Logarithmic-Time Updates and Queries in Probabilistic Networks

TL;DR

This paper introduces a dynamic data structure for Bayesian networks that enables logarithmic-time updates and queries, significantly improving efficiency for real-time probabilistic reasoning in large networks.

Contribution

The authors present a practical algorithm that reduces query time to O(log N) after preprocessing, with evidence absorption in O(log N) time, enhancing real-time performance.

Findings

Queries answered in O(log N) time after preprocessing

Evidence absorption takes O(log N) time

Applicable to large probabilistic networks for real-time processing

Abstract

In this paper we propose a dynamic data structure that supports efficient algorithms for updating and querying singly connected Bayesian networks (causal trees and polytrees). In the conventional algorithms, new evidence in absorbed in time O(1) and queries are processed in time O(N), where N is the size of the network. We propose a practical algorithm which, after a preprocessing phase, allows us to answer queries in time O(log N) at the expense of O(logn N) time per evidence absorption. The usefulness of sub-linear processing time manifests itself in applications requiring (near) real-time response over large probabilistic databases.