hmmlearn¶

Simple algorithms and models to learn HMMs (Hidden Markov Models) in Python,
Follows scikit-learn API as close as possible, but adapted to sequence data,
Built on scikit-learn, NumPy, SciPy, and matplotlib,
Open source, commercially usable — BSD license.

User guide: table of contents¶

Tutorial¶

hmmlearn implements the Hidden Markov Models (HMMs). The HMM is a generative probabilistic model, in which a sequence of observable \(\mathbf{X}\) variables is generated by a sequence of internal hidden states \(\mathbf{Z}\). The hidden states are not observed directly. The transitions between hidden states are assumed to have the form of a (first-order) Markov chain. They can be specified by the start probability vector \(\boldsymbol{\pi}\) and a transition probability matrix \(\mathbf{A}\). The emission probability of an observable can be any distribution with parameters \(\boldsymbol{\theta}\) conditioned on the current hidden state. The HMM is completely determined by \(\boldsymbol{\pi}\), \(\mathbf{A}\) and \(\boldsymbol{\theta}\).

There are three fundamental problems for HMMs:

Given the model parameters and observed data, estimate the optimal sequence of hidden states.
Given the model parameters and observed data, calculate the likelihood of the data.
Given just the observed data, estimate the model parameters.

The first and the second problem can be solved by the dynamic programming algorithms known as the Viterbi algorithm and the Forward-Backward algorithm, respectively. The last one can be solved by an iterative Expectation-Maximization (EM) algorithm, known as the Baum-Welch algorithm.

References:

Lawrence R. Rabiner “A tutorial on hidden Markov models and selected applications in speech recognition”, Proceedings of the IEEE 77.2, pp. 257-286, 1989.
Jeff A. Bilmes, “A gentle tutorial of the EM algorithm and its application to parameter estimation for Gaussian mixture and hidden Markov models.”, 1998.

Available models¶

`hmm.GaussianHMM`	Hidden Markov Model with Gaussian emissions.
`hmm.GMMHMM`	Hidden Markov Model with Gaussian mixture emissions.
`hmm.MultinomialHMM`	Hidden Markov Model with multinomial (discrete) emissions

Read on for details on how to implement a HMM with a custom emission probability.

Building HMM and generating samples¶

You can build a HMM instance by passing the parameters described above to the constructor. Then, you can generate samples from the HMM by calling sample.

>>> import numpy as np
>>> from hmmlearn import hmm
>>> np.random.seed(42)
>>>
>>> model = hmm.GaussianHMM(n_components=3, covariance_type="full")
>>> model.startprob_ = np.array([0.6, 0.3, 0.1])
>>> model.transmat_ = np.array([[0.7, 0.2, 0.1],
...                             [0.3, 0.5, 0.2],
...                             [0.3, 0.3, 0.4]])
>>> model.means_ = np.array([[0.0, 0.0], [3.0, -3.0], [5.0, 10.0]])
>>> model.covars_ = np.tile(np.identity(2), (3, 1, 1))
>>> X, Z = model.sample(100)

The transition probability matrix need not to be ergodic. For instance, a left-right HMM can be defined as follows:

>>> lr = hmm.GaussianHMM(n_components=3, covariance_type="diag",
...                      init_params="cm", params="cmt")
>>> lr.startprob_ = np.array([1.0, 0.0, 0.0])
>>> lr.transmat_ = np.array([[0.5, 0.5, 0.0],
...                          [0.0, 0.5, 0.5],
...                          [0.0, 0.0, 1.0]])

If any of the required parameters are missing, sample will raise an exception:

>>> model = hmm.GaussianHMM(n_components=3)
>>> X, Z = model.sample(100)
Traceback (most recent call last):
    ...
sklearn.utils.validation.NotFittedError: This GaussianHMM instance is not fitted yet. Call 'fit' with appropriate arguments before using this method.

Fixing parameters¶

Each HMM parameter has a character code which can be used to customize its initialization and estimation. The EM algorithm needs a starting point to proceed, thus prior to training each parameter is assigned a value either random or computed from the data. It is possible to hook into this process and provide a starting point explicitly. To do so

ensure that the character code for the parameter is missing from init_params and then
set the parameter to the desired value.

For example, consider a HMM with an explicitly initialized transition probability matrix:

>>> model = hmm.GaussianHMM(n_components=3, n_iter=100, init_params="mcs")
>>> model.transmat_ = np.array([[0.7, 0.2, 0.1],
...                             [0.3, 0.5, 0.2],
...                             [0.3, 0.3, 0.4]])

A similar trick applies to parameter estimation. If you want to fix some parameter at a specific value, remove the corresponding character from params and set the parameter value before training.

Examples:

Sampling from HMM

Training HMM parameters and inferring the hidden states¶

You can train an HMM by calling the fit method. The input is a matrix of concatenated sequences of observations (aka samples) along with the lengths of the sequences (see Working with multiple sequences).

Note, since the EM algorithm is a gradient-based optimization method, it will generally get stuck in local optima. You should in general try to run fit with various initializations and select the highest scored model.

The score of the model can be calculated by the score method.

The inferred optimal hidden states can be obtained by calling predict method. The predict method can be specified with a decoder algorithm. Currently the Viterbi algorithm ("viterbi"), and maximum a posteriori estimation ("map") are supported.

This time, the input is a single sequence of observed values. Note, the states in remodel will have a different order than those in the generating model.

>>> remodel = hmm.GaussianHMM(n_components=3, covariance_type="full", n_iter=100)
>>> remodel.fit(X)
GaussianHMM(algorithm='viterbi', ...
>>> Z2 = remodel.predict(X)

Monitoring convergence¶

The number of EM algorithm iterations is upper bounded by the n_iter parameter. The training proceeds until n_iter steps were performed or the change in score is lower than the specified threshold tol. Note, that depending on the data, the EM algorithm may or may not achieve convergence in the given number of steps.

You can use the monitor_ attribute to diagnose convergence:

>>> remodel.monitor_
ConvergenceMonitor(
    history=[...],
    iter=10,
    n_iter=100,
    tol=0.01,
    verbose=False,
)
>>> remodel.monitor_.converged
True

Working with multiple sequences¶

All of the examples so far were using a single sequence of observations. The input format in the case of multiple sequences is a bit involved and is best understood by example.

Consider two 1D sequences:

>>> X1 = [[0.5], [1.0], [-1.0], [0.42], [0.24]]
>>> X2 = [[2.4], [4.2], [0.5], [-0.24]]

To pass both sequences to fit or predict, first concatenate them into a single array and then compute an array of sequence lengths:

>>> X = np.concatenate([X1, X2])
>>> lengths = [len(X1), len(X2)]

Finally, just call the desired method with X and lengths:

>>> hmm.GaussianHMM(n_components=3).fit(X, lengths)
GaussianHMM(algorithm='viterbi', ...

Saving and loading HMM¶

After training, a HMM can be easily persisted for future use with the standard pickle module:

>>> import pickle
>>> with open("filename.pkl", "wb") as file: pickle.dump(remodel, file)
>>> with open("filename.pkl", "rb") as file: pickle.load(file)
GaussianHMM(algorithm='viterbi', ...

Implementing HMMs with custom emission probabilities¶

If you want to implement a custom emission probability (e.g. Poisson), you have to subclass _BaseHMM and override the following methods

`base._BaseHMM._init`(X, lengths)	Initializes model parameters prior to fitting.
`base._BaseHMM._check`()	Validates model parameters prior to fitting.
`base._BaseHMM._generate_sample_from_state`(state)	Generates a random sample from a given component.
`base._BaseHMM._compute_log_likelihood`(X)	Computes per-component log probability under the model.
`base._BaseHMM._initialize_sufficient_statistics`()	Initializes sufficient statistics required for M-step.
`base._BaseHMM._accumulate_sufficient_statistics`(…)	Updates sufficient statistics from a given sample.
`base._BaseHMM._do_mstep`(stats)	Performs the M-step of EM algorithm.

Examples¶

Sampling from HMM

Note

Click here to download the full example code

Sampling from HMM¶

This script shows how to sample points from a Hiden Markov Model (HMM): we use a 4-components with specified mean and covariance.

The plot show the sequence of observations generated with the transitions between them. We can see that, as specified by our transition matrix, there are no transition between component 1 and 3.

print(__doc__)

import numpy as np
import matplotlib.pyplot as plt

from hmmlearn import hmm

Prepare parameters for a 4-components HMM Initial population probability

startprob = np.array([0.6, 0.3, 0.1, 0.0])
# The transition matrix, note that there are no transitions possible
# between component 1 and 3
transmat = np.array([[0.7, 0.2, 0.0, 0.1],
                     [0.3, 0.5, 0.2, 0.0],
                     [0.0, 0.3, 0.5, 0.2],
                     [0.2, 0.0, 0.2, 0.6]])
# The means of each component
means = np.array([[0.0,  0.0],
                  [0.0, 11.0],
                  [9.0, 10.0],
                  [11.0, -1.0]])
# The covariance of each component
covars = .5 * np.tile(np.identity(2), (4, 1, 1))

# Build an HMM instance and set parameters
model = hmm.GaussianHMM(n_components=4, covariance_type="full")

# Instead of fitting it from the data, we directly set the estimated
# parameters, the means and covariance of the components
model.startprob_ = startprob
model.transmat_ = transmat
model.means_ = means
model.covars_ = covars

# Generate samples
X, Z = model.sample(500)

# Plot the sampled data
plt.plot(X[:, 0], X[:, 1], ".-", label="observations", ms=6,
         mfc="orange", alpha=0.7)

# Indicate the component numbers
for i, m in enumerate(means):
    plt.text(m[0], m[1], 'Component %i' % (i + 1),
             size=17, horizontalalignment='center',
             bbox=dict(alpha=.7, facecolor='w'))
plt.legend(loc='best')
plt.show()

_images/sphx_glr_plot_hmm_sampling_001.png

Total running time of the script: ( 0 minutes 0.650 seconds)

Gallery generated by Sphinx-Gallery

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)

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.
bwdlattice (fwdlattice,) – 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, )

_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.

See also

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.

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:	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

See also

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.

See also

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_weight (means_prior,) – Mean and precision of the Normal prior distribtion for means_.
covars_weight (covars_prior,) –
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

transmat_¶

Matrix of transition probabilities between states.

Type:	array, shape (n_components, n_components)

startprob_¶

Initial state occupation distribution.

Type:	array, shape (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_features, n_features)                if "tied",
(n_components, n_features)              if "diag",
(n_components, n_features, n_features)  if "full"

Type:	array

Examples

>>> from hmmlearn.hmm import GaussianHMM
>>> GaussianHMM(n_components=2)
...                             #doctest: +ELLIPSIS +NORMALIZE_WHITESPACE
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.

See also

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.

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:	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

See also

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.

See also

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 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_.
weights_prior (array, shape (n_mix, ), optional) – Parameters of the Dirichlet prior distribution for weights_.
means_weight (means_prior,) – Mean and precision of the Normal prior distribtion for means_.
covars_weight (covars_prior,) –
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_features, n_features)         if "tied",
(n_components, n_mix, n_features)              if "diag",
(n_components, n_mix, n_features, n_features)  if "full"

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.

See also

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.

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:	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

See also

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.

See also

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

transmat_¶

Matrix of transition probabilities between states.

Type:	array, shape (n_components, n_components)

startprob_¶

Initial state occupation distribution.

Type:	array, shape (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)
...                             #doctest: +ELLIPSIS +NORMALIZE_WHITESPACE
MultinomialHMM(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.

See also

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.

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:	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

See also

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.

See also

score: Compute the log probability under the model.
decode: Find most likely state sequence corresponding to X.

hmmlearn Changelog¶

Here you can see the full list of changes between each hmmlearn release.

Version 0.2.2¶

Released on May 5th, 2019.

This version was cut in particular in order to clear up the confusion between the “real” v0.2.1 and the pseudo-0.2.1 that were previously released by various third-party packagers.

Custom ConvergenceMonitors subclasses can be used (#218).
MultinomialHMM now accepts unsigned symbols (#258).
The get_stationary_distribution returns the stationary distribution of the transition matrix (i.e., the rescaled left-eigenvector of the transition matrix that is associated with the eigenvalue 1) (#141).

Version 0.2.1¶

Released on October 17th, 2018.

GMMHMM was fully rewritten (#107).
Fixed underflow when dealing with logs. Thanks to @aubreyli. See PR #105 on GitHub.
Reduced worst-case memory consumption of the M-step from O(S^2 T) to O(S T). See issue #313 on GitHub.
Dropped support for Python 2.6. It is no longer supported by scikit-learn.

Version 0.2.0¶

Released on March 1st, 2016.

The release contains a known bug: fitting GMMHMM with covariance types other than "diag" does not work. This is going to be fixed in the following version. See issue #78 on GitHub for details.

Removed deprecated re-exports from hmmlean.hmm.
Speed up forward-backward algorithms and Viterbi decoding by using Cython typed memoryviews. Thanks to @cfarrow. See PR#82 on GitHub.
Changed the API to accept multiple sequences via a single feature matrix X and an array of sequence lengths. This allowed to use the HMMs as part of scikit-learn Pipeline. The idea was shamelessly plugged from seqlearn package by @larsmans. See issue #29 on GitHub.
Removed params and init_params from internal methods. Accepting these as arguments was redundant and confusing, because both available as instance attributes.
Implemented ConvergenceMonitor, a class for convergence diagnostics. The idea is due to @mvictor212.
Added support for non-fully connected architectures, e.g. left-right HMMs. Thanks to @matthiasplappert. See issue #33 and PR #38 on GitHub.
Fixed normalization of emission probabilities in MultinomialHMM, see issue #19 on GitHub.
GaussianHMM is now initialized from all observations, see issue #1 on GitHub.
Changed the models to do input validation lazily as suggested by the scikit-learn guidelines.
Added min_covar parameter for controlling overfitting of GaussianHMM, see issue #2 on GitHub.
Accelerated M-step fro GaussianHMM with full and tied covariances. See PR #97 on GitHub. Thanks to @anntzer.
Fixed M-step for GMMHMM, which incorrectly expected GMM.score_samples to return log-probabilities. See PR #4 on GitHub for discussion. Thanks to @mvictor212 and @michcio1234.

Version 0.1.1¶

Initial release, released on February 9th 2015.

hmmlearn¶

User guide: table of contents¶

Tutorial¶

Available models¶

Building HMM and generating samples¶

Fixing parameters¶

Training HMM parameters and inferring the hidden states¶

Monitoring convergence¶

Working with multiple sequences¶

Saving and loading HMM¶

Implementing HMMs with custom emission probabilities¶

Examples¶

Sampling from HMM¶

API Reference¶

hmmlearn.base¶

ConvergenceMonitor¶

_BaseHMM¶

hmmlearn.hmm¶

GaussianHMM¶

GMMHMM¶

MultinomialHMM¶

hmmlearn Changelog¶

Version 0.2.2¶

Version 0.2.1¶

Version 0.2.0¶

Version 0.1.1¶

hmmlearn

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