Pre-processing for Triangulation of Probabilistic Networks

TL;DR

This paper introduces a pre-processing approach that simplifies probabilistic network graphs, enabling more efficient triangulation with minimal maximum clique size, thus improving inference performance.

Contribution

It presents a set of reduction rules for preprocessing graphs that facilitate optimal triangulation of probabilistic networks, reducing computational complexity.

Findings

Preprocessing can lead to optimal triangulations of some real-world networks.

Significant graph size reductions are achievable for certain networks.

Preprocessing enhances the efficiency of triangulation algorithms.

Abstract

The currently most efficient algorithm for inference with a probabilistic network builds upon a triangulation of a network's graph. In this paper, we show that pre-processing can help in finding good triangulations forprobabilistic networks, that is, triangulations with a minimal maximum clique size. We provide a set of rules for stepwise reducing a graph, without losing optimality. This reduction allows us to solve the triangulation problem on a smaller graph. From the smaller graph's triangulation, a triangulation of the original graph is obtained by reversing the reduction steps. Our experimental results show that the graphs of some well-known real-life probabilistic networks can be triangulated optimally just by preprocessing; for other networks, huge reductions in their graph's size are obtained.