Class-Level Bayes Nets 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. Most of these models aim to support instance-level predictions about the attributes or links of specific entities. In this paper we focus on learning class-level dependencies, which model the database statistics over attributes of links and linked objects. Class-level statistical relationships are of interest in themselves, and they support applications like policy making, strategic planning, and query optimization. While a class-level model does not support instance-level predictions, learning and inference are simpler at the class-level. We describe efficient and scalable algorithms for structure learning and parameter estimation in class-level Bayes nets that directly leverage the efficiency of single-table non-relational Bayes net learners. An evaluation of our methods on three data sets shows that our algorithms are computationally feasible for realistic table sizes, and that the learned structures represented the statistical information in the databases well. After learning has compiled the database statistics into a Join Bayes net, querying these statistics via the net is faster than directly with SQL queries, and does not depend on the size of the database.