MAP segmentation in Bayesian hidden Markov models: a case study

Abstract

We consider the problem of estimating the maximum posterior probability (MAP) state sequence for a finite state and finite emission alphabet hidden Markov model (HMM) in the Bayesian setup, where both emission and transition matrices have Dirichlet priors. We study a training set consisting of thousands of protein alignment pairs. The training data is used to set the prior hyperparameters for Bayesian MAP segmentation. Since the Viterbi algorithm is not applicable any more, there is no simple procedure to find the MAP path, and several iterative algorithms are considered and compared. The main goal of the paper is to test the Bayesian setup against the frequentist one, where the parameters of HMM are estimated using the training data.

Keywords:

• Hidden Markov model
• Bayesian inference
• MAP sequence
• viterbi algorithm
• EM algorithm

Acknowledgments

This work was supported by the Estonian Institutional Research Funding IUT34-5 and by the Estonian Research CouncilPRG865.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the Estonian Institutional Research Funding [grant numberIUT34-5] and by the Estonian Research Council [grant number PRG865].