Junction trees construction: Application to Bayesian networks

L. Smail, Zayed University

Document Type

Conference Proceeding

Source of Publication

AIP Conference Proceedings

Publication Date

10-25-2018

Abstract

© 2018 Author(s). All exact inference algorithms for computing a posterior probability in general Bayesian networks have two conceptual phases: One phase handles operations on the graphical structure itself, and the other performs probabilistic computations. The junction tree is introduced to show the important relationship between graph theory and efficient probabilistic inference through a very important and interesting mathematical property of junction trees, the running intersection property. This paper examines an alternative method for constructing junction trees that is essential for the efficient computations of probabilistic enquiries posed on Bayesian networks. It presents a new method for converting a sequence of subsets that covers the Bayesian network into a junction tree; in other words, it converts a sequence of subsets in a Bayesian network into a proper set of cliques satisfying the running intersection property. We propose an algorithm in two versions (one of which is original) that allows a sequence of cliques possessing the running intersection property to be built, hence can be used with the junction tree algorithm for local computations on graphs. The input is an existing covering and the algorithm sequentially modifies the existing sequence of subsets to produce a new one with the required property. The obtained set of cliques and separators coincide with the junction trees obtained by the moralization and triangulation process, but it has the advantage of adapting to any computational task by adding links to the Bayesian network graph.

ISBN

9780735417458

ISSN

0094-243X

Publisher

American Institute of Physics Inc.

Volume

2025

Disciplines

Mathematics

Keywords

Bayesian networks, junction trees, proper mapping, reversed running intersection property, running intersection property

Scopus ID

85056206146

Indexed in Scopus

yes

Open Access

no

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