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# hmmtrain

Hidden Markov model parameter estimates from emissions

## Syntax

[ESTTR,ESTEMIT] = hmmtrain(seq,TRGUESS,EMITGUESS)
hmmtrain(...,'Algorithm',algorithm)
hmmtrain(...,'Symbols',SYMBOLS)
hmmtrain(...,'Tolerance',tol)
hmmtrain(...,'Maxiterations',maxiter)
hmmtrain(...,'Verbose',true)
hmmtrain(...,'Pseudoemissions',PSEUDOE)
hmmtrain(...,'Pseudotransitions',PSEUDOTR)

## Description

[ESTTR,ESTEMIT] = hmmtrain(seq,TRGUESS,EMITGUESS) estimates the transition and emission probabilities for a hidden Markov model using the Baum-Welch algorithm. seq can be a row vector containing a single sequence, a matrix with one row per sequence, or a cell array with each cell containing a sequence. TRGUESS and EMITGUESS are initial estimates of the transition and emission probability matrices. TRGUESS(i,j) is the estimated probability of transition from state i to state j. EMITGUESS(i,k) is the estimated probability that symbol k is emitted from state i.

hmmtrain(...,'Algorithm',algorithm) specifies the training algorithm. algorithm can be either 'BaumWelch' or 'Viterbi'. The default algorithm is 'BaumWelch'.

hmmtrain(...,'Symbols',SYMBOLS) specifies the symbols that are emitted. SYMBOLS can be a numeric array or a cell array of the names of the symbols. The default symbols are integers 1 through N, where N is the number of possible emissions.

hmmtrain(...,'Tolerance',tol) specifies the tolerance used for testing convergence of the iterative estimation process. The default tolerance is 1e-4.

hmmtrain(...,'Maxiterations',maxiter) specifies the maximum number of iterations for the estimation process. The default maximum is 100.

hmmtrain(...,'Verbose',true) returns the status of the algorithm at each iteration.

hmmtrain(...,'Pseudoemissions',PSEUDOE) specifies pseudocount emission values for the Viterbi training algorithm. Use this argument to avoid zero probability estimates for emissions with very low probability that might not be represented in the sample sequence. PSEUDOE should be a matrix of size m-by-n, where m is the number of states in the hidden Markov model and n is the number of possible emissions. If the ik emission does not occur in seq, you can set PSEUDOE(i,k) to be a positive number representing an estimate of the expected number of such emissions in the sequence seq.

hmmtrain(...,'Pseudotransitions',PSEUDOTR) specifies pseudocount transition values for the Viterbi training algorithm. Use this argument to avoid zero probability estimates for transitions with very low probability that might not be represented in the sample sequence. PSEUDOTR should be a matrix of size m-by-m, where m is the number of states in the hidden Markov model. If the ij transition does not occur in states, you can set PSEUDOTR(i,j) to be a positive number representing an estimate of the expected number of such transitions in the sequence states.

If you know the states corresponding to the sequences, use hmmestimate to estimate the model parameters.

### Tolerance

The input argument 'tolerance' controls how many steps the hmmtrain algorithm executes before the function returns an answer. The algorithm terminates when all of the following three quantities are less than the value that you specify for tolerance:

• The log likelihood that the input sequence seq is generated by the currently estimated values of the transition and emission matrices

• The change in the norm of the transition matrix, normalized by the size of the matrix

• The change in the norm of the emission matrix, normalized by the size of the matrix

The default value of 'tolerance' is .0001. Increasing the tolerance decreases the number of steps the hmmtrain algorithm executes before it terminates.

### maxiterations

The maximum number of iterations, 'maxiterations', controls the maximum number of steps the algorithm executes before it terminates. If the algorithm executes maxiter iterations before reaching the specified tolerance, the algorithm terminates and the function returns a warning. If this occurs, you can increase the value of 'maxiterations' to make the algorithm reach the desired tolerance before terminating.

## Examples

```trans = [0.95,0.05;
0.10,0.90];
emis = [1/6, 1/6, 1/6, 1/6, 1/6, 1/6;
1/10, 1/10, 1/10, 1/10, 1/10, 1/2];

seq1 = hmmgenerate(100,trans,emis);
seq2 = hmmgenerate(200,trans,emis);
seqs = {seq1,seq2};
[estTR,estE] = hmmtrain(seqs,trans,emis);```

## References

[1] Durbin, R., S. Eddy, A. Krogh, and G. Mitchison. Biological Sequence Analysis. Cambridge, UK: Cambridge University Press, 1998.

## See Also

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