# API Reference¶

This is the class and function reference of hmmlearn.

Please refer to the full user guide for further details, as the class and function raw specifications may not be enough to give full guidelines on their uses.

## hmmlearn.base¶

### ConvergenceMonitor¶

class hmmlearn.base.ConvergenceMonitor(tol, n_iter, verbose)

Monitors and reports convergence to sys.stderr.

Parameters
• tol (double) – Convergence threshold. EM has converged either if the maximum number of iterations is reached or the log probability improvement between the two consecutive iterations is less than threshold.

• n_iter (int) – Maximum number of iterations to perform.

• verbose (bool) – If True then per-iteration convergence reports are printed, otherwise the monitor is mute.

history

The log probability of the data for the last two training iterations. If the values are not strictly increasing, the model did not converge.

Type

deque

iter

Number of iterations performed while training the model.

Type

int

Examples

Use custom convergence criteria by subclassing ConvergenceMonitor and redefining the converged method. The resulting subclass can be used by creating an instance and pointing a model’s monitor_ attribute to it prior to fitting.

>>> from hmmlearn.base import ConvergenceMonitor
>>> from hmmlearn import hmm
>>>
>>> class ThresholdMonitor(ConvergenceMonitor):
...     @property
...     def converged(self):
...         return (self.iter == self.n_iter or
...                 self.history[-1] >= self.tol)
>>>
>>> model = hmm.GaussianHMM(n_components=2, tol=5, verbose=True)
>>> model.monitor_ = ThresholdMonitor(model.monitor_.tol,
...                                   model.monitor_.n_iter,
...                                   model.monitor_.verbose)

property converged

True if the EM algorithm converged and False otherwise.

report(logprob)

Reports convergence to sys.stderr.

The output consists of three columns: iteration number, log probability of the data at the current iteration and convergence rate. At the first iteration convergence rate is unknown and is thus denoted by NaN.

Parameters

logprob (float) – The log probability of the data as computed by EM algorithm in the current iteration.

### _BaseHMM¶

class hmmlearn.base._BaseHMM(n_components=1, startprob_prior=1.0, transmat_prior=1.0, algorithm='viterbi', random_state=None, n_iter=10, tol=0.01, verbose=False, params='abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ', init_params='abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ')

Base class for Hidden Markov Models.

This class allows for easy evaluation of, sampling from, and maximum a posteriori estimation of the parameters of a HMM.

See the instance documentation for details specific to a particular object.

Parameters
• n_components (int) – Number of states in the model.

• startprob_prior (array, shape (n_components, ), optional) – Parameters of the Dirichlet prior distribution for startprob_.

• transmat_prior (array, shape (n_components, n_components), optional) – Parameters of the Dirichlet prior distribution for each row of the transition probabilities transmat_.

• algorithm (string, optional) – Decoder algorithm. Must be one of “viterbi” or “map”. Defaults to “viterbi”.

• random_state (RandomState or an int seed, optional) – A random number generator instance.

• n_iter (int, optional) – Maximum number of iterations to perform.

• tol (float, optional) – Convergence threshold. EM will stop if the gain in log-likelihood is below this value.

• verbose (bool, optional) – When True per-iteration convergence reports are printed to sys.stderr. You can diagnose convergence via the monitor_ attribute.

• 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 emission 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 emission parameters. Defaults to all parameters.

monitor\_

Monitor object used to check the convergence of EM.

Type

ConvergenceMonitor

startprob\_

Initial state occupation distribution.

Type

array, shape (n_components, )

transmat\_

Matrix of transition probabilities between states.

Type

array, shape (n_components, n_components)

_accumulate_sufficient_statistics(stats, X, framelogprob, posteriors, fwdlattice, bwdlattice)

Updates sufficient statistics from a given sample.

Parameters
• stats (dict) – Sufficient statistics as returned by _initialize_sufficient_statistics().

• X (array, shape (n_samples, n_features)) – Sample sequence.

• framelogprob (array, shape (n_samples, n_components)) – Log-probabilities of each sample under each of the model states.

• posteriors (array, shape (n_samples, n_components)) – Posterior probabilities of each sample being generated by each of the model states.

• fwdlattice (array, shape (n_samples, n_components)) – Log-forward and log-backward probabilities.

• bwdlattice (array, shape (n_samples, n_components)) – Log-forward and log-backward probabilities.

_check()

Validates model parameters prior to fitting.

Raises

ValueError – If any of the parameters are invalid, e.g. if startprob_ don’t sum to 1.

_compute_log_likelihood(X)

Computes per-component log probability under the model.

Parameters

X (array-like, shape (n_samples, n_features)) – Feature matrix of individual samples.

Returns

logprob – Log probability of each sample in X for each of the model states.

Return type

array, shape (n_samples, n_components)

_do_mstep(stats)

Performs the M-step of EM algorithm.

Parameters

stats (dict) – Sufficient statistics updated from all available samples.

_generate_sample_from_state(state, random_state=None)

Generates a random sample from a given component.

Parameters
• state (int) – Index of the component to condition on.

• random_state (RandomState or an int seed) – A random number generator instance. If None, the object’s random_state is used.

Returns

X – A random sample from the emission distribution corresponding to a given component.

Return type

array, shape (n_features, )

_get_n_fit_scalars_per_param()

Return a mapping of fittable parameter name (as in self.params) to the number of corresponding scalar parameters that will actually be fitted.

This is used to detect whether the user did not pass enough data points for a non-degenerate fit.

_init(X, lengths)

Initializes model parameters prior to fitting.

Parameters
• X (array-like, shape (n_samples, n_features)) – Feature matrix of individual samples.

• lengths (array-like of integers, shape (n_sequences, )) – Lengths of the individual sequences in X. The sum of these should be n_samples.

_initialize_sufficient_statistics()

Initializes sufficient statistics required for M-step.

The method is pure, meaning that it doesn’t change the state of the instance. For extensibility computed statistics are stored in a dictionary.

Returns

• nobs (int) – Number of samples in the data.

• start (array, shape (n_components, )) – An array where the i-th element corresponds to the posterior probability of the first sample being generated by the i-th state.

• trans (array, shape (n_components, n_components)) – An array where the (i, j)-th element corresponds to the posterior probability of transitioning between the i-th to j-th states.

decode(X, lengths=None, algorithm=None)

Find most likely state sequence corresponding to X.

Parameters
• X (array-like, shape (n_samples, n_features)) – Feature matrix of individual samples.

• lengths (array-like of integers, shape (n_sequences, ), optional) – Lengths of the individual sequences in X. The sum of these should be n_samples.

• algorithm (string) – Decoder algorithm. Must be one of “viterbi” or “map”. If not given, decoder is used.

Returns

• logprob (float) – Log probability of the produced state sequence.

• state_sequence (array, shape (n_samples, )) – Labels for each sample from X obtained via a given decoder algorithm.

score_samples

Compute the log probability under the model and posteriors.

score

Compute the log probability under the model.

fit(X, lengths=None)

Estimate model parameters.

An initialization step is performed before entering the EM algorithm. If you want to avoid this step for a subset of the parameters, pass proper init_params keyword argument to estimator’s constructor.

Parameters
• X (array-like, shape (n_samples, n_features)) – Feature matrix of individual samples.

• lengths (array-like of integers, shape (n_sequences, )) – Lengths of the individual sequences in X. The sum of these should be n_samples.

Returns

self – Returns self.

Return type

object

get_stationary_distribution()

Compute the stationary distribution of states.

predict(X, lengths=None)

Find most likely state sequence corresponding to X.

Parameters
• X (array-like, shape (n_samples, n_features)) – Feature matrix of individual samples.

• lengths (array-like of integers, shape (n_sequences, ), optional) – Lengths of the individual sequences in X. The sum of these should be n_samples.

Returns

state_sequence – Labels for each sample from X.

Return type

array, shape (n_samples, )

predict_proba(X, lengths=None)

Compute the posterior probability for each state in the model.

Xarray-like, shape (n_samples, n_features)

Feature matrix of individual samples.

lengthsarray-like of integers, shape (n_sequences, ), optional

Lengths of the individual sequences in X. The sum of these should be n_samples.

Returns

posteriors – State-membership probabilities for each sample from X.

Return type

array, shape (n_samples, n_components)

sample(n_samples=1, random_state=None)

Generate random samples from the model.

Parameters
• n_samples (int) – Number of samples to generate.

• random_state (RandomState or an int seed) – A random number generator instance. If None, the object’s random_state is used.

Returns

• X (array, shape (n_samples, n_features)) – Feature matrix.

• state_sequence (array, shape (n_samples, )) – State sequence produced by the model.

score(X, lengths=None)

Compute the log probability under the model.

Parameters
• X (array-like, shape (n_samples, n_features)) – Feature matrix of individual samples.

• lengths (array-like of integers, shape (n_sequences, ), optional) – Lengths of the individual sequences in X. The sum of these should be n_samples.

Returns

logprob – Log likelihood of X.

Return type

float

score_samples

Compute the log probability under the model and posteriors.

decode

Find most likely state sequence corresponding to X.

score_samples(X, lengths=None)

Compute the log probability under the model and compute posteriors.

Parameters
• X (array-like, shape (n_samples, n_features)) – Feature matrix of individual samples.

• lengths (array-like of integers, shape (n_sequences, ), optional) – Lengths of the individual sequences in X. The sum of these should be n_samples.

Returns

• logprob (float) – Log likelihood of X.

• posteriors (array, shape (n_samples, n_components)) – State-membership probabilities for each sample in X.

score

Compute the log probability under the model.

decode

Find most likely state sequence corresponding to X.

## hmmlearn.hmm¶

### GaussianHMM¶

class hmmlearn.hmm.GaussianHMM(n_components=1, covariance_type='diag', min_covar=0.001, startprob_prior=1.0, transmat_prior=1.0, means_prior=0, means_weight=0, covars_prior=0.01, covars_weight=1, algorithm='viterbi', random_state=None, n_iter=10, tol=0.01, verbose=False, params='stmc', init_params='stmc')

Hidden Markov Model with Gaussian emissions.

Parameters
• n_components (int) – Number of states.

• covariance_type (string, optional) –

String describing the type of covariance parameters to use. Must be one of

• ”spherical” — each state uses a single variance value that applies 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, optional) – Floor on the diagonal of the covariance matrix to prevent overfitting. Defaults to 1e-3.

• startprob_prior (array, shape (n_components, ), optional) – Parameters of the Dirichlet prior distribution for startprob_.

• transmat_prior (array, shape (n_components, n_components), optional) – Parameters of the Dirichlet prior distribution for each row of the transition probabilities transmat_.

• means_prior (array, shape (n_components, ), optional) – Mean and precision of the Normal prior distribtion for means_.

• means_weight (array, shape (n_components, ), optional) – Mean and precision of the Normal prior distribtion for means_.

• covars_prior (array, shape (n_components, ), optional) –

Parameters of the prior distribution for the covariance matrix covars_.

If covariance_type is “spherical” or “diag” the prior is the inverse gamma distribution, otherwise — the inverse Wishart distribution.

• covars_weight (array, shape (n_components, ), optional) –

Parameters of the prior distribution for the covariance matrix covars_.

If covariance_type is “spherical” or “diag” the prior is the inverse gamma distribution, otherwise — the inverse Wishart distribution.

• algorithm (string, optional) – Decoder algorithm. Must be one of “viterbi” or”map”. Defaults to “viterbi”.

• random_state (RandomState or an int seed, optional) – A random number generator instance.

• n_iter (int, optional) – Maximum number of iterations to perform.

• tol (float, optional) – Convergence threshold. EM will stop if the gain in log-likelihood is below this value.

• verbose (bool, optional) – When True per-iteration convergence reports are printed to sys.stderr. You can diagnose convergence via the monitor_ attribute.

• 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. 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. Defaults to all parameters.

n_features

Dimensionality of the Gaussian emissions.

Type

int

monitor\_

Monitor object used to check the convergence of EM.

Type

ConvergenceMonitor

startprob\_

Initial state occupation distribution.

Type

array, shape (n_components, )

transmat\_

Matrix of transition probabilities between states.

Type

array, shape (n_components, n_components)

means\_

Mean parameters for each state.

Type

array, shape (n_components, n_features)

covars\_

Covariance parameters for each state.

The shape depends on covariance_type:

(n_components, )                        if "spherical",
(n_components, n_features)              if "diag",
(n_components, n_features, n_features)  if "full"
(n_features, n_features)                if "tied",

Type

array

Examples

>>> from hmmlearn.hmm import GaussianHMM
>>> GaussianHMM(n_components=2)
GaussianHMM(algorithm='viterbi',...

decode(X, lengths=None, algorithm=None)

Find most likely state sequence corresponding to X.

Parameters
• X (array-like, shape (n_samples, n_features)) – Feature matrix of individual samples.

• lengths (array-like of integers, shape (n_sequences, ), optional) – Lengths of the individual sequences in X. The sum of these should be n_samples.

• algorithm (string) – Decoder algorithm. Must be one of “viterbi” or “map”. If not given, decoder is used.

Returns

• logprob (float) – Log probability of the produced state sequence.

• state_sequence (array, shape (n_samples, )) – Labels for each sample from X obtained via a given decoder algorithm.

score_samples

Compute the log probability under the model and posteriors.

score

Compute the log probability under the model.

fit(X, lengths=None)

Estimate model parameters.

An initialization step is performed before entering the EM algorithm. If you want to avoid this step for a subset of the parameters, pass proper init_params keyword argument to estimator’s constructor.

Parameters
• X (array-like, shape (n_samples, n_features)) – Feature matrix of individual samples.

• lengths (array-like of integers, shape (n_sequences, )) – Lengths of the individual sequences in X. The sum of these should be n_samples.

Returns

self – Returns self.

Return type

object

get_stationary_distribution()

Compute the stationary distribution of states.

predict(X, lengths=None)

Find most likely state sequence corresponding to X.

Parameters
• X (array-like, shape (n_samples, n_features)) – Feature matrix of individual samples.

• lengths (array-like of integers, shape (n_sequences, ), optional) – Lengths of the individual sequences in X. The sum of these should be n_samples.

Returns

state_sequence – Labels for each sample from X.

Return type

array, shape (n_samples, )

predict_proba(X, lengths=None)

Compute the posterior probability for each state in the model.

Xarray-like, shape (n_samples, n_features)

Feature matrix of individual samples.

lengthsarray-like of integers, shape (n_sequences, ), optional

Lengths of the individual sequences in X. The sum of these should be n_samples.

Returns

posteriors – State-membership probabilities for each sample from X.

Return type

array, shape (n_samples, n_components)

sample(n_samples=1, random_state=None)

Generate random samples from the model.

Parameters
• n_samples (int) – Number of samples to generate.

• random_state (RandomState or an int seed) – A random number generator instance. If None, the object’s random_state is used.

Returns

• X (array, shape (n_samples, n_features)) – Feature matrix.

• state_sequence (array, shape (n_samples, )) – State sequence produced by the model.

score(X, lengths=None)

Compute the log probability under the model.

Parameters
• X (array-like, shape (n_samples, n_features)) – Feature matrix of individual samples.

• lengths (array-like of integers, shape (n_sequences, ), optional) – Lengths of the individual sequences in X. The sum of these should be n_samples.

Returns

logprob – Log likelihood of X.

Return type

float

score_samples

Compute the log probability under the model and posteriors.

decode

Find most likely state sequence corresponding to X.

score_samples(X, lengths=None)

Compute the log probability under the model and compute posteriors.

Parameters
• X (array-like, shape (n_samples, n_features)) – Feature matrix of individual samples.

• lengths (array-like of integers, shape (n_sequences, ), optional) – Lengths of the individual sequences in X. The sum of these should be n_samples.

Returns

• logprob (float) – Log likelihood of X.

• posteriors (array, shape (n_samples, n_components)) – State-membership probabilities for each sample in X.

score

Compute the log probability under the model.

decode

Find most likely state sequence corresponding to X.

### GMMHMM¶

class hmmlearn.hmm.GMMHMM(n_components=1, n_mix=1, min_covar=0.001, 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=0.01, verbose=False, params='stmcw', init_params='stmcw')

Hidden Markov Model with Gaussian mixture emissions.

Parameters
• n_components (int) – Number of states in the model.

• n_mix (int) – Number of states in the GMM.

• covariance_type (string, optional) –

String describing the type of covariance parameters to use. Must be one of

• ”spherical” — each state uses a single variance value that applies to all features.

• ”diag” — each state uses a diagonal covariance matrix.

• ”full” — each state uses a full (i.e. unrestricted) covariance matrix.

• ”tied” — all mixture components of each state use the same full covariance matrix (note that this is not the same as for GaussianHMM).

Defaults to “diag”.

• min_covar (float, optional) – Floor on the diagonal of the covariance matrix to prevent overfitting. Defaults to 1e-3.

• startprob_prior (array, shape (n_components, ), optional) – Parameters of the Dirichlet prior distribution for startprob_.

• transmat_prior (array, shape (n_components, n_components), optional) – Parameters of the Dirichlet prior distribution for each row of the transition probabilities transmat_.

• weights_prior (array, shape (n_mix, ), optional) – Parameters of the Dirichlet prior distribution for weights_.

• means_prior (array, shape (n_mix, ), optional) – Mean and precision of the Normal prior distribtion for means_.

• means_weight (array, shape (n_mix, ), optional) – Mean and precision of the Normal prior distribtion for means_.

• covars_prior (array, shape (n_mix, ), optional) –

Parameters of the prior distribution for the covariance matrix covars_.

If covariance_type is “spherical” or “diag” the prior is the inverse gamma distribution, otherwise — the inverse Wishart distribution.

• covars_weight (array, shape (n_mix, ), optional) –

Parameters of the prior distribution for the covariance matrix covars_.

If covariance_type is “spherical” or “diag” the prior is the inverse gamma distribution, otherwise — the inverse Wishart distribution.

• algorithm (string, optional) – Decoder algorithm. Must be one of “viterbi” or “map”. Defaults to “viterbi”.

• random_state (RandomState or an int seed, optional) – A random number generator instance.

• n_iter (int, optional) – Maximum number of iterations to perform.

• tol (float, optional) – Convergence threshold. EM will stop if the gain in log-likelihood is below this value.

• verbose (bool, optional) – When True per-iteration convergence reports are printed to sys.stderr. You can diagnose convergence via the monitor_ attribute.

• 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, ‘c’ for covars, and ‘w’ for GMM mixing weights. Defaults to all parameters.

• 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, and ‘w’ for GMM mixing weights. Defaults to all parameters.

monitor\_

Monitor object used to check the convergence of EM.

Type

ConvergenceMonitor

startprob\_

Initial state occupation distribution.

Type

array, shape (n_components, )

transmat\_

Matrix of transition probabilities between states.

Type

array, shape (n_components, n_components)

weights\_

Mixture weights for each state.

Type

array, shape (n_components, n_mix)

means\_

Mean parameters for each mixture component in each state.

Type

array, shape (n_components, n_mix)

covars\_

Covariance parameters for each mixture components in each state.

The shape depends on covariance_type:

(n_components, n_mix)                          if "spherical",
(n_components, n_mix, n_features)              if "diag",
(n_components, n_mix, n_features, n_features)  if "full"
(n_components, n_features, n_features)         if "tied",

Type

array

decode(X, lengths=None, algorithm=None)

Find most likely state sequence corresponding to X.

Parameters
• X (array-like, shape (n_samples, n_features)) – Feature matrix of individual samples.

• lengths (array-like of integers, shape (n_sequences, ), optional) – Lengths of the individual sequences in X. The sum of these should be n_samples.

• algorithm (string) – Decoder algorithm. Must be one of “viterbi” or “map”. If not given, decoder is used.

Returns

• logprob (float) – Log probability of the produced state sequence.

• state_sequence (array, shape (n_samples, )) – Labels for each sample from X obtained via a given decoder algorithm.

score_samples

Compute the log probability under the model and posteriors.

score

Compute the log probability under the model.

fit(X, lengths=None)

Estimate model parameters.

An initialization step is performed before entering the EM algorithm. If you want to avoid this step for a subset of the parameters, pass proper init_params keyword argument to estimator’s constructor.

Parameters
• X (array-like, shape (n_samples, n_features)) – Feature matrix of individual samples.

• lengths (array-like of integers, shape (n_sequences, )) – Lengths of the individual sequences in X. The sum of these should be n_samples.

Returns

self – Returns self.

Return type

object

get_stationary_distribution()

Compute the stationary distribution of states.

predict(X, lengths=None)

Find most likely state sequence corresponding to X.

Parameters
• X (array-like, shape (n_samples, n_features)) – Feature matrix of individual samples.

• lengths (array-like of integers, shape (n_sequences, ), optional) – Lengths of the individual sequences in X. The sum of these should be n_samples.

Returns

state_sequence – Labels for each sample from X.

Return type

array, shape (n_samples, )

predict_proba(X, lengths=None)

Compute the posterior probability for each state in the model.

Xarray-like, shape (n_samples, n_features)

Feature matrix of individual samples.

lengthsarray-like of integers, shape (n_sequences, ), optional

Lengths of the individual sequences in X. The sum of these should be n_samples.

Returns

posteriors – State-membership probabilities for each sample from X.

Return type

array, shape (n_samples, n_components)

sample(n_samples=1, random_state=None)

Generate random samples from the model.

Parameters
• n_samples (int) – Number of samples to generate.

• random_state (RandomState or an int seed) – A random number generator instance. If None, the object’s random_state is used.

Returns

• X (array, shape (n_samples, n_features)) – Feature matrix.

• state_sequence (array, shape (n_samples, )) – State sequence produced by the model.

score(X, lengths=None)

Compute the log probability under the model.

Parameters
• X (array-like, shape (n_samples, n_features)) – Feature matrix of individual samples.

• lengths (array-like of integers, shape (n_sequences, ), optional) – Lengths of the individual sequences in X. The sum of these should be n_samples.

Returns

logprob – Log likelihood of X.

Return type

float

score_samples

Compute the log probability under the model and posteriors.

decode

Find most likely state sequence corresponding to X.

score_samples(X, lengths=None)

Compute the log probability under the model and compute posteriors.

Parameters
• X (array-like, shape (n_samples, n_features)) – Feature matrix of individual samples.

• lengths (array-like of integers, shape (n_sequences, ), optional) – Lengths of the individual sequences in X. The sum of these should be n_samples.

Returns

• logprob (float) – Log likelihood of X.

• posteriors (array, shape (n_samples, n_components)) – State-membership probabilities for each sample in X.

score

Compute the log probability under the model.

decode

Find most likely state sequence corresponding to X.

### MultinomialHMM¶

class hmmlearn.hmm.MultinomialHMM(n_components=1, startprob_prior=1.0, transmat_prior=1.0, algorithm='viterbi', random_state=None, n_iter=10, tol=0.01, verbose=False, params='ste', init_params='ste')

Hidden Markov Model with multinomial (discrete) emissions.

Parameters
• n_components (int) – Number of states.

• startprob_prior (array, shape (n_components, ), optional) – Parameters of the Dirichlet prior distribution for startprob_.

• transmat_prior (array, shape (n_components, n_components), optional) – Parameters of the Dirichlet prior distribution for each row of the transition probabilities transmat_.

• algorithm (string, optional) – Decoder algorithm. Must be one of “viterbi” or “map”. Defaults to “viterbi”.

• random_state (RandomState or an int seed, optional) – A random number generator instance.

• n_iter (int, optional) – Maximum number of iterations to perform.

• tol (float, optional) – Convergence threshold. EM will stop if the gain in log-likelihood is below this value.

• verbose (bool, optional) – When True per-iteration convergence reports are printed to sys.stderr. You can diagnose convergence via the monitor_ attribute.

• 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 emissionprob. 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 emissionprob. Defaults to all parameters.

n_features

Number of possible symbols emitted by the model (in the samples).

Type

int

monitor\_

Monitor object used to check the convergence of EM.

Type

ConvergenceMonitor

startprob\_

Initial state occupation distribution.

Type

array, shape (n_components, )

transmat\_

Matrix of transition probabilities between states.

Type

array, shape (n_components, n_components)

emissionprob\_

Probability of emitting a given symbol when in each state.

Type

array, shape (n_components, n_features)

Examples

>>> from hmmlearn.hmm import MultinomialHMM
>>> MultinomialHMM(n_components=2)
MultinomialHMM(algorithm='viterbi',...

decode(X, lengths=None, algorithm=None)

Find most likely state sequence corresponding to X.

Parameters
• X (array-like, shape (n_samples, 1)) – Feature matrix of individual samples.

• lengths (array-like of integers, shape (n_sequences, ), optional) – Lengths of the individual sequences in X. The sum of these should be n_samples.

• algorithm (string) – Decoder algorithm. Must be one of “viterbi” or “map”. If not given, decoder is used.

Returns

• logprob (float) – Log probability of the produced state sequence.

• state_sequence (array, shape (n_samples, )) – Labels for each sample from X obtained via a given decoder algorithm.

score_samples

Compute the log probability under the model and posteriors.

score

Compute the log probability under the model.

Notes

Unlike other HMM classes, MultinomialHMM X arrays have shape (n_samples, 1) (instead of (n_samples, n_features)). Consider using sklearn.preprocessing.LabelEncoder to transform your input to the right format.

fit(X, lengths=None)

Estimate model parameters.

An initialization step is performed before entering the EM algorithm. If you want to avoid this step for a subset of the parameters, pass proper init_params keyword argument to estimator’s constructor.

Parameters
• X (array-like, shape (n_samples, 1)) – Feature matrix of individual samples.

• lengths (array-like of integers, shape (n_sequences, )) – Lengths of the individual sequences in X. The sum of these should be n_samples.

Returns

self – Returns self.

Return type

object

Notes

Unlike other HMM classes, MultinomialHMM X arrays have shape (n_samples, 1) (instead of (n_samples, n_features)). Consider using sklearn.preprocessing.LabelEncoder to transform your input to the right format.

get_stationary_distribution()

Compute the stationary distribution of states.

predict(X, lengths=None)

Find most likely state sequence corresponding to X.

Parameters
• X (array-like, shape (n_samples, 1)) – Feature matrix of individual samples.

• lengths (array-like of integers, shape (n_sequences, ), optional) – Lengths of the individual sequences in X. The sum of these should be n_samples.

Returns

state_sequence – Labels for each sample from X.

Return type

array, shape (n_samples, )

Notes

Unlike other HMM classes, MultinomialHMM X arrays have shape (n_samples, 1) (instead of (n_samples, n_features)). Consider using sklearn.preprocessing.LabelEncoder to transform your input to the right format.

predict_proba(X, lengths=None)

Compute the posterior probability for each state in the model.

Xarray-like, shape (n_samples, 1)

Feature matrix of individual samples.

lengthsarray-like of integers, shape (n_sequences, ), optional

Lengths of the individual sequences in X. The sum of these should be n_samples.

Returns

posteriors – State-membership probabilities for each sample from X.

Return type

array, shape (n_samples, n_components)

Notes

Unlike other HMM classes, MultinomialHMM X arrays have shape (n_samples, 1) (instead of (n_samples, n_features)). Consider using sklearn.preprocessing.LabelEncoder to transform your input to the right format.

sample(n_samples=1, random_state=None)

Generate random samples from the model.

Parameters
• n_samples (int) – Number of samples to generate.

• random_state (RandomState or an int seed) – A random number generator instance. If None, the object’s random_state is used.

Returns

• X (array, shape (n_samples, 1)) – Feature matrix.

• state_sequence (array, shape (n_samples, )) – State sequence produced by the model.

Notes

Unlike other HMM classes, MultinomialHMM X arrays have shape (n_samples, 1) (instead of (n_samples, n_features)). Consider using sklearn.preprocessing.LabelEncoder to transform your input to the right format.

score(X, lengths=None)

Compute the log probability under the model.

Parameters
• X (array-like, shape (n_samples, 1)) – Feature matrix of individual samples.

• lengths (array-like of integers, shape (n_sequences, ), optional) – Lengths of the individual sequences in X. The sum of these should be n_samples.

Returns

logprob – Log likelihood of X.

Return type

float

score_samples

Compute the log probability under the model and posteriors.

decode

Find most likely state sequence corresponding to X.

Notes

Unlike other HMM classes, MultinomialHMM X arrays have shape (n_samples, 1) (instead of (n_samples, n_features)). Consider using sklearn.preprocessing.LabelEncoder to transform your input to the right format.

score_samples(X, lengths=None)

Compute the log probability under the model and compute posteriors.

Parameters
• X (array-like, shape (n_samples, 1)) – Feature matrix of individual samples.

• lengths (array-like of integers, shape (n_sequences, ), optional) – Lengths of the individual sequences in X. The sum of these should be n_samples.

Returns

• logprob (float) – Log likelihood of X.

• posteriors (array, shape (n_samples, n_components)) – State-membership probabilities for each sample in X.

score
decode
Find most likely state sequence corresponding to X.
Unlike other HMM classes, MultinomialHMM X arrays have shape (n_samples, 1) (instead of (n_samples, n_features)). Consider using sklearn.preprocessing.LabelEncoder` to transform your input to the right format.