An efficient particle-based online EM algorithm for general state-space models

TL;DR

This paper introduces a fast, memory-efficient online EM algorithm for general state-space models, leveraging the particle-based PaRIS method to address degeneracy and complexity issues in parameter estimation.

Contribution

The paper presents a novel online EM algorithm that integrates the PaRIS particle smoother, achieving linear complexity and improved stability for state-space model parameter estimation.

Findings

Algorithm demonstrates high efficiency in simulations.

Memory requirements are significantly reduced.

Computational complexity scales linearly with particles.

Abstract

Estimating the parameters of general state-space models is a topic of importance for 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 online expectation-maximization (EM) for state-space models proposed by Capp\'e (2011). Previous such particle-based implementations of online EM suffer typically from either the well-known degeneracy of the genealogical particle paths or a quadratic complexity in the number of particles. However, by using the computationally efficient and numerically stable PaRIS algorithm for estimating smoothed expectations of time-averaged sufficient statistics of the model we obtain a fast algorithm with very limited memory requirements and a computational complexity that grows only linearly with the number of particles. The efficiency of the algorithm is illustrated in a simulation study.