Convergence of a particle-based approximation of the Block Online Expectation Maximization algorithm

Online variants of the Expectation Maximization (EM) algorithm have recently been proposed to perform parameter inference with large data sets or data streams, in independent latent models and in hidden Markov models. Nevertheless, the convergence properties of these algorithms re-main an open problem at least in the hidden Markov case. This contribu-tion deals with a new online EM algorithm which updates the parameter at some deterministic times. Some convergence results have been de-rived even in general latent models such as hidden Markov models. These properties rely on the assumption that some intermediate quantities are available in closed form or can be approximated by Monte Carlo meth-ods when the Monte Carlo error vanishes rapidly enough. In this paper, we propose an algorithm which approximates these quantities using Se-quential Monte Carlo methods. The convergence of this algorithm and of an averaged version is established and their performance is illustrated through Monte Carlo experiments. This extended version of the paper “Convergence of a Particle-based Ap-proximation of the Block Online Expectation Maximization Algorithm“, by S. Le Corff and G. Fort, provides detailed proofs which have been omitted in the submitted paper since they are very close to existing results. These additional proofs are postponed to Appendix B