Revising the structure of Bayesian network classifiers in the presence of missing data

Abstract

Traditionally, algorithms that learn the structure of Bayesian Networks either start from an empty graph and add edges to it bit by bit or add/ remove/reverse edges in a randomly initialized graph. In both cases, the search space is constituted of all the nodes and edges connecting them. Searching within such a vast scope is a hard task, which gets worse in the presence of a dataset with missing values. However, it may be the case that an initial structure already exists and to make it reflect the set of examples it would be required to modify only a subset of the graph. Thus, instead of searching through the entire space of possible connections between the nodes, the problem could be reduced to selecting a subset of the edges and revising them. In this work, we present a novel algorithm for refining the structure of Bayesian networks from incomplete data, named BaBReN (Bayes Ball for Revising Networks). BaBReN has as ultimate goal to improve the inference value of the class variable. Thus, the algorithm tries to solve classification issues by proposing local modifications to the edges connecting the nodes that influence the erroneous classification. The Bayes Ball algorithm – based on the d-separation criteria – is responsible for selecting those relevant nodes. By focusing only on the influential nodes, BaBReN is executed independently of the number of variables in the domain. BaBReN is compared to a constraint-based algorithm (GS), a hybrid one (MMHC) and a score-based one (SEM with GHC), presenting better or competitive results regarding time and classification score.