Package dev.nm.stat.hmm.mixture

Class MixtureHMMEM

java.lang.Object

dev.nm.stat.markovchain.SimpleMC

dev.nm.stat.hmm.HMMRNG

dev.nm.stat.hmm.HiddenMarkovModel

dev.nm.stat.hmm.mixture.MixtureHMM

dev.nm.stat.hmm.mixture.MixtureHMMEM

All Implemented Interfaces:

RandomNumberGenerator, Seedable

public class MixtureHMMEM
extends MixtureHMM

The EM algorithm is used to find the unknown parameters of a hidden Markov model (HMM) by making use of the forward-backward algorithm. It does the following.

• the E step: Compute the conditional expectations given the observations and the current estimates of the parameters.
• the M step: Maximize, with respect to the estimated parameters and the data set, log-likelihood.

These two steps are repeated until some convergence criterion has been satisfied.

See Also:

• • W. Zucchini and I. L. MacDonald, "Hidden Markov Models for Time Series: An Introduction Using R," Boca Raton, Florida, CRC Press, 2009.
  • L. R. Rabiner, "A tutorial on hidden Markov models and selected applications in speech recognition," Proceedings of the IEEE, Volume: 77, Issue:2, 257 - 286, Feb 1989."

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static class	MixtureHMMEM.TrainedModel	the result of the EM algorithm

Constructor Summary

Constructors

Constructor	Description
MixtureHMMEM(double[] observations, MixtureHMM model0, double epsilon, int maxIterations)	Constructs a mixture HMM model by training an initial model using the Baum-Welch algorithm.

Method Summary

Modifier and Type	Method	Description
static MixtureHMMEM.TrainedModel	train(MixtureHMM model0, double[] observations)	Constructs a trained mixture hidden Markov model, one iteration.

Methods inherited from class dev.nm.stat.hmm.mixture.MixtureHMM

density, getDistribution

Methods inherited from class dev.nm.stat.hmm.HiddenMarkovModel

logProbability, logProbability, logProbability

Methods inherited from class dev.nm.stat.hmm.HMMRNG

next, nextDouble, seed

Methods inherited from class dev.nm.stat.markovchain.SimpleMC

A, bin, getStationaryProbabilities, nextState, nStates, PI

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Details

MixtureHMMEM

public MixtureHMMEM(double[] observations,
 MixtureHMM model0,
 double epsilon,
 int maxIterations)

Constructs a mixture HMM model by training an initial model using the Baum-Welch algorithm.

Parameters:

observations - the observations

model0 - an initial model

epsilon - a precision parameter: when a number |x| ≤ ε, it is considered 0

maxIterations - the maximum number of iterations

Method Details

train

public static MixtureHMMEM.TrainedModel train(MixtureHMM model0,
 double[] observations)

Constructs a trained mixture hidden Markov model, one iteration.

Parameters:

model0 - the initial hidden Markov model

observations - the observations

Returns:

a trained mixture hidden Markov model