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Comments on approximating discrete probability distributions with dependence trees

C.K. Chow and C.N. Liu (1968) introduced the notion of three dependence to approximate a kth-order probability distribution. More recently, A.K.C. Wong and C.C. Wang (1977) proposed a different product approximation. The present authors show that the tree dependence approximation suggested by Chow a...

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Published in:	IEEE transactions on pattern analysis and machine intelligence 1989-03, Vol.11 (3), p.333-335
Main Authors:	Wong, S.K.M., Poon, F.C.S.
Format:	Article
Language:	English
Subjects:	Applied sciences Artificial intelligence Classification tree analysis Computer science control theory systems Entropy Error analysis Exact sciences and technology Information systems Information theory Intelligent systems Learning and adaptive systems Mutual information Pattern recognition Probability distribution Upper bound
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description	C.K. Chow and C.N. Liu (1968) introduced the notion of three dependence to approximate a kth-order probability distribution. More recently, A.K.C. Wong and C.C. Wang (1977) proposed a different product approximation. The present authors show that the tree dependence approximation suggested by Chow and Liu can be derived by minimizing an upper bound of the Bayes error rate under certain assumptions. They also show that the method proposed by Wong and Wang does not necessarily lead to fewer misclassifications, because it is a special case of such a minimization procedure.< >
doi_str_mv	10.1109/34.21803
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Chow and C.N. Liu (1968) introduced the notion of three dependence to approximate a kth-order probability distribution. More recently, A.K.C. Wong and C.C. Wang (1977) proposed a different product approximation. The present authors show that the tree dependence approximation suggested by Chow and Liu can be derived by minimizing an upper bound of the Bayes error rate under certain assumptions. 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Chow and C.N. Liu (1968) introduced the notion of three dependence to approximate a kth-order probability distribution. More recently, A.K.C. Wong and C.C. Wang (1977) proposed a different product approximation. The present authors show that the tree dependence approximation suggested by Chow and Liu can be derived by minimizing an upper bound of the Bayes error rate under certain assumptions. They also show that the method proposed by Wong and Wang does not necessarily lead to fewer misclassifications, because it is a special case of such a minimization procedure.< ></abstract><cop>Los Alamitos, CA</cop><pub>IEEE</pub><doi>10.1109/34.21803</doi><tpages>3</tpages></addata></record>
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subjects	Applied sciences Artificial intelligence Classification tree analysis Computer science control theory systems Entropy Error analysis Exact sciences and technology Information systems Information theory Intelligent systems Learning and adaptive systems Mutual information Pattern recognition Probability distribution Upper bound
title	Comments on approximating discrete probability distributions with dependence trees
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