Design of Evolutionary Methods Applied to the Learning of Bayesian Network Structures

Abstract

Bayesian networks (BN) are a family of probabilistic graphical models representing a joint distribution for a set of random variables. Conditional dependencies between these variables are symbolized by a Directed Acyclic Graph (DAG). Two classical approaches are often encountered when automatically determining an appropriate graphical structure from a database of cases. The first one consists in the detection of (in)dependencies between the variables (Cheng et al., 2002; Spirtes et al., 2001). The second one uses a scoring metric (Chickering, 2002a). But neither the first nor the second are really satisfactory. The first one uses statistical tests which are not reliable enough when in presence of small datasets. If numerous variables are required, it is the computing time that highly increases. Even if score-based methods require relatively less computation, their disadvantage lies in that the searcher is often confronted with the presence of many local optima within the search space of candidate DAGs. Finally, in the case of the automatic determination of the appropriate graphical structure of a BN, it was shown that the search space is huge (Robinson, 1976) and that is a NP-hard problem (Chickering et al., 1994) for a scoring approach.