Simulation Approaches to General Probabilistic Inference on Belief Networks

TL;DR

This paper explores Monte Carlo sampling methods for probabilistic inference in belief networks, focusing on techniques that perform well in complex networks with extreme probabilities and proposing enhancements to improve their efficiency.

Contribution

It introduces a family of forward Monte Carlo sampling techniques suitable for multiply connected networks with extreme probabilities and provides a framework for selecting effective enhancements.

Findings

Monte Carlo methods perform well in complex belief networks

Enhancements reduce posterior variance effectively

Framework guides when to apply specific improvements

Abstract

A number of algorithms have been developed to solve probabilistic inference problems on belief networks. These algorithms can be divided into two main groups: exact techniques which exploit the conditional independence revealed when the graph structure is relatively sparse, and probabilistic sampling techniques which exploit the "conductance" of an embedded Markov chain when the conditional probabilities have non-extreme values. In this paper, we investigate a family of "forward" Monte Carlo sampling techniques similar to Logic Sampling [Henrion, 1988] which appear to perform well even in some multiply connected networks with extreme conditional probabilities, and thus would be generally applicable. We consider several enhancements which reduce the posterior variance using this approach and propose a framework and criteria for choosing when to use those enhancements.