hmm transition matrix estimation

2
votes

In the context of a quantum physics experiment, I am interested in estimating some parameters of the hidden Markov model describing my experiments. I am aware of the Baum-Welch algorithm for estimating all parameters of a hmm. I am, however, only interested in estimating the transition matrix as I have additional data for estimating the emission matrix. What is the best way to proceed? Can I use the Baum-Welch algorithm for updating only the transition matrix while keeping the emission matrix fixed or is there a better approach?

[the hmm I am interested one, has only two hidden states and two (or four) output states.]

1
algorithmhidden-markov-models
The Baum-Welch algorithm does not require you to estimate the emission matrix from the data if you already know what it is. - mcdowella
thanks for the reply. Are are also other ways of restraining parameters, like for a example in a case of a hidden Markov model with two states, 'a' and 'b', where one would like to estimate the transition probability p(a->b) with the constraint that p(a->b)=p(b->a)? - Christian
Sounds OK, but check that e.g. en.wikipedia.org/wiki/… still applies. If you find a theta such that Q(theta| theta(t)) >= Q(theta(t)|theta(t)) then the proof says that L(theta) >= L(theta(t)) - which is the EM proof, that your modified value of theta provides a log likelihood is at least as good as the one given by the theta(t) you started from. If you have a constraint such as p(a->b)=p(b->a) you are probably OK as long as you maximize Q() subject to the constraint and start from a point where the constraint holds. - mcdowella

1 Answers

0
votes

If you know the emissions distribution you can decode the sequence of states (assuming uniform transition matrix) and feed back the observed decoded transition matrix to the model and repeat until the transition matrix is self consistent.