Incremental Compilation of Bayesian networks

Abstract: Most methods of exact probability propagation in Bayesian networks do not carry out the inference directly over the network, but over a secondary structure known as a junction tree or a join tree (JT). The process of obtaining a JT is usually termed {sl compilation}. As compilation is usually viewed as a whole process; each time the network is modified, a new compilation process has to be carried out. The possibility of reusing an already existing JT, in order to obtain the new one regarding only the modifications in the network has received only little attention in the literature. In this paper we present a method for incremental compilation of a Bayesian network, following the classical scheme in which triangulation plays the key role. In order to perform incremental compilation we propose to recompile only those parts of the JT which can have been affected by the networks modifications. To do so, we exploit the technique OF maximal prime subgraph decomposition in determining the minimal subgraph(s) that have to be recompiled, and thereby the minimal subtree(s) of the JT that should be replaced by new subtree(s).We focus on structural modifications : addition and deletion of links and variables.