Fast Factorisation of Probabilistic Potentials and Its Application to Approximate Inference in Bayesian Networks

Abstract

<jats:p>We present an efficient procedure for factorising probabilistic potentials represented as probability trees. This new procedure is able to detect some regularities that cannot be captured by existing methods. In cases where an exact decomposition is not achievable, we propose a heuristic way to carry out approximate factorisations guided by a parameter called factorisation degree, which is fast to compute. We show how this parameter can be used to control the tradeoff between complexity and accuracy in approximate inference algorithms for Bayesian networks.</jats:p>

Inference in Bayesian Networks with Recursive Probability Trees: Data Structure Definition and Operations

“…In Refs. , PTs are used to represent each factor and algorithms are given to decompose PTs into two or more factors in exact or approximate ways, using these favorable factorizations in inference algorithms for BNs.…”

New strategies for finding multiplicative decompositions of probability trees

“…Another scenario in which one could be interested in decomposing a tree is when space limitations do not allow to represent fully expanded probability trees, and then it is necessary to tradeoff accuracy for space requirements. This happens, for instance, when probability trees are used for carrying out inference in Bayesian networks [4].…”

“…The problem of obtaining multiplicative factorisations has been previously studied in the literature [12], being the most recent contribution the socalled fast-factorisation [4]. Though fast factorisation has the advantage of efficiency, as it can be computed quickly, it is only able to benefit of rather restrictive scenarios, namely those in which a potential can be decomposed as the product of two functions, one of them containing only one variable.…”