A Concise Information-Theoretic Derivation of the Baum-Welch algorithm

TL;DR

This paper presents a concise information-theoretic derivation of the Baum-Welch algorithm for hidden Markov models, using cross-entropy, which simplifies the derivation and extends naturally to multiple observations.

Contribution

It introduces a novel, concise derivation of the Baum-Welch algorithm based on information theory, differing from traditional Lagrange multiplier methods.

Findings

Provides a more straightforward derivation of Baum-Welch

Generalizes the algorithm to multiple observations

Enhances understanding of HMM parameter estimation

Abstract

We derive the Baum-Welch algorithm for hidden Markov models (HMMs) through an information-theoretical approach using cross-entropy instead of the Lagrange multiplier approach which is universal in machine learning literature. The proposed approach provides a more concise derivation of the Baum-Welch method and naturally generalizes to multiple observations.