On Disjunctive Representations of Distributions and Randomization

• Published in: Research and Development in Intelligent Systems XXI pp. 327 - 340
• Main Author: Satish Kumar, T. K.
• Format: Book Chapter
• Language: English
• Published: London Springer London
• Subjects: Complete Assignment; Conditional Probability Table; Joint Distribution; Positive Linear Combination; Tabular Representation
• DOI: 10.1007/1-84628-102-4_24
• ISBN: 1852339071; 9781852339074

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.