Computational Investigation of Low-Discrepancy Sequences in Simulation Algorithms for Bayesian Networks
This work addresses performance bottlenecks in Bayesian network inference for researchers and practitioners, but it is incremental as it builds on existing quasi-Monte Carlo methods.
The paper tackled the problem of improving simulation algorithms for Bayesian networks by investigating quasi-Monte Carlo methods based on low-discrepancy sequences, proposing an algorithm for selecting direction numbers for the Sobol sequence, and showing that these sequences significantly enhance performance compared to Monte Carlo sampling, with concrete improvements noted in experimental results.
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.