A Randomized Approximation Algorithm of Logic Sampling

TL;DR

This paper extends previous work on randomized approximation algorithms for belief networks by analyzing the convergence of logic sampling, an alternative probabilistic inference method, providing bounds and trade-offs between accuracy and computation time.

Contribution

It introduces a new analysis of convergence for logic sampling, broadening the framework of randomized approximation schemes for belief network inference.

Findings

Derived convergence bounds for logic sampling

Demonstrated trade-offs between accuracy and runtime

Extended the applicability of randomized approximation methods

Abstract

In recent years, researchers in decision analysis and artificial intelligence (AI) 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 exact probabilistic inference on belief networks almost certainly requires exponential computation in the worst ease [3]. We have previously described a randomized approximation scheme, called BN-RAS, for computation on belief networks [ 1, 2, 4]. We gave precise analytic bounds on the convergence of BN-RAS and showed how to trade running time for accuracy in the evaluation of posterior marginal probabilities. We now extend our previous results and demonstrate the generality of our framework by applying similar mathematical techniques to the analysis of convergence for logic sampling [7], an alternative simulation algorithm for probabilistic inference.