baumWelch {HMM}

Inferring the parameters of a Hidden Markov Model via the Baum-Welch algorithm

Description

For an initial Hidden Markov Model (HMM) and a given sequence of observations, the Baum-Welch algorithm infers optimal parameters to the HMM. Since the Baum-Welch algorithm is a variant of the Expectation-Maximisation algorithm, the algorithm converges to a local solution which might not be the global optimum.

Usage

baumWelch(hmm, observation, maxIterations=100, delta=1E-9, pseudoCount=0)

Arguments

hmm

A Hidden Markov Model.

observation

A sequence of observations.

maxIterations

The maximum number of iterations in the Baum-Welch algorithm.

delta

Additional termination condition, if the transition and emission matrices converge, before reaching the maximum number of iterations (maxIterations). The difference of transition and emission parameters in consecutive iterations must be smaller than delta to terminate the algorithm.

pseudoCount

Adding this amount of pseudo counts in the estimation-step of the Baum-Welch algorithm.

Format

Dimension and Format of the Arguments.

hmm

A valid Hidden Markov Model, for example instantiated by initHMM.

observation

A vector of observations.

Value

Return Values:

hmm

The inferred HMM. The representation is equivalent to the representation in initHMM.

difference

Vector of differences calculated from consecutive transition and emission matrices in each iteration of the Baum-Welch procedure. The difference is the sum of the distances between consecutive transition and emission matrices in the L2-Norm.

Author(s)

Lin Himmelmann <[e-mail]>, Scientific Software Development

References

For details see: Lawrence R. Rabiner: A Tutorial on Hidden Markov Models and Selected Applications in Speech Recognition. Proceedings of the IEEE 77(2) p.257-286, 1989.

See Also

See viterbiTraining.

Examples

# Initial HMM
hmm = initHMM(c("A","B"),c("L","R"),
	transProbs=matrix(c(.9,.1,.1,.9),2),
	emissionProbs=matrix(c(.5,.51,.5,.49),2))
print(hmm)
# Sequence of observation
a = sample(c(rep("L",100),rep("R",300)))
b = sample(c(rep("L",300),rep("R",100)))
observation = c(a,b)
# Baum-Welch
bw = baumWelch(hmm,observation,10)
print(bw$hmm)