31,936 research outputs found

    Exact approximation of Rao-Blackwellised particle filters

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    Particle methods are a category of Monte Carlo algorithms that have become popular for performing inference in non-linear non-Gaussian state-space models. The class of 'Rao-Blackwellised' particle filters exploits the analytic marginalisation that is possible for some state- space models to reduce the variance of the Monte Carlo estimates. Despite being applicable to only a restricted class of state-space models, such as conditionally linear Gaussian models, these algorithms have found numerous applications. In scenarios where no such analytical integration is possible, it has recently been proposed in Chen et al. [2011] to use 'local' particle filters to carry out this integration numerically. We propose here an alternative approach also relying on \local" particle filters which is more broadly applicable and has attractive theoretical properties. Proof-of-concept simulation results are presented

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

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    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
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