On Disjunctive Representations of Distributions and Randomization

Abstract

We study the usefulness of representing a given joint distribution as a positive linear combination of disjunctions of hypercubes, and generalize the associated results and techniques to Bayesian networks (BNs). The fundamental idea is to pre-compile a given distribution into this form, and employ a host of randomization techniques at runtime to answer various kinds of queries efficiently. Generalizing to BNs, we show that these techniques can be effectively combined with the dynamic programming-based ideas of message-passing and clique-trees to exploit both the topology (conditional independence relationships between the variables) and the numerical structure (structure of the conditional probability tables) of a given BN in efficiently answering queries at runtime.