DL-Lite Bayesian networks: A tractable probabilistic graphical model

Abstract

The construction of probabilistic models that can represent large systems requires the ability to describe repetitive and hierarchical structures. To do so, one can resort to constructs from description logics. In this paper we present a class of relational Bayesian networks based on the popular description logic DL-Lite. Our main result is that, for this modeling language, marginal inference and most probable explanation require polynomial effort. We show this by reductions to edge covering problems, and derive a result of independent interest; namely, that counting edge covers in a particular class of graphs requires polynomial effort.