Package dev.nm.stat.hmm.discrete

Class BaumWelch

java.lang.Object

dev.nm.stat.markovchain.SimpleMC

dev.nm.stat.hmm.HMMRNG

dev.nm.stat.hmm.HiddenMarkovModel

dev.nm.stat.hmm.discrete.DiscreteHMM

dev.nm.stat.hmm.discrete.BaumWelch

All Implemented Interfaces:

RandomNumberGenerator, Seedable

public class BaumWelch
extends DiscreteHMM

This implementation trains an HMM model by observations using the Baum–Welch algorithm.

See Also:

• • 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

Constructor Summary

Constructors

Constructor	Description
BaumWelch(int[] observations, DiscreteHMM model0, int nIteraions)	Constructs an HMM model by training an initial model using the Baum–Welch algorithm.

Method Summary

Modifier and Type	Method	Description
static Vector[]	gamma(HiddenMarkovModel model, int[] observations, Matrix[] xi)	Gets the (T-1 * N) γ matrix, where the (t, i)-th entry is γt(i).
static DiscreteHMM	train(int[] observations, DiscreteHMM model0)	Constructs a trained (discrete) hidden Markov model, one iteration.
static Matrix[]	xi(HiddenMarkovModel model, int[] observations, ForwardBackwardProcedure fb)	Gets the ξ matrices, where for 1 ≤ t ≤ T - 1, the t-th entry of ξ is an (N * N) matrix, for which the (i, j)-th entry is ξt(i, j).

Methods inherited from class dev.nm.stat.hmm.discrete.DiscreteHMM

B, density, nSymbols

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

BaumWelch

public BaumWelch(int[] observations,
 DiscreteHMM model0,
 int nIteraions)

Constructs an HMM model by training an initial model using the Baum–Welch algorithm.

Parameters:

observations - an integer array of observation symbols (length = T). Each symbol is a positive integer less than or equal to M (the number of observation symbols per state).

model0 - an initial model

nIteraions - the number of iterations

Method Details

train

public static DiscreteHMM train(int[] observations,
 DiscreteHMM model0)

Constructs a trained (discrete) hidden Markov model, one iteration.

Parameters:

observations - an integer array of observation symbols (length = T). Each symbol is a positive integer less than or equal to M (the number of observation symbols per state).

model0 - the initial hidden Markov model

Returns:

a trained (discrete) hidden Markov model

xi

public static Matrix[] xi(HiddenMarkovModel model,
 int[] observations,
 ForwardBackwardProcedure fb)

Gets the ξ matrices, where for 1 ≤ t ≤ T - 1, the t-th entry of ξ is an (N * N) matrix, for which the (i, j)-th entry is ξ_t(i, j). ξ_t(i, j) is the probability of the system being in state s_i at time t and state s_j at time t+1 and the observations, given the model.

ξ_t(i, j) = P(q_t = s_i, q_t+1 = s_j, Ω | λ)

This implementation works for both unscaled and scaled alpha-beta probabilities in terms of transition probability estimation. The actual value for the unscaled fwd-bwd probabilities computed using scaled alpha-beta differ by a factor of L(x) the likelihood of observations. But this term appears in both the numerator and denominator so they cancel out. See eq. 18 in hmm-scaling-implementation.

Parameters:

model - an HMM model

observations - an array of observations (length = T).

fb - the alpha-beta

Returns:

the ξ matrices, one for each time; the 0-th entry is not used to match the time index

gamma

public static Vector[] gamma(HiddenMarkovModel model,
 int[] observations,
 Matrix[] xi)

Gets the (T-1 * N) γ matrix, where the (t, i)-th entry is γ_t(i). γ is the probability of the system in state s_i and the observations, given the model.

γ_t(i) = P(q_t = s_i, Ω | λ)

Parameters:

model - an HMM model

observations - an array of observations (length = T).

xi - the ξ matrices; the 0-th entry is not used to match the time index

Returns:

the gamma matrix