Convergence of a Particle-based Approximation of the Block Online Expectation Maximization Algorithm

Details Convergence of a Particle-based Approximation of the Block Online Expectation Maximization Algorithm Convergence of a Particle-based Approximation of the Block Online Expectation Maximization Algorithm

2011-11-05

arxiv.org/abs/1111.1307v2

Mathematics

Statistics Theory

Scientific paper

Online variants of the Expectation Maximization 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. The convergence properties of the Block Online EM algorithm have been derived, even in general latent models such as the Hidden Markov one. These properties rely on the assumption that some intermediate quantities are available analytically. Unfortunately, this is not the case in hidden Markov models with general state-spaces. 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 are illustrated through Monte Carlo experiments.

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