On Adaptive Resampling Procedures for Sequential Monte Carlo Methods

Pierre Del Moral 1, 2, * Arnaud Doucet 3, 4 Ajay Jasra 5
* Auteur correspondant
2 ALEA - Advanced Learning Evolutionary Algorithms
Inria Bordeaux - Sud-Ouest, UB - Université de Bordeaux, CNRS - Centre National de la Recherche Scientifique : UMR5251
Abstract : Sequential Monte Carlo (SMC) methods are a general class of techniques to sample approximately from any sequence of probability distributions. These distributions are approximated by a cloud of weighted samples which are propagated over time using a combination of importance sampling and resampling steps. This article is concerned with the convergence analysis of a class of SMC methods where the times at which resampling occurs are computed on-line using criteria such as the effective sample size. This is a popular approach amongst practitioners but there are very few convergence results available for these methods. It is shown here that these SMC algorithms correspond to a particle approximation of a Feynman-Kac flow of measures on adaptive excursion spaces. By combining a non-linear distribution flow analysis to an original coupling technique, we obtain functional central limit theorems and uniform exponential concentration estimates for these algorithms. The original exponential concentration theorems presented in this study significantly improve previous concentration estimates obtained for SMC algorithms.
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Bernoulli, Bernoulli Society for Mathematical Statistics and Probability, 2012, 18 (1), pp.252-278
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Pierre Del Moral, Arnaud Doucet, Ajay Jasra. On Adaptive Resampling Procedures for Sequential Monte Carlo Methods. Bernoulli, Bernoulli Society for Mathematical Statistics and Probability, 2012, 18 (1), pp.252-278. 〈inria-00332436v4〉

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