On the accuracy of the Viterbi alignment

TL;DR

This paper introduces an iterative method to improve the Viterbi alignment in hidden Markov models, addressing its potential untypical behavior and demonstrating its advantages over simpler approaches.

Contribution

It proposes a novel iterative procedure for refining Viterbi alignments and compares it with a basic bunch approach, showing its superior efficiency and applicability.

Findings

Iterative approach outperforms bunch method in alignment quality

Lower bounds for classification probabilities are established

Method applicable when hidden states can be revealed (peeping)

Abstract

In a hidden Markov model, the underlying Markov chain is usually hidden. Often, the maximum likelihood alignment (Viterbi alignment) is used as its estimate. Although having the biggest likelihood, the Viterbi alignment can behave very untypically by passing states that are at most unexpected. To avoid such situations, the Viterbi alignment can be modified by forcing it not to pass these states. In this article, an iterative procedure for improving the Viterbi alignment is proposed and studied. The iterative approach is compared with a simple bunch approach where a number of states with low probability are all replaced at the same time. It can be seen that the iterative way of adjusting the Viterbi alignment is more efficient and it has several advantages over the bunch approach. The same iterative algorithm for improving the Viterbi alignment can be used in the case of peeping, that is when it is possible to reveal hidden states. In addition, lower bounds for classification probabilities of the Viterbi alignment under different conditions on the model parameters are studied.