com.numericalmethod.suanshu.stats.hmm.mixture

Class HmmBaumWelch

java.lang.Object

com.numericalmethod.suanshu.stats.markovchain.SimpleMC

com.numericalmethod.suanshu.stats.hmm.HiddenMarkovModel

com.numericalmethod.suanshu.stats.hmm.mixture.HiddenMarkovModel

com.numericalmethod.suanshu.stats.hmm.mixture.HmmBaumWelch

All Implemented Interfaces:

RandomNumberGenerator, java.io.Serializable

public class HmmBaumWelch
extends HiddenMarkovModel

The Baum–Welch 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:

• 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."
• W. Zucchini and I. L. MacDonald, "Hidden Markov Models for Time Series: An Introduction Using R," Boca Raton, Florida, CRC Press, 2009.
• L. R. Welch, "Hidden Markov models and the Baum–Welch algorithm," IEEE Information Theory Society Newsletter Volume 53, pp. 1, 10-13, Dec 2003.
• Wikipedia: Baum–Welch algorithm

, Serialized Form

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	HmmBaumWelch.TrainedModel the result of the Baum-Welch algorithm

Constructor Summary

Constructors

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

Method Summary

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

Methods inherited from class com.numericalmethod.suanshu.stats.hmm.mixture.HiddenMarkovModel

density, getDistribution

Methods inherited from class com.numericalmethod.suanshu.stats.hmm.HiddenMarkovModel

next, nextDouble, seed

Methods inherited from class com.numericalmethod.suanshu.stats.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 Detail

HmmBaumWelch

public HmmBaumWelch(double[] observations,
                    HiddenMarkovModel model0,
                    double epsilon,
                    int maxIterations)

Construct 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 Detail

train

public static HmmBaumWelch.TrainedModel train(HiddenMarkovModel model0,
                                              double[] observations)

Construct 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