Adaptive Sequential Monte Carlo Methods

• Activity Number: 163
• Type: Topic Contributed
• Date/Time: Monday, August 1, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Julien Cornebise*+ and Eric Moulines and Eric Moulines
• Companies: University College London and Telecom ParisTech and Telecom ParisTech
• Keywords: Sequential Monte Carlo algorithms ; Adaptation ; Kullback Leibler divergence ; Computational statistics ; Central Limit Theorems ; Particle filter

Abstract

We focus on the design and analysis of Adaptive Sequential Monte Carlo (SMC) algorithms. Our aim: enable them to automatically tune their parameters -- such as first stage resampling weights and proposal kernel -- for maximum computational efficiency and accuracy of the resulting estimates. We first formalize and study the existing practices from a theoretical point of view, asymptotically linking the coefficient of variation and the entropy of the importance weights (currently used on an empirical basis) to chi-square and Kullback-Leibler divergences (KLD) between distributions on an extended space. We develop new criteria decoupling of the adaptation of the first stage weights and that of the proposal kernel. Based on those and with inspiration from Stochastic Approximation and Monte Carlo EM, we build new algorithms able to deal with intricate non-linearities and multi-modality, and illustrate their performances in terms of KLD reduction and distribution of importance weights on several thoroughly examined numerical examples.