An Empirical Evaluation of a Randomized Algorithm for Probabilistic Inference

TL;DR

This paper evaluates a randomized algorithm for probabilistic inference in belief networks, demonstrating its efficiency and providing bounds on its performance through both theoretical analysis and empirical testing.

Contribution

It introduces a novel randomized approximation scheme for probabilistic inference that computes bounds on running time based on network structure and analyzes its empirical behavior.

Findings

The algorithm performs efficient approximate inference in large belief networks.

Good trial generation is more critical than numerous mediocre trials for performance.

Empirical results support the theoretical analysis of the algorithm's efficiency.

Abstract

In recent years, researchers in decision analysis and artificial intelligence (Al) have used Bayesian belief networks to build models of expert opinion. Using standard methods drawn from the theory of computational complexity, workers in the field have shown that the problem of probabilistic inference in belief networks is difficult and almost certainly intractable. K N ET, a software environment for constructing knowledge-based systems within the axiomatic framework of decision theory, contains a randomized approximation scheme for probabilistic inference. The algorithm can, in many circumstances, perform efficient approximate inference in large and richly interconnected models of medical diagnosis. Unlike previously described stochastic algorithms for probabilistic inference, the randomized approximation scheme computes a priori bounds on running time by analyzing the structure and contents of the belief network. In this article, we describe a randomized algorithm for probabilistic inference and analyze its performance mathematically. Then, we devote the major portion of the paper to a discussion of the algorithm's empirical behavior. The results indicate that the generation of good trials (that is, trials whose distribution closely matches the true distribution), rather than the computation of numerous mediocre trials, dominates the performance of stochastic simulation. Key words: probabilistic inference, belief networks, stochastic simulation, computational complexity theory, randomized algorithms.