Marginalized Beam Search Algorithms for Hierarchical HMMs

TL;DR

This paper introduces two novel algorithms for hierarchical HMM inference that better approximate the most likely outer state sequence than traditional methods, demonstrated through simulations and nanopore data.

Contribution

The paper presents the greedy marginalized BS and local focus BS algorithms, addressing limitations of existing methods in hierarchical HMM inference.

Findings

The new algorithms outperform Viterbi in approximating outer states.

They effectively handle large state spaces through marginalization.

Performance validated on simulation and nanopore data.

Abstract

Inferring a state sequence from a sequence of measurements is a fundamental problem in bioinformatics and natural language processing. The Viterbi and the Beam Search (BS) algorithms are popular inference methods, but they have limitations when applied to Hierarchical Hidden Markov Models (HHMMs), where the interest lies in the outer state sequence. The Viterbi algorithm can not infer outer states without inner states, while the BS algorithm requires marginalization over prohibitively large state spaces. We propose two new algorithms to overcome these limitations: the greedy marginalized BS algorithm and the local focus BS algorithm. We show that they approximate the most likely outer state sequence with higher performance than the Viterbi algorithm, and we evaluate the performance of these algorithms on an explicit duration HMM with simulation and nanopore base calling data.