Hybrid classifiers of pairwise Markov models

TL;DR

This paper explores pairwise Markov models for segmentation, introduces hybrid path estimators that interpolate between existing methods, and demonstrates their properties across various PMMs, emphasizing careful method selection.

Contribution

It develops formulas for hybrid path estimators in pairwise Markov models, extending segmentation techniques beyond traditional Viterbi and PMAP methods.

Findings

Hybrid estimators interpolate between Viterbi and PMAP paths.

Segmentation method effectiveness varies significantly across different PMMs.

Careful selection of segmentation method is crucial depending on the model.

Abstract

The article studies segmentation problem (also known as classification problem) with pairwise Markov models (PMMs). A PMM is a process where the observation process and underlying state sequence form a two-dimensional Markov chain, it is a natural generalization of a hidden Markov model. To demonstrate the richness of the class of PMMs, we examine closer a few examples of rather different types of PMMs: a model for two related Markov chains, a model that allows to model an inhomogeneous Markov chain as a homogeneous one and a semi-Markov model. The segmentation problem assumes that one of the marginal processes is observed and the other one is not, the problem is to estimate the unobserved state path given the observations. The standard state path estimators often used are the so-called Viterbi path (a sequence with maximum state path probability given the observations) or the pointwise maximum a posteriori (PMAP) path (a sequence that maximizes the conditional state probability for given observations pointwise). Both these estimators have their limitations, therefore we derive formulas for calculating the so-called hybrid path estimators which interpolate between the PMAP and Viterbi path. We apply the introduced algorithms to the studied models in order to demonstrate the properties of different segmentation methods, and to illustrate large variation in behaviour of different segmentation methods in different PMMs. The studied examples show that a segmentation method should always be chosen with care by taking into account the particular model of interest.