'n_features') and \
means.shape != (self.n_components, self.n_features):
raise ValueError('means must have shape' +
'(n_components, n_features)')
self._means_ = means.copy()
self.n_features = self._means_.shape[1]
means_ = property(_get_means, _set_means)
def _get_covars(self):
"""Return covars as a full matrix."""
if self._covariance_type == 'full':
return self._covars_
elif self._covariance_type == 'diag':
return [np.diag(cov) for cov in self._covars_]
elif self._covariance_type == 'tied':
return [self._covars_] * self.n_components
elif self._covariance_type == 'spherical':
return [np.eye(self.n_features) * f for f in self._covars_]
def _set_covars(self, covars):
covars = np.asarray(covars)
_validate_covars(covars, self._covariance_type, self.n_components)
self._covars_ = covars.copy()
covars_ = property(_get_covars, _set_covars)
def _compute_log_likelihood(self, obs):
return log_multivariate_normal_density(
obs, self._means_, self._covars_, self._covariance_type)
def _generate_sample_from_state(self, state, random_state=None):
if self._covariance_type == 'tied':
cv = self._covars_
else:
cv = self._covars_[state]
return sample_gaussian(self._means_[state], cv, self._covariance_type,
random_state=random_state)
def _init(self, obs, params='stmc'):
super(GaussianHMM, self)._init(obs, params=params)
if (hasattr(self, 'n_features')
and self.n_features != obs[0].shape[1]):
raise ValueError('Unexpected number of dimensions, got %s but '
'expected %s' % (obs[0].shape[1],
self.n_features))
self.n_features = obs[0].shape[1]
if 'm' in params:
self._means_ = cluster.KMeans(
k=self.n_components).fit(obs[0]).cluster_centers_
if 'c' in params:
cv = np.cov(obs[0].T)
if not cv.shape:
cv.shape = (1, 1)
self._covars_ = distribute_covar_matrix_to_match_covariance_type(
cv, self._covariance_type, self.n_components)
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))
stats['obs*obs.T'] = np.zeros((self.n_components, self.n_features,
self.n_features))
return stats
def _accumulate_sufficient_statistics(self, stats, obs, framelogprob,
posteriors, fwdlattice, bwdlattice,
params):
super(GaussianHMM, self)._accumulate_sufficient_statistics(
stats, obs, framelogprob, posteriors, fwdlattice, bwdlattice,
params)
if 'm' in params or 'c' in params:
stats['post'] += posteriors.sum(axis=0)
stats['obs'] += np.dot(posteriors.T, obs)
if 'c' in params:
if self._covariance_type in ('spherical', 'diag'):
stats['obs**2'] += np.dot(posteriors.T, obs ** 2)
elif self._covariance_type in ('tied', 'full'):
for t, o in enumerate(obs):
obsobsT = np.outer(o, o)
for c in xrange(self.n_components):
stats['obs*obs.T'][c] += posteriors[t, c] * obsobsT
def _do_mstep(self, stats, params):
super(GaussianHMM, self)._do_mstep(stats, params)
# Based on Huang, Acero, Hon, "Spoken Language Processing",
# p. 443 - 445
denom = stats['post'][:, np.newaxis]
if 'm' in params:
prior = self.means_prior
weight = self.means_weight
if prior is None:
weight = 0
prior = 0
self._means_ = (weight * prior + stats['obs']) / (weight + denom)
if 'c' in params:
covars_prior = self.covars_prior
covars_weight = self.covars_weight
if covars_prior is None:
covars_weight = 0
covars_prior = 0
means_prior = self.means_prior
means_weight = self.means_weight
if means_prior is None:
means_weight = 0
means_prior = 0
meandiff = self._means_ - means_prior
if 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) + denom
self._covars_ = (covars_prior + cv_num) / cv_den
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'):
cvnum = np.empty((self.n_components, self.n_features,
self.n_features))
for c in xrange(self.n_components):
obsmean = np.outer(stats['obs'][c], self._means_[c])
cvnum[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 + cvnum.sum(axis=0))
/ (cvweight + stats['post'].sum()))
elif self._covariance_type == 'full':
self._covars_ = ((covars_prior + cvnum)
/ (cvweight + stats['post'][:, None, None]))
class MultinomialHMM(_BaseHMM):
"""Hidden Markov Model with multinomial (discrete) emissions
Attributes
----------
n_components : int
Number of states in the model.
n_symbols : int
Number of possible symbols emitted by the model (in the observations).
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_symbols`)
Probability of emitting a given symbol when in each state.
random_state: RandomState or an int seed (0 by default)
A random number generator instance
Examples
--------
>>> from sklearn.hmm import MultinomialHMM
>>> MultinomialHMM(n_components=2)
... #doctest: +ELLIPSIS +NORMALIZE_WHITESPACE
MultinomialHMM(algorithm='viterbi', n_components=2, random_state=None,
startprob=None, startprob_prior=1.0, transmat=None,
transmat_prior=1.0)
See Also
--------
GaussianHMM : HMM with Gaussian emissions
"""
def __init__(self, n_components=1, startprob=None, transmat=None,
startprob_prior=None, transmat_prior=None,
algorithm="viterbi", random_state=None):
"""Create a hidden Markov model with multinomial emissions.
Parameters
----------
n_components : int
Number of states.
"""
_BaseHMM.__init__(self, n_components, startprob, transmat,
startprob_prior=startprob_prior,
transmat_prior=transmat_prior,
algorithm=algorithm,
random_state=random_state)
def _get_emissionprob(self):
"""Emission probability distribution for each state."""
return np.exp(self._log_emissionprob)
def _set_emissionprob(self, emissionprob):
emissionprob = np.asarray(emissionprob)
if hasattr(self, 'n_symbols') and \
emissionprob.shape != (self.n_components, self.n_symbols):
raise ValueError('emissionprob must have shape '
'(n_components, n_symbols)')
self._log_emissionprob = np.log(emissionprob)
underflow_idx = np.isnan(self._log_emissionprob)
self._log_emissionprob[underflow_idx] = NEGINF
self.n_symbols = self._log_emissionprob.shape[1]
emissionprob_ = property(_get_emissionprob, _set_emissionprob)
def _compute_log_likelihood(self, obs):
return self._log_emissionprob[:, obs].T
def _generate_sample_from_state(self, state, random_state=None):
cdf = np.cumsum(self.emissionprob_[state, :])
random_state = check_random_state(random_state)
rand = random_state.rand()
symbol = (cdf > rand).argmax()
return symbol
def _init(self, obs, params='ste'):
super(MultinomialHMM, self)._init(obs, params=params)
self.random_state = check_random_state(self.random_state)
if 'e' in params:
emissionprob = normalize(self.random_state.rand(self.n_components,
self.n_symbols), 1)
self.emissionprob_ = emissionprob
def _initialize_sufficient_statistics(self):
stats = super(MultinomialHMM, self)._initialize_sufficient_statistics()
stats['obs'] = np.zeros((self.n_components, self.n_symbols))
return stats
def _accumulate_sufficient_statistics(self, stats, obs, framelogprob,
posteriors, fwdlattice, bwdlattice,
params):
super(MultinomialHMM, self)._accumulate_sufficient_statistics(
stats, obs, framelogprob, posteriors, fwdlattice, bwdlattice,
params)
if 'e' in params:
for t, symbol in enumerate(obs):
stats['obs'][:, symbol] += posteriors[t]
def _do_mstep(self, stats, params):
super(MultinomialHMM, self)._do_mstep(stats, params)
if 'e' in params:
self.emissionprob_ = (stats['obs']
/ stats['obs'].sum(1)[:, np.newaxis])
class GMMHMM(_BaseHMM):
"""Hidden Markov Model with Gaussin mixture emissions
Attributes
----------
n_components : int
Number of states in the model.
transmat : array, shape (`n_components`, `n_components`)
Matrix of transition probabilities between states.
startprob : array, shape ('n_components`,)
Initial state occupation distribution.
gmms : array of GMM objects, length `n_components`
GMM emission distributions for each state.
random_state: RandomState or an int seed (0 by default)
A random number generator instance
Examples
--------
>>> from sklearn.hmm import GMMHMM
>>> GMMHMM(n_components=2, n_mix=10, covariance_type='diag')
... # doctest: +ELLIPSIS, +NORMALIZE_WHITESPACE
GMMHMM(algorithm='viterbi', covariance_type='diag', covars_prior=0.01,
gmms=[GMM(covariance_type=None, init_params='wmc', min_covar=0.001,
n_components=10, n_init=1, n_iter=100, params='wmc', random_state=None,
thresh=0.01), GMM(covariance_type=None, init_params='wmc',
min_covar=0.001, n_components=10, n_init=1, n_iter=100, params='wmc',
random_state=None, thresh=0.01)], n_components=2, n_mix=10,
random_state=None, startprob=None, startprob_prior=1.0, transmat=None,
transmat_prior=1.0)
See Also
--------
GaussianHMM : HMM with Gaussian emissions
"""
def __init__(self, n_components=1, n_mix=1, startprob=None, transmat=None,
startprob_prior=None, transmat_prior=None, algorithm="viterbi",
gmms=None, covariance_type='diag', covars_prior=1e-2,
random_state=None):
"""Create a hidden Markov model with GMM emissions.
Parameters
----------
n_components : int
Number of states.
"""
_BaseHMM.__init__(self, n_components, startprob, transmat,
startprob_prior=startprob_prior,
transmat_prior=transmat_prior,
algorithm=algorithm,
random_state=random_state)
# XXX: Hotfit for n_mix that is incompatible with the scikit's
# BaseEstimator API
self.n_mix = n_mix
self._covariance_type = covariance_type
self.covars_prior = covars_prior
if gmms is None:
gmms = []
for x in xrange(self.n_components):
if covariance_type is None:
g = GMM(n_mix)
else:
g = GMM(n_mix, covariance_type=covariance_type)
gmms.append(g)
self.gmms = gmms
# Read-only properties.
@property
def covariance_type(self):
"""Covariance type of the model.
Must be one of 'spherical', 'tied', 'diag', 'full'.
"""
return self._covariance_type
def _compute_log_likelihood(self, obs):
return np.array([g.score(obs) for g in self.gmms]).T
def _generate_sample_from_state(self, state, random_state=None):
return self.gmms[state].sample(1, random_state=random_state).flatten()
def _init(self, obs, params='stwmc'):
super(GMMHMM, self)._init(obs, params=params)
allobs = np.concatenate(obs, 0)
for g in self.gmms:
g.set_params(init_params=params, n_iter=0)
g.fit(allobs)
def _initialize_sufficient_statistics(self):
stats = super(GMMHMM, self)._initialize_sufficient_statistics()
stats['norm'] = [np.zeros(g.weights_.shape) for g in self.gmms]
stats['means'] = [np.zeros(np.shape(g.means_)) for g in self.gmms]
stats['covars'] = [np.zeros(np.shape(g.covars_)) for g in self.gmms]
return stats
def _accumulate_sufficient_statistics(self, stats, obs, framelogprob,
posteriors, fwdlattice, bwdlattice,
params):
super(GMMHMM, self)._accumulate_sufficient_statistics(
stats, obs, framelogprob, posteriors, fwdlattice, bwdlattice,
params)
for state, g in enumerate(self.gmms):
_, lgmm_posteriors = g.eval(obs)
lgmm_posteriors += np.log(posteriors[:, state][:, np.newaxis]
+ np.finfo(np.float).eps)
gmm_posteriors = np.exp(lgmm_posteriors)
tmp_gmm = GMM(g.n_components, covariance_type=g._covariance_type)
n_features = g.means_.shape[1]
tmp_gmm._set_covars(
distribute_covar_matrix_to_match_covariance_type(
np.eye(n_features), g._covariance_type,
g.n_components))
norm = tmp_gmm._do_mstep(obs, gmm_posteriors, params)
if np.any(np.isnan(tmp_gmm.covars_)):
raise ValueError
stats['norm'][state] += norm
if 'm' in params:
stats['means'][state] += tmp_gmm.means_ * norm[:, np.newaxis]
if 'c' in params:
if tmp_gmm._covariance_type == 'tied':
stats['covars'][state] += tmp_gmm.covars_ * norm.sum()
else:
cvnorm = np.copy(norm)
shape = np.ones(tmp_gmm.covars_.ndim)
shape[0] = np.shape(tmp_gmm.covars_)[0]
cvnorm.shape = shape
stats['covars'][state] += tmp_gmm.covars_ * cvnorm
def _do_mstep(self, stats, params):
super(GMMHMM, self)._do_mstep(stats, params)
# All that is left to do is to apply covars_prior to the
# parameters updated in _accumulate_sufficient_statistics.
for state, g in enumerate(self.gmms):
n_features = g.means_.shape[1]
norm = stats['norm'][state]
if 'w' in params:
g.weights_ = normalize(norm)
if 'm' in params:
g.means_ = stats['means'][state] / norm[:, np.newaxis]
if 'c' in params:
if g._covariance_type == 'tied':
g.covars_ = ((stats['covars'][state]
+ self.covars_prior * np.eye(n_features))
/ norm.sum())
else:
cvnorm = np.copy(norm)
shape = np.ones(g.covars_.ndim)
shape[0] = np.shape(g.covars_)[0]
cvnorm.shape = shape
if (g._covariance_type in ['spherical', 'diag']):
g.covars_ = (stats['covars'][state]
+ self.covars_prior) / cvnorm
elif g._covariance_type == 'full':
eye = np.eye(n_features)
g.covars_ = ((stats['covars'][state]
+ self.covars_prior * eye[np.newaxis])
/ cvnorm)
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