Join Bayes Nets: A new type of Bayes net for relational data

Many databases store data in relational format, with different types of entities and information about links between the entities. The field of statistical-relational learning has developed a number of new statistical models for such data. Instead of introducing a new model class, we propose using a standard model class--Bayes nets--in a new way: Join Bayes nets contain nodes that correspond to the descriptive attributes of the database tables, plus Boolean relationship nodes that indicate the presence of a link. Join Bayes nets are class-level models whose random variables describe attributes of generic individuals (e.g., $\age(\P)$ rather than $\age(\jack)$ where $\P$ stands for a randomly selected person). As Join Bayes nets are just a special type of Bayes net, their semantics is standard (edges denote direct associations, d-separation implies probabilistic independence etc.), and Bayes net inference algorithms can be used "as is" to answer probabilistic queries involving relations. We present a dynamic programming algorithm for estimating the parameters of a Join Bayes net and discuss how Join Bayes Nets model various well-known statistical-relational phenomena like autocorrelation and aggregation.