  The Expectation Maximization (EM) algorithm is a versatile tool for model
parameter estimation in latent data models. When processing large data sets or
data stream however, EM becomes intractable since it requires the whole data
set to be available at each iteration of the algorithm. In this contribution, a
new generic online EM algorithm for model parameter inference in general Hidden
Markov Model is proposed. This new algorithm updates the parameter estimate
after a block of observations is processed (online). The convergence of this
new algorithm is established, and the rate of convergence is studied showing
the impact of the block size. An averaging procedure is also proposed to
improve the rate of convergence. Finally, practical illustrations are presented
to highlight the performance of these algorithms in comparison to other online
maximum likelihood procedures.
