Sidestepping the Triangulation Problem in Bayesian Net Computations

TL;DR

This paper introduces a novel method for computing posterior probabilities in Bayesian networks that avoids the complex triangulation step by decomposing the network into smaller components and arranging them into a tree structure.

Contribution

The paper proposes a decomposition-based approach using Tarjan's algorithm to sidestep the triangulation problem in Bayesian net computations.

Findings

Reduces complexity by avoiding triangulation.

Efficiently computes posteriors through component decomposition.

Sidesteps NP-hard triangulation problem.

Abstract

This paper presents a new approach for computing posterior probabilities in Bayesian nets, which sidesteps the triangulation problem. The current state of art is the clique tree propagation approach. When the underlying graph of a Bayesian net is triangulated, this approach arranges its cliques into a tree and computes posterior probabilities by appropriately passing around messages in that tree. The computation in each clique is simply direct marginalization. When the underlying graph is not triangulated, one has to first triangulated it by adding edges. Referred to as the triangulation problem, the problem of finding an optimal or even a ?good? triangulation proves to be difficult. In this paper, we propose to first decompose a Bayesian net into smaller components by making use of Tarjan's algorithm for decomposing an undirected graph at all its minimal complete separators. Then, the components are arranged into a tree and posterior probabilities are computed by appropriately passing around messages in that tree. The computation in each component is carried out by repeating the whole procedure from the beginning. Thus the triangulation problem is sidestepped.