Probabilistic Relational Models

Abstract

Probabilistic models provide a sound and coherent foundation for dealing with the noise and uncertainty encountered in most real- world domains. Bayesian networks are a language for representing complex probabilistic models in a compact and natural way. A Bayesian network can be used to reason about any attribute in the domain, given any set of observations. It can thus be used for a variety tasks, including prediction, explanation, and decision making. The probabilistic seman- tics also gives a strong foundation for the task of learning models from data. Techniques currently exist for learning both the structure and the parameters, for dealing with missing data and hidden variables, and for discovering causal structure.

One of the main limitations of Bayesian networks is that they represent the world in terms of a fixed set of “attributes”. Like propositional logic, they are incapable of reasoning explicitly about entities, and thus cannot represent models over domains where the set of entities and the relations between them are not fixed in advance. As a consequence, Bayesian networks are limited in their ability to model large and complex domains. Probabilistic relational models are a language for describing probabilistic models based on the significantly more expressive basis of relational logic. They allow the domain to be represented in terms of entities, their properties, and the relations between them. These models represent the uncertainty over the properties of an entity, representing its probabilistic dependence both on other properties of that entity and on properties of related entities. They can even represent uncertainty over the relational structure itself. Some of the techniques for Bayesian network learning can be generalized to this setting, but the learning problem is far from solved. Probabilistic relational models provide a new framework, and new challenges, for the endeavor of learning relational models for real-world domains.