Efficient parameter inference in general hidden Markov models using the filter derivatives

TL;DR

This paper introduces a fast, stable online parameter estimation algorithm for general hidden Markov models, leveraging a particle-based smoother to improve efficiency and address previous computational challenges.

Contribution

The paper adapts the PaRIS particle smoother for recursive maximum likelihood estimation, achieving linear complexity and enhanced stability in parameter inference.

Findings

Algorithm is computationally efficient and stable

Linear complexity in the number of particles

Demonstrated effectiveness in simulation studies

Abstract

Estimating online the parameters of general state-space hidden Markov models is a topic of importance in many scientific and engineering disciplines. In this paper we present an online parameter estimation algorithm obtained by casting our recently proposed particle-based, rapid incremental smoother (PaRIS) into the framework of recursive maximum likelihood estimation for general hidden Markov models. Previous such particle implementations suffer from either quadratic complexity in the number of particles or from the well-known degeneracy of the genealogical particle paths. By using the computational efficient and numerically stable PaRIS algorithm for estimating the needed prediction filter derivatives we obtain a fast algorithm with a computational complexity that grows only linearly with the number of particles. The efficiency and stability of the proposed algorithm are illustrated in a simulation study.