  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 remain an open
problem at least in the hidden Markov case. This contribution deals with a new
online EM algorithm which updates the parameter at some deterministic times.
Some convergence results have been derived 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 methods when the Monte Carlo error vanishes rapidly enough. In this
paper, we propose an algorithm which approximates these quantities using
Sequential Monte Carlo methods. The convergence of this algorithm and of an
averaged version is established and their performance is illustrated through
Monte Carlo experiments.
