Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
Implementation and tests of low-discrepancy sequences
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Quasi-random sequences and their discrepancies
SIAM Journal on Scientific Computing
Algorithm 659: Implementing Sobol's quasirandom sequence generator
ACM Transactions on Mathematical Software (TOMS)
Journal of Computational Physics
Computational investigations of low-discrepancy sequences
ACM Transactions on Mathematical Software (TOMS)
Faster evaluation of multidimensional integrals
Computers in Physics
Simulation Approaches to General Probabilistic Inference on Belief Networks
UAI '89 Proceedings of the Fifth Annual Conference on Uncertainty in Artificial Intelligence
Weighing and Integrating Evidence for Stochastic Simulation in Bayesian Networks
UAI '89 Proceedings of the Fifth Annual Conference on Uncertainty in Artificial Intelligence
Low-Discrepancy Sequences and Global Function Fields with Many Rational Places
Finite Fields and Their Applications
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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.