Conditioning Graphs: Practical Structures for Inference in Bayesian Networks

Probability is a useful tool for reasoning when faced with uncertainty. Bayesian networks offer a compact representation of a probabilistic problem, exploiting independence amongst variables that allows a factorization of the joint probability into much smaller local probability distributions. The standard approach to probabilistic inference in Bayesian networks is to compile the graph into a join-tree, and perform computation over this secondary structure. While join-trees are among the most time-efficient methods of inference in Bayesian networks, they are not always appropriate for certain applications. The memory requirements of join-tree can be prohibitively large. The algorithms for computing over join-trees are large and involved, making them difficult to port to other systems or be understood by general programmers without Bayesian network expertise. This thesis proposes a different method for probabilistic inference in Bayesian networks. We present a data structure called a conditioning graph, which is a runtime representation of Bayesian network inference. The structure mitigates many of the problems of join-tree inference. For example, conditioning graphs require much less space to store and compute over. The algorithm for calculating probabilities from a conditioning graph is small and basic, making it portable to virtually any architecture. And the details of Bayesian network inference are compiled away during the construction of the conditioning graph, leaving an intuitive structure that is easy to understand and implement without any Bayesian network expertise. In addition to the conditioning graph architecture, we present several improvements to the model, that maintain its small and simplistic style while reducing the runtime required for computing over it. We present two heuristics for choosing variable orderings that result in shallower elimination trees, reducing the overall complexity of computing over conditioning graphs. We also demonstrate several compile