Adaptive sequential Monte Carlo by means of mixture of experts

Selecting appropriately the proposal kernel of particle filters is an issue of significant importance, since a bad choice may lead to deterioration of the particle sample and, consequently, waste of computational power. In this paper we introduce a novel algorithm approximating adaptively the so-called optimal proposal kernel by a mixture of integrated curved exponential distributions with logistic weights. This family of distributions, referred to as mixtures of experts, is broad enough to be used in the presence of multi-modality or strongly skewed distributions. The mixtures are fitted, via Monte Carlo EM or online-EM methods, to the optimal kernel through minimization of the Kullback-Leibler divergence between the auxiliary target and instrumental distributions of the particle filter. At each iteration of the particle filter, the algorithm is required to solve only a single optimization problem for the whole particle sample, as opposed to existing methods solving one problem per particle. In addition, we illustrate in a simulation study how the method can be successfully applied to optimal filtering in nonlinear state-space models.