Optimal Monte Carlo Estimation of Belief Network Inference

TL;DR

This paper introduces two improved Monte Carlo sampling algorithms for belief network inference that guarantee polynomial-time convergence and demonstrate better empirical performance than existing methods.

Contribution

The paper proposes novel variants of likelihood weighting algorithms with theoretical guarantees and empirical improvements for probabilistic inference in belief networks.

Findings

Algorithms guarantee polynomial-time convergence.

Empirical evaluation shows improved performance.

Achieves inference with specified error and failure probability.

Abstract

We present two Monte Carlo sampling algorithms for probabilistic inference that guarantee polynomial-time convergence for a larger class of network than current sampling algorithms provide. These new methods are variants of the known likelihood weighting algorithm. We use of recent advances in the theory of optimal stopping rules for Monte Carlo simulation to obtain an inference approximation with relative error epsilon and a small failure probability delta. We present an empirical evaluation of the algorithms which demonstrates their improved performance.