Adaptive sequential Monte Carlo by means of mixture of experts. Working paper, Telecom ParisTech

Abstract: Appropriately designing the proposal kernel of particle filters is an issue of significant importance, since a bad choice may lead to deterioration of the particle sam-ple and, consequently, waste of computational power. In this paper we introduce a novel algorithm adaptively approximating the so-called optimal proposal kernel by a mixture of integrated curved exponential distributions with logistic weights. This family of distri-butions, referred to as mixtures of experts, is broad enough to be used in the presence of multi-modality or strongly skewed distribu-tions. The mixtures are fitted, via online-EM methods, to the optimal kernel through min-imisation of the Kullback-Leibler divergence between the auxiliary target and instrumen-tal distributions of the particle filter. At each iteration of the particle filter, the algorithm is required to solve only a single optimisation problem for the whole particle sample, yield-ing an algorithm with only linear complexity. In addition, we illustrate in a simulation study how the method can be successfully applied to optimal filtering in nonlinear state-space mod-els