Adaptive sequential Monte Carlo by means of mixture of experts

TL;DR

This paper introduces an adaptive particle filtering algorithm that uses a mixture of experts to approximate the optimal proposal kernel, improving performance in complex, multi-modal, or skewed distributions with linear complexity.

Contribution

It proposes a novel adaptive method employing mixture of experts and online-EM to efficiently approximate the optimal proposal kernel in particle filters.

Findings

Effective in multi-modal and skewed distributions

Maintains linear computational complexity

Successful application to nonlinear state-space models

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 sample 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 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 online-EM methods, to the optimal kernel through minimisation 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 optimisation problem for the whole particle sample, yielding 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 models.