basehmm.py

#!/usr/bin/env python

#Copyright (C) 2014 by Glenn Hickey
#
#Released under the MIT license, see LICENSE.txt

"""
Moving the multinomial hmm from Scikit-Learn into this package so I can speed up the dynamic programming.  Also take the opportunity to cut off the dependenciy to scikit which was a bit of an overkill since the basic hmm we use is only a fe w lines of code.  Bordering on a total rewrite here, which is probably for the best since the hmm seems on it's way out of scikit anyway.  

-- Glenn Hickey, 2014

 Derived from scikit-learn/sklearn/hmm.py
 See below:

Copyright (c) 2007-2014 the scikit-learn developers.
All rights reserved.

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     this list of conditions and the following disclaimer.
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  c. Neither the name of the Scikit-learn Developers  nor the names of
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"""# Hidden Markov Models
#
# Author: Ron Weiss <ronweiss@gmail.com>
# and Shiqiao Du <lucidfrontier.45@gmail.com>
# API changes: Jaques Grobler <jaquesgrobler@gmail.com>

"""
The :mod:`sklearn.hmm` module implements hidden Markov models.

**Warning:** :mod:`sklearn.hmm` is orphaned, undocumented and has known
numerical stability issues. This module will be removed in version 0.17.
"""

import string
import numpy as np
import numbers
import copy

from . import _basehmm
from .common import logger

ZEROLOGPROB = -1e200
EPS = np.finfo(float).eps
NEGINF = -np.inf
decoder_algorithms = ("viterbi", "map")

def logsumexp(arr, axis=0):
    """Computes the sum of arr assuming arr is in the log domain.

    Returns log(sum(exp(arr))) while minimizing the possibility of
    over/underflow.

    Examples
    --------

    >>> import numpy as np
    >>> from sklearn.utils.extmath import logsumexp
    >>> a = np.arange(10)
    >>> np.log(np.sum(np.exp(a)))
    9.4586297444267107
    >>> logsumexp(a)
    9.4586297444267107
    """
    arr = np.rollaxis(arr, axis)
    # Use the max to normalize, as with the log this is what accumulates
    # the less errors
    vmax = arr.max(axis=0)
    out = np.log(np.sum(np.exp(arr - vmax), axis=0))
    out += vmax
    return out


def check_random_state(seed):
    """Turn seed into a np.random.RandomState instance

    If seed is None, return the RandomState singleton used by np.random.
    If seed is an int, return a new RandomState instance seeded with seed.
    If seed is already a RandomState instance, return it.
    Otherwise raise ValueError.
    """
    if seed is None or seed is np.random:
        return np.random.mtrand._rand
    if isinstance(seed, (numbers.Integral, np.integer)):
        return np.random.RandomState(seed)
    if isinstance(seed, np.random.RandomState):
        return seed
    raise ValueError('%r cannot be used to seed a numpy.random.RandomState'
                     ' instance' % seed)

def normalize(A, axis=None):
    """ Normalize the input array so that it sums to 1.

    WARNING: The HMM module and its functions will be removed in 0.17
    as it no longer falls within the project's scope and API.

    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(object):
    """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.

    .. warning::

       The HMM module and its functions will be removed in 0.17
       as it no longer falls within the project's scope and API.

    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

    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, and other characters for subclass-specific
        emmission parameters. 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, and other characters for
        subclass-specific emmission parameters. Defaults to all
        parameters.

    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 publicly.

    def __init__(self, n_components=1, startprob=None, transmat=None,
                 startprob_prior=None, transmat_prior=None,
                 algorithm="viterbi", random_state=None,
                 n_iter=10, thresh=1e-2, params=string.ascii_letters,
                 init_params=string.ascii_letters):

        self.n_components = n_components
        self.n_iter = n_iter
        self.thresh = thresh
        self.params = params
        self.init_params = init_params
        self.startprob_ = startprob
        self.startprob_prior = startprob_prior
        self.transmat_ = transmat
        self.transmat_prior = transmat_prior
        self._algorithm = algorithm
        self.random_state = random_state

    def eval(self, X):
        return self.score_samples(X)

    def score_samples(self, obs):
        """Compute the log probability under the model and compute posteriors.

        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
        --------
        score_samples : 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)
            Sequence of n_features-dimensional data points. Each row
            corresponds to a single point in the sequence.

        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
        --------
        score_samples : Compute the log probability under the model and
            posteriors.

        score : Compute the log probability under the model
        """
        framelogprob = self._compute_log_likelihood(np.asarray(obs))
        viterbi_logprob, state_sequence = self._do_viterbi_pass(framelogprob,
                                                                obs = obs)
        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)
            Sequence of n_features-dimensional data points. Each row
            corresponds to a single point in the sequence.

        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
        --------
        score_samples : Compute the log probability under the model and
            posteriors.
        score : Compute the log probability under the model.
        """
        _, posteriors = self.score_samples(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)
            Sequence of n_features-dimensional data points. Each row
            corresponds to a single point in the sequence.

        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
        --------
        score_samples : 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)
            Sequence of n_features-dimensional data points. Each row
            corresponds to a single point in the sequence.

        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)
            Sequence of n_features-dimensional data points. Each row
            corresponds to a single point in the sequence.

        Returns
        -------
        T : array-like, shape (n, n_components)
            Returns the probability of the sample for each state in the model.
        """
        _, posteriors = self.score_samples(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 range(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)

    def fit(self, obs):
        """Estimate model parameters.

        An initialization step is performed before entering the EM
        algorithm. If you want to avoid this step, pass proper
        ``init_params`` keyword argument to estimator's constructor.

        Parameters
        ----------
        obs : list
            List of array-like observation sequences, each of which
            has shape (n_i, n_features), where n_i is the length of
            the i_th observation.

        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 strengthening the appropriate subclass-specific regularization
        parameter.
        """

        if self.algorithm not in decoder_algorithms:
            self._algorithm = "viterbi"

        self._init(obs, self.init_params)

        logprob = []
        for i in range(copy.deepcopy(self.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, obs = seq)
                bwdlattice = self._do_backward_pass(framelogprob, obs = seq)
                logger.debug("Computing posteriors from forward/backward"
                             " tables. (last unoptimized part that needs"
                             " redoing for both time and memory)")
                gamma = fwdlattice + bwdlattice
                posteriors = np.exp(gamma.T - logsumexp(gamma, axis=1)).T
                logger.debug("Done posteriors")
                curr_logprob += lpr
                self._accumulate_sufficient_statistics(
                    stats, seq, framelogprob, posteriors, fwdlattice,
                    bwdlattice, self.params)
            logprob.append(curr_logprob)
            logMsgString = "BW Iteration %d: LogProb %f" % (i, curr_logprob)
            if i > 0:
                logMsgString += " (delta %f)" % (logprob[-1] - logprob[-2])
            logger.info(logMsgString)

            # Check for convergence.
            if i > 0 and abs(logprob[-1] - logprob[-2]) < self.thresh:
                logger.debug("Coverged.  Logprobhistory: %s" % str(logprob))
                break
            if i == self.n_iter - 1:
                logger.debug("Finished without converging."
                             "  Logprobhistory: %s" % str(logprob))
                break

            # Maximization step
            self._do_mstep(stats, self.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 startprob is None:
            startprob = np.tile(1.0 / self.n_components, self.n_components)
        else:
            startprob = np.asarray(startprob, dtype=np.float)

        # check if there exists a component whose value is exactly zero
        # if so, add a small number and re-normalize
        if not np.alltrue(startprob):
            normalize(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 transmat is None:
            transmat = np.tile(1.0 / self.n_components,
                               (self.n_components, self.n_components))

        # check if there exists a component whose value is exactly zero
        # if so, add a small number and re-normalize
        if not np.alltrue(transmat):
            normalize(transmat, axis=1)

        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, obs = None):
        n_observations, n_components = framelogprob.shape
        state_sequence, logprob = _basehmm._viterbi(
            n_observations, n_components, self._log_startprob,
            self._log_transmat, framelogprob)
        return logprob, state_sequence

    def _do_forward_pass(self, framelogprob, obs = None):
        n_observations, n_components = framelogprob.shape
        fwdlattice = np.zeros((n_observations, n_components))
        _basehmm._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, obs = None):
        n_observations, n_components = framelogprob.shape
        bwdlattice = np.zeros((n_observations, n_components))
        _basehmm._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_.fill(1.0 / self.n_components)
        if 't' in params:
            self.transmat_.fill(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:
            n_observations, n_components = framelogprob.shape
            # when the sample is of length 1, it contains no transitions
            # so there is no reason to update our trans. matrix estimate
            if n_observations > 1:
                lneta = np.zeros((n_observations - 1, n_components, n_components))
                lnP = logsumexp(fwdlattice[-1])
                _basehmm._compute_lneta(n_observations, n_components, fwdlattice,
                                     self._log_transmat, bwdlattice, framelogprob,
                                     lnP, lneta)
                stats["trans"] += np.exp(logsumexp(lneta, 0))

    def _do_mstep(self, stats, params):
        # Based on Huang, Acero, Hon, "Spoken Language Processing",
        # p. 443 - 445
        if self.startprob_prior is None:
            self.startprob_prior = 1.0
        if self.transmat_prior is None:
            self.transmat_prior = 1.0

        if 's' in params:
            self.startprob_ = normalize(
                np.maximum(self.startprob_prior - 1.0 + stats['start'], 1e-20))
        if 't' in params:
            transmat_ = normalize(
                np.maximum(self.transmat_prior - 1.0 + stats['trans'], 1e-20),
                axis=1)
            self.transmat_ = transmat_

            
class MultinomialHMM(BaseHMM):
    """Hidden Markov Model with multinomial (discrete) emissions

    .. warning::

       The HMM module and its functions will be removed in 0.17
       as it no longer falls within the project's scope and API.

    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

    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, 'e' for emmissionprob.
        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, 'e' for emmissionprob.
        Defaults to all parameters.

    Examples
    --------
    >>> from sklearn.hmm import MultinomialHMM
    >>> MultinomialHMM(n_components=2)
    ...                             #doctest: +ELLIPSIS +NORMALIZE_WHITESPACE
    MultinomialHMM(algorithm='viterbi',...

    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,
                 n_iter=10, thresh=1e-2, params=string.ascii_letters,
                 init_params=string.ascii_letters):
        """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,
                          n_iter=n_iter,
                          thresh=thresh,
                          params=params,
                          init_params=init_params)

    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)')

        # check if there exists a component whose value is exactly zero
        # if so, add a small number and re-normalize
        if not np.alltrue(emissionprob):
            normalize(emissionprob)

        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:
            if not hasattr(self, 'n_symbols'):
                symbols = set()
                for o in obs:
                    symbols = symbols.union(set(o))
                self.n_symbols = len(symbols)
            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])

    def _check_input_symbols(self, obs):
        """check if input can be used for Multinomial.fit input must be both
        positive integer array and every element must be continuous.
        e.g. x = [0, 0, 2, 1, 3, 1, 1] is OK and y = [0, 0, 3, 5, 10] not
        """

        symbols = np.asarray(obs).flatten()

        if symbols.dtype.kind != 'i':
            # input symbols must be integer
            return False

        if len(symbols) == 1:
            # input too short
            return False

        if np.any(symbols < 0):
            # input contains negative intiger
            return False

        symbols.sort()
        if np.any(np.diff(symbols) > 1):
            # input is discontinous
            return False

        return True

    def fit(self, obs, **kwargs):
        """Estimate model parameters.

        An initialization step is performed before entering the EM
        algorithm. If you want to avoid this step, pass proper
        ``init_params`` keyword argument to estimator's constructor.

        Parameters
        ----------
        obs : list
            List of array-like observation sequences, each of which
            has shape (n_i, n_features), where n_i is the length of
            the i_th observation.
        """
        err_msg = ("Input must be both positive integer array and "
                   "every element must be continuous, but %s was given.")

        if not self._check_input_symbols(obs):
            raise ValueError(err_msg % obs)

        return BaseHMM.fit(self, obs, **kwargs)