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D-Separation and computation of probability distributions in Bayesian networks

D-Separation and computation of probability distributions in Bayesian networks Consider a family $${(X_i)_{i \in I}}$$ of random variables endowed with the structure of a Bayesian network, and a subset S of I. This paper examines the problem of computing the probability distribution of the subfamily $${(X_{a})_{a \in S}}$$ (respectively the probability distribution of $${ (X_{b})_{b \in {\bar{S}}}}$$ , where $${{\bar{S}} = I - S}$$ , conditional on $${(X_{a})_{a \in S}}$$ ). This paper presents some theoretical results that makes it possible to compute joint and conditional probabilities over a subset of variables by computing over separate components. In other words, it is demonstrated that it is possible to decompose this task into several parallel computations, each related to a subset of S (respectively of $${{\bar{S}}}$$ ); these partial results are then put together as a final product. In computing the probability distribution over $${(X_a)_{a \in S}}$$ , this procedure results in the production of a structure of level two Bayesian network structure for S. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Artificial Intelligence Review Springer Journals

D-Separation and computation of probability distributions in Bayesian networks

Artificial Intelligence Review , Volume 31 (4) – Oct 22, 2009

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References (22)

Publisher
Springer Journals
Copyright
Copyright © 2009 by Springer Science+Business Media B.V.
Subject
Computer Science; Computer Science, general; Artificial Intelligence (incl. Robotics)
ISSN
0269-2821
eISSN
1573-7462
DOI
10.1007/s10462-009-9128-3
Publisher site
See Article on Publisher Site

Abstract

Consider a family $${(X_i)_{i \in I}}$$ of random variables endowed with the structure of a Bayesian network, and a subset S of I. This paper examines the problem of computing the probability distribution of the subfamily $${(X_{a})_{a \in S}}$$ (respectively the probability distribution of $${ (X_{b})_{b \in {\bar{S}}}}$$ , where $${{\bar{S}} = I - S}$$ , conditional on $${(X_{a})_{a \in S}}$$ ). This paper presents some theoretical results that makes it possible to compute joint and conditional probabilities over a subset of variables by computing over separate components. In other words, it is demonstrated that it is possible to decompose this task into several parallel computations, each related to a subset of S (respectively of $${{\bar{S}}}$$ ); these partial results are then put together as a final product. In computing the probability distribution over $${(X_a)_{a \in S}}$$ , this procedure results in the production of a structure of level two Bayesian network structure for S.

Journal

Artificial Intelligence ReviewSpringer Journals

Published: Oct 22, 2009

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