An efficient stochastic approximation EM algorithm using conditional particle filters

Abstract

I present a novel method for maximum likelihood parameter estimation in nonlinear/non-Gaussian state-space models. It is an expectation maximization (EM) like method, which uses sequential Monte Carlo (SMC) for the intermediate state inference problem. Contrary to existing SMC-based EM algorithms, however, it makes efficient use of the simulated particles through the use of particle Markov chain Monte Carlo (PMCMC) theory. More precisely, the proposed method combines the efficient conditional particle filter with ancestor sampling (CPF-AS) with the stochastic approximation EM (SAEM) algorithm. This results in a procedure which does not rely on asymptotics in the number of particles for convergence, meaning that the method is very computationally competitive. Indeed, the method is evaluated in a simulation study, using a small number of particles, with promising results.