Variance-Reduced Stochastic Optimization for Efficient Inference of Hidden Markov Models

TL;DR

This paper introduces a variance-reduced stochastic optimization algorithm for Hidden Markov Models that significantly speeds up parameter fitting on large datasets, demonstrated through simulations and real-world whale data.

Contribution

The paper presents a novel optimization method combining a partial E step with variance reduction, enabling efficient HMM inference without full data iteration.

Findings

Faster convergence in fewer epochs compared to standard methods

Higher likelihood regions achieved more efficiently

Effective on large-scale time-series data

Abstract

Hidden Markov models (HMMs) are popular models to identify a finite number of latent states from sequential data. However, fitting them to large data sets can be computationally demanding because most likelihood maximization techniques require iterating through the entire underlying data set for every parameter update. We propose a novel optimization algorithm that updates the parameters of an HMM without iterating through the entire data set. Namely, we combine a partial E step with variance-reduced stochastic optimization within the M step. We prove the algorithm converges under certain regularity conditions. We test our algorithm empirically using a simulation study as well as a case study of kinematic data collected using suction-cup attached biologgers from eight northern resident killer whales (Orcinus orca) off the western coast of Canada. In both, our algorithm converges in fewer epochs and to regions of higher likelihood compared to standard numerical optimization techniques. Our algorithm allows practitioners to fit complicated HMMs to large time-series data sets more efficiently than existing baselines.