Parametric families on large binary spaces

TL;DR

This paper explores constructing flexible parametric families on large binary spaces for adaptive Monte Carlo algorithms, addressing the challenge of choosing suitable proxies in high-dimensional binary sampling problems.

Contribution

It introduces methods for developing parametric families on large binary spaces, extending techniques used in continuous spaces to binary sampling challenges.

Findings

Proposes new parametric families for binary spaces.

Addresses proxy distribution selection in high dimensions.

Enhances adaptive Monte Carlo sampling efficiency.

Abstract

In the context of adaptive Monte Carlo algorithms, we cannot directly generate independent samples from the distribution of interest but use a proxy which we need to be close to the target. Generally, such a proxy distribution is a parametric family on the sampling spaces of the target distribution. For continuous sampling problems in high dimensions, we often use the multivariate normal distribution as a proxy for we can easily parametrise it by its moments and quickly sample from it. Our objective is to construct similarly flexible parametric families on binary sampling spaces too large for exhaustive enumeration. The binary sampling problem is more difficult than its continuous counterpart since the choice of a suitable proxy distribution is not obvious.