Statistics: hmmviterbi

### Function Reference: `hmmviterbi`

statistics: vpath = hmmviterbi (sequence, transprob, outprob)
statistics: vpath = hmmviterbi (…, `"symbols"`, symbols)
statistics: vpath = hmmviterbi (…, `"statenames"`, statenames)

Viterbi path of a hidden Markov model.

Use the Viterbi algorithm to find the Viterbi path of a hidden Markov model given a sequence of outputs. The model assumes that the generation starts in state `1` at step `0` but does not include step `0` in the generated states and sequence.

### Arguments

- sequence is the vector of length len of given outputs. The outputs must be integers ranging from `1` to `columns (outprob)`.
- transprob is the matrix of transition probabilities of the states. `transprob(i, j)` is the probability of a transition to state `j` given state `i`.
- outprob is the matrix of output probabilities. `outprob(i, j)` is the probability of generating output `j` given state `i`.

### Return values

- vpath is the vector of the same length as sequence of the estimated hidden states. The states are integers ranging from `1` to `columns (transprob)`.

If `"symbols"` is specified, then sequence is expected to be a sequence of the elements of symbols instead of integers ranging from `1` to `columns (outprob)`. symbols can be a cell array.

If `"statenames"` is specified, then the elements of statenames are used for the states in vpath instead of integers ranging from `1` to `columns (transprob)`. statenames can be a cell array.

### Examples

     transprob = [0.8, 0.2; 0.4, 0.6];
     outprob = [0.2, 0.4, 0.4; 0.7, 0.2, 0.1];
     [sequence, states] = hmmgenerate (25, transprob, outprob);
     vpath = hmmviterbi (sequence, transprob, outprob);
     symbols = {"A", "B", "C"};
     statenames = {"One", "Two"};
     [sequence, states] = hmmgenerate (25, transprob, outprob, ...
                          "symbols", symbols, "statenames", statenames);
     vpath = hmmviterbi (sequence, transprob, outprob, ...
             "symbols", symbols, "statenames", statenames);

### 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: hmmviterbi