On Disjunctive Representations of Distributions and Randomization

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...

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Bibliographic Details
Published inResearch and Development in Intelligent Systems XXI pp. 327 - 340
Main Author Satish Kumar, T. K.
Format Book Chapter
LanguageEnglish
Published London Springer London
Subjects
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Conditional Probability Table
Joint Distribution
Positive Linear Combination
Tabular Representation
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Summary: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.
ISBN:1852339071
9781852339074
DOI:10.1007/1-84628-102-4_24