com.numericalmethod.suanshu.stats.hmm.rabiner

Class HmmForwardBackward

java.lang.Object

com.numericalmethod.suanshu.stats.hmm.rabiner.HmmForwardBackward

All Implemented Interfaces:

java.io.Serializable

public class HmmForwardBackward
extends java.lang.Object
implements java.io.Serializable

The forward–backward algorithm is an inference algorithm for hidden Markov models which computes the posterior marginals of all hidden state variables given a sequence of observations. This inference task is usually called smoothing. The algorithm makes use of the principle of dynamic programming to efficiently compute the values that are required to obtain the posterior marginal distributions in two passes. The first pass goes forward in time while the second goes backward in time; hence the name forward–backward algorithm.

The forward probability, α, is the probability of the partial observation sequence until time t and the system in state s_i and time t.

α_t(i) = p(ω₁, ω₂, ... ω_t, q_t = s_i | λ)

The backward probability, β, is the probability of the system in state s_i at time t, and the partial observations from then onward till time t.

β_t(i) = p(ω_t+1, ω_t+2, ... ω_T | q_t = s_i, λ)

See Also:

Wikipedia: Forward–backward algorithm, Serialized Form

Constructor Summary

Constructors

Constructor and Description
HmmForwardBackward(HiddenMarkovModel model) Construct the forward and backward probability matrix generator for an HMM model.

Method Summary

Modifier and Type	Method and Description
Matrix	scaledAlpha(int[] observations) Get the scaled forward probability matrix, dimension (T * N).
Matrix	scaledBeta(int[] observations) Get the scaled backward probability matrix, dimension (T * N).

Methods inherited from class java.lang.Object

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

Constructor Detail

HmmForwardBackward

public HmmForwardBackward(HiddenMarkovModel model)

Construct the forward and backward probability matrix generator for an HMM model.

Parameters:

model - a (discrete) hidden Markov model

Method Detail

scaledAlpha

public Matrix scaledAlpha(int[] observations)

Get the scaled forward probability matrix, dimension (T * N).

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).

Returns:

scaled alpha, the scaled forward probability matrix

scaledBeta

public Matrix scaledBeta(int[] observations)

Get the scaled backward probability matrix, dimension (T * N).

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).

Returns:

scaled beta, the scaled backward probability matrix