Estimation of Viterbi path in Bayesian hidden Markov models

TL;DR

This paper compares various methods for estimating the Viterbi path in Bayesian hidden Markov models, introducing a new EM-type algorithm and demonstrating that non-stochastic iterative methods can outperform MCMC approaches in segmentation tasks.

Contribution

A new EM-type algorithm for MAP path estimation in Bayesian HMMs is proposed and shown to be competitive with or superior to existing stochastic methods.

Findings

Non-stochastic iterative methods perform as well or better than MCMC methods.

Direct segmentation considering parameters as nuisances is more effective.

The new EM-type algorithm provides efficient MAP path estimation.

Abstract

The article studies different methods for estimating the Viterbi path in the Bayesian framework. The Viterbi path is an estimate of the underlying state path in hidden Markov models (HMMs), which has a maximum posterior probability (MAP). For an HMM with given parameters, the Viterbi path can be easily found with the Viterbi algorithm. In the Bayesian framework the Viterbi algorithm is not applicable and several iterative methods can be used instead. We introduce a new EM-type algorithm for finding the MAP path and compare it with various other methods for finding the MAP path, including the variational Bayes approach and MCMC methods. Examples with simulated data are used to compare the performance of the methods. The main focus is on non-stochastic iterative methods and our results show that the best of those methods work as well or better than the best MCMC methods. Our results demonstrate that when the primary goal is segmentation, then it is more reasonable to perform segmentation directly by considering the transition and emission parameters as nuisance parameters.