Comments on approximating discrete probability distributions with dependence trees

Author

Poon, F.C.S.

Volume

11

Issue

3

fYear

1989

fDate

3/1/1989 12:00:00 AM

Firstpage

333

Lastpage

335

Abstract

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.<>

Keywords

Bayes methods; approximation theory; error statistics; minimisation; pattern recognition; probability; trees (mathematics); Bayes error rate; classification; discrete probability distributions; minimization; pattern recognition; probability distribution; product approximation; tree dependence approximation; Classification tree analysis; Entropy; Error analysis; Information systems; Information theory; Intelligent systems; Mutual information; Pattern recognition; Probability distribution; Upper bound;

fLanguage

English

Journal_Title

Pattern Analysis and Machine Intelligence, IEEE Transactions on

Publisher

ieee

ISSN

0162-8828

Type

jour

DOI

10.1109/34.21803

Filename

21803