Cutset Sampling with Likelihood Weighting

TL;DR

This paper presents a novel likelihood weighting method on cutsets in Bayesian networks, reducing sample complexity and improving efficiency by leveraging network structure and caching techniques.

Contribution

It extends cutset sampling principles to likelihood weighting, demonstrating theoretical and empirical improvements in convergence and rejection rates.

Findings

LWLC requires fewer samples for convergence.

LWLC has a lower rejection rate than standard LW.

Caching sampling distributions enhances LWLC performance.

Abstract

The paper analyzes theoretically and empirically the performance of likelihood weighting (LW) on a subset of nodes in Bayesian networks. The proposed scheme requires fewer samples to converge due to reduction in sampling variance. The method exploits the structure of the network to bound the complexity of exact inference used to compute sampling distributions, similar to Gibbs cutset sampling. Yet, the extension of the previosly proposed cutset sampling principles to likelihood weighting is non-trivial due to differences in the sampling processes of Gibbs sampler and LW. We demonstrate empirically that likelihood weighting on a cutset (LWLC) is effective time-wise and has a lower rejection rate than LW when applied to networks with many deterministic probabilities. Finally, we show that the performance of likelihood weighting on a cutset can be improved further by caching computed sampling distributions and, consequently, learning 'zeros' of the target distribution.