Probabilistic Entity-Relationship Models, PRMs, and Plate Models

Abstract

We introduce a graphical language for re- lational data called the probabilistic entity- relationship (PER) model. The model is an extension of the entity-relationship model, a common model for the abstract repre- sentation of database structure. We con- centrate on the directed version of this model—the directed acyclic probabilistic entity-relationship (DAPER) model. The DAPER model is closely related to the plate model and the probabilistic relational model (PRM), existing models for relational data. The DAPER model is more expressive than either existing model, and also helps to demonstrate their similarity. dinary graphical models (e.g., directed-acyclic graphs and undirected graphs) are to flat data. In this paper, we introduce a new graphical model for relational data—the probabilistic entity-relationship (PER) model. This model class is more expressive than either PRMs or plate models. We concentrate on a particular type of PER model—the directed acyclic probabilistic entity-relationship (DAPER) model—in which all probabilistic arcs are directed. It is this ver- sion of PER model that is most similar to the plate model and PRM. We define new versions of the plate model and PRM such their expressiveness is equivalent to the DAPER model, and then (in the expanded tech report, Heckerman, Meek, and Koller, 2004) compare the new and old definitions. Consequently, we both demonstrate the similarity among the original lan- guages as well as enhance their abilities to express con- ditional independence in relational data. Our hope is that this demonstration of similarity will foster greater communication and collaboration among statisticians who mostly use plate models and computer scientists who mostly use PRMs. We in fact began this work with an effort to unify traditional PRMs and plate models. In the process, we discovered that it was important to make both entities and relationships (concepts discussed in de- tail in the next section) first class objects in the lan- guage. We in turn discovered an existing language that does this—the entity-relationship (ER) model—a commonly used model for the abstract representation of database structure. We then extended this language to handle probabilistic relationships, creating the PER model. We should emphasize that the languages we discuss are neither meant to serve as a database schema nor meant to be built on top of one. In practice, database schemas are built up over a long period of time as the needs of the database consumers change. Conse-