Asymptotic risks of Viterbi segmentation

TL;DR

This paper investigates the long-term behavior of the Viterbi segmentation in hidden Markov models by establishing the existence of asymptotic risks, which serve as data-independent characteristics of the model.

Contribution

It proves the existence of asymptotic risks for Viterbi segmentation, providing a theoretical foundation for understanding its long-term performance.

Findings

Asymptotic risks exist for Viterbi segmentation.

These risks are independent of data.

They characterize the model's long-run behavior.

Abstract

We consider the maximum likelihood (Viterbi) alignment of a hidden Markov model (HMM). In an HMM, the underlying Markov chain is usually hidden and the Viterbi alignment is often used as the estimate of it. This approach will be referred to as the Viterbi segmentation. The goodness of the Viterbi segmentation can be measured by several risks. In this paper, we prove the existence of asymptotic risks. Being independent of data, the asymptotic risks can be considered as the characteristics of the model that illustrate the long-run behavior of the Viterbi segmentation.