Logarithmic Time Parallel Bayesian Inference

TL;DR

This paper introduces a parallel algorithm for exact Bayesian inference that significantly reduces computation time to logarithmic scale for certain network types, leveraging parallel processing capabilities.

Contribution

The paper presents the first parallel algorithm achieving logarithmic time complexity for exact inference in polytrees and extends it to arbitrary networks with complexity bounds.

Findings

Logarithmic time complexity for polytrees on parallel machines.

Efficient inference in arbitrary networks with complexity depending on network parameters.

Scalability of the algorithm with respect to network size and structure.

Abstract

I present a parallel algorithm for exact probabilistic inference in Bayesian networks. For polytree networks with n variables, the worst-case time complexity is O(log n) on a CREW PRAM (concurrent-read, exclusive-write parallel random-access machine) with n processors, for any constant number of evidence variables. For arbitrary networks, the time complexity is O(r^{3w}*log n) for n processors, or O(w*log n) for r^{3w}*n processors, where r is the maximum range of any variable, and w is the induced width (the maximum clique size), after moralizing and triangulating the network.