Adaptive sequential Monte Carlo by means of mixture of experts

作者：Cornebise Julien^*; Moulines Eric; Olsson Jimmy

来源：Statistics and Computing, 2014, 24(3): 317-337.

DOI：10.1007/s11222-012-9372-2

• Optimal proposal kernel
• Adaptive algorithms
• Kullback-Leibler divergence
• Coefficient of variation
• Expectation-maximisation
• Particle filter
• Sequential Monte Carlo
• Shannon entropy

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.

• 出版日期2014-5