Optimal Junction Trees

TL;DR

This paper presents a method for constructing optimal junction trees from triangulated networks and discusses the efficiency and optimality issues related to belief updating in probabilistic networks.

Contribution

It introduces a simple algorithm for optimal junction tree construction and analyzes the limitations of local calculation methods in belief updating.

Findings

Optimal junction trees can be constructed efficiently from triangulated networks.

Local calculation methods are either less efficient or have similar optimality issues as triangulation.

The paper clarifies the computational trade-offs in belief updating algorithms.

Abstract

The paper deals with optimality issues in connection with updating beliefs in networks. We address two processes: triangulation and construction of junction trees. In the first part, we give a simple algorithm for constructing an optimal junction tree from a triangulated network. In the second part, we argue that any exact method based on local calculations must either be less efficient than the junction tree method, or it has an optimality problem equivalent to that of triangulation.