Computational Investigation of Low-Discrepancy Sequences in Simulation Algorithms for Bayesian Networks

TL;DR

This paper explores the use of low-discrepancy sequences, particularly Sobol sequences, to enhance the efficiency of simulation algorithms for approximate inference in Bayesian networks, demonstrating significant performance improvements.

Contribution

It introduces a method for selecting direction numbers for Sobol sequences and evaluates their effectiveness in Bayesian network inference.

Findings

Low-discrepancy sequences outperform traditional Monte Carlo sampling.

Sobol sequences significantly improve simulation efficiency.

Proposed algorithm aids in selecting optimal direction numbers.

Abstract

Monte Carlo sampling has become a major vehicle for approximate inference in Bayesian networks. In this paper, we investigate a family of related simulation approaches, known collectively as quasi-Monte Carlo methods based on deterministic low-discrepancy sequences. We first outline several theoretical aspects of deterministic low-discrepancy sequences, show three examples of such sequences, and then discuss practical issues related to applying them to belief updating in Bayesian networks. We propose an algorithm for selecting direction numbers for Sobol sequence. Our experimental results show that low-discrepancy sequences (especially Sobol sequence) significantly improve the performance of simulation algorithms in Bayesian networks compared to Monte Carlo sampling.