Complex Probabilistic Modeling with Recursive Relational Bayesian Networks

Abstract

A number of representation systems have been proposed that extend the purely propositional Bayesian network paradigm with representation tools for some types of first-order probabilistic dependencies. Examples of such systems are dynamic Bayesian networks and systems for knowledge based model construction. We can identify the representation of probabilistic relational models as a common well-defined semantic core of such systems.

Recursive relational Bayesian networks (RRBNs) are a framework for the representation of probabilistic relational models. A main design goal for RRBNs is to achieve greatest possible expressiveness with as few elementary syntactic constructs as possible. The advantage of such an approach is that a system based on a small number of elementary constructs will be much more amenable to a thorough mathematical investigation of its semantic and algorithmic properties than a system based on a larger number of high-level constructs. In this paper we show that with RRBNs we have achieved our goal, by showing, first, how to solve within that framework a number of non-trivial representation problems. In the second part of the paper we show how to construct from a RRBN and a specific query, a standard Bayesian network in which the answer to the query can be computed with standard inference algorithms. Here the simplicity of the underlying representation framework greatly facilitates the development of simple algorithms and correctness proofs. As a result we obtain a construction algorithm that even for RRBNs that represent models for complex first-order and statistical dependencies generates standard Bayesian networks of size polynomial in the size of the domain given in a specific application instance.