Hidden Markov - Inferring the transition and emission matrices as well as state?

MartinGale7 · July 9th, 2013, 12:55 pm

I've been spending a bit of time looking into using Forward-Backward algorithms to solve Hidden Markov problems. All of the examples I've seen assume that transition and emission matrices are known in advance. Given these two matrices, boundary conditions and a time series of observations, we can estimate the probability of the 'hidden' state at each point in time.My question is, if we don't have the transition and emission matrices in advance, can we infer them from the data too?

Alan · July 9th, 2013, 2:05 pm

Generally, the right order of things is:1. Parameterize the HMM 2. Estimate the parameters via maximum likelihood3. Finally, estimate the states using the forward-backward relations.Since you already have done 3, you've coded the likelihood, as it follows immediately from the forward recursion.Google some intro on HMM's for details.

acastaldo · July 9th, 2013, 8:30 pm

Quote if we don't have the transition and emission matrices in advance, can we infer them from the data too?In voice recognition applications, the matrices are estimated by analzying a "corpus" of utterances and determining for example how often the sound "ph-" is followed by "-ish" or "-one" or "-uck" and so forth and assigning probabilities accordingly.

rusti999 · July 17th, 2013, 5:57 pm

QuoteMy question is, if we don't have the transition and emission matrices in advance, can we infer them from the data too?Yes, use Baum-Welch algorithm. It's basically a type of EM (expectation maximization) algorithm, so you'll get the maximum likelihood estimates of the transition and emission matrices.