Given one or more observed output sequences and initial guesses for the transition and output probability matrices, hmmtrain finds maximum likelihood estimates of the two matrices using the Baum-Welch algorithm (the default) or Viterbi training. The model assumes that the generation starts in state 1 at step 0 but does not include step 0 in the sequence.

Arguments

• sequence is a vector of a sequence of given outputs, or, for training from several sequences, a cell array of such vectors or a matrix whose rows are individual sequences. The outputs must be integers ranging from 1 to columns (outguess).
• transguess is the initial guess for the matrix of transition probabilities. transguess(i, j) is the probability of a transition to state j given state i.
• outguess is the initial guess for the matrix of output probabilities. outguess(i, j) is the probability of generating output j given state i.

Return values

• esttr is the estimated matrix of transition probabilities.
• estout is the estimated matrix of output probabilities.

Name-Value pair arguments

• "algorithm" selects the training algorithm, either "BaumWelch" (default) or "Viterbi". "BaumWelch" performs the standard forward-backward re-estimation and is recommended for most uses. "Viterbi" performs segmental (hard) re-estimation from the most likely state path of each sequence; it is faster but only approximates the maximum-likelihood estimate.
• "symbols" specifies the possible outputs. If given, sequence is expected to hold the elements of symbols instead of integers. symbols can be a cell array.
• "tolerance" is the convergence tolerance (default 1e-6). The algorithm terminates when the change in the log-likelihood and in both estimated matrices falls below tol.
• "maxiterations" is the maximum number of iterations (default 500). A warning is issued if the algorithm has not converged within this many iterations.
• "pseudotransitions" and "pseudoemissions" supply pseudo-count matrices for Viterbi training, used to keep transitions or outputs that are very unlikely to occur from collapsing to zero probability.
• "verbose", when true, prints the log-likelihood and the change in the estimates at each iteration.

Examples

 transprob = [0.8, 0.2; 0.4, 0.6];
 outprob = [0.2, 0.4, 0.4; 0.7, 0.2, 0.1];
 sequence = hmmgenerate (100, transprob, outprob);
 transguess = [0.6, 0.4; 0.5, 0.5];
 outguess = [0.3, 0.3, 0.4; 0.5, 0.3, 0.2];
 [esttr, estout] = hmmtrain (sequence, transguess, outguess);

Two results of Viterbi training differ from MATLAB’s, deliberately.

Given several sequences, the counts of every sequence are pooled and normalized once, so a sequence contributes in proportion to its length. MATLAB normalizes each sequence separately and averages the results, which weights an eight-symbol sequence as heavily as a twenty-four-symbol one and is not the maximum likelihood estimate. Its own Baum-Welch pools expected counts, as both algorithms do here.

Given "pseudotransitions" or "pseudoemissions", the pseudo-counts are added to the counted transitions and outputs, once per iteration, before the row is normalized. MATLAB does the same on its first iteration; from its second it adds them to an estimate that has already been normalized, so its iterate mixes counts with probabilities and is no longer a count matrix of any state path.

References

1. Wendy L. Martinez and Angel R. Martinez. Computational Statistics Handbook with MATLAB. Appendix E, pages 547-557, Chapman & Hall/CRC, 2001.
2. Lawrence R. Rabiner. A Tutorial on Hidden Markov Models and Selected Applications in Speech Recognition. Proceedings of the IEEE, 77(2), pages 257-286, February 1989.

Source Code: hmmtrain