From instances to classes in probabilistic relational models

Probabilistic graphical models, in particular Bayesian networks, are useful models for representing statistical patterns in propositional domains. Recent work develops effective techniques for learning these models directly from data. However these techniques apply only to attribute-value (ie, flat) representations of the data. Probabilistic relational models (PRMs) allow us to represent much richer dependency structures, involving multiple entities and the relations between them; they allow the properties of an entity to depend probabilistically on properties of related entities. PRMs represent a generic dependence, which is then instantiated for specific circumstances, ie, for a particular set of entities and relations between them. Friedman et al. showed how to learn PRMs from relational data, and presented techniques for learning both parameters and probabilistic dependency structure for the attributes in a relational model. Here we examine the benefit that class hierarchies can provide PRMs. We show how the introduction of subclasses allows us to use inheritance and specialization to refine our models. We show how to learn PRMs with class hierarchies (PRMCH) in two settings. In the first, the class hierarchy is provided, as part of the input, in the relational schema for the domain. In the second setting, in addition to learning the PRM, we must learn the class hierarchy. Finally we discuss how PRM-CHs allow us to build models that can represent models for both particular instances in our domain, and classes of objects in our domain, bridging the gap between a class-based model and an attribute-value-based model.