Sequential Monte Carlo on large binary sampling spaces

TL;DR

This paper develops an adaptive Sequential Monte Carlo method tailored for high-dimensional binary spaces, improving variable selection in Bayesian linear regression by incorporating correlation-aware proposals.

Contribution

Introduces a new binary parametric family for adaptive sampling in high-dimensional spaces, enhancing SMC efficiency for variable selection tasks.

Findings

Outperforms standard Markov chain methods on real datasets

Effectively captures correlations in binary sampling spaces

Improves sampling efficiency in high-dimensional variable selection

Abstract

A Monte Carlo algorithm is said to be adaptive if it automatically calibrates its current proposal distribution using past simulations. The choice of the parametric family that defines the set of proposal distributions is critical for good performance. In this paper, we present such a parametric family for adaptive sampling on high-dimensional binary spaces. A practical motivation for this problem is variable selection in a linear regression context. We want to sample from a Bayesian posterior distribution on the model space using an appropriate version of Sequential Monte Carlo. Raw versions of Sequential Monte Carlo are easily implemented using binary vectors with independent components. For high-dimensional problems, however, these simple proposals do not yield satisfactory results. The key to an efficient adaptive algorithm are binary parametric families which take correlations into account, analogously to the multivariate normal distribution on continuous spaces. We provide a review of models for binary data and make one of them work in the context of Sequential Monte Carlo sampling. Computational studies on real life data with about a hundred covariates suggest that, on difficult instances, our Sequential Monte Carlo approach clearly outperforms standard techniques based on Markov chain exploration.