Statistical Distance Based Deterministic Offspring Selection in SMC Methods
This work addresses a bottleneck in SMC methods for researchers in computational statistics, offering incremental improvements over existing resampling techniques.
The authors tackled the problem of improving resampling in sequential Monte Carlo methods by proposing two deterministic offspring selection methods that minimize statistical distances, resulting in superior or comparable performance to state-of-the-art schemes on benchmark models.
Over the years, sequential Monte Carlo (SMC) and, equivalently, particle filter (PF) theory has gained substantial attention from researchers. However, the performance of the resampling methodology, also known as offspring selection, has not advanced recently. We propose two deterministic offspring selection methods, which strive to minimize the Kullback-Leibler (KL) divergence and the total variation (TV) distance, respectively, between the particle distribution prior and subsequent to the offspring selection. By reducing the statistical distance between the selected offspring and the joint distribution, we obtain a heuristic search procedure that performs superior to a maximum likelihood search in precisely those contexts where the latter performs better than an SMC. For SMC and particle Markov chain Monte Carlo (pMCMC), our proposed offspring selection methods always outperform or compare favorably with the two state-of-the-art resampling schemes on two models commonly used as benchmarks from the literature.