Conditional Importance Resampling for an Enhanced Sequential Monte Carlo Sampler

Soodeh Habibi, Efthyvoulos Drousiotis, Alessandro Varsi, Simon Maskell, Robert E. Moore, Paul G. Spirakis

Abstract: Sequential Monte Carlo (SMC) samplers are a family of powerful Bayesian inference methods that combine sampling and resampling to sample from challenging posterior distributions. This makes SMC widely used in several application domains of statistics and Machine Learning. The aim of this paper is to introduce a new resampling framework, called Conditional Importance Resampling (CIR) that reduces the quantization error arising in the application of traditional resampling schemes. To assess the impact of this approach, we conduct a comparative study between two SMC samplers, differing solely in their resampling schemes: one utilizing systematic resampling and the other employing CIR. The overall improvement is demonstrated by theoretical results and numerical experiments for sampling a forest of Bayesian Decision Trees, focusing on its application in classification and regression tasks.