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Theory of Probability and Mathematical Statistics

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Gibbs classifiers

Author: B. A. Zalesky
Translated by: The author
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 70 (2004).
Journal: Theor. Probability and Math. Statist. 70 (2005), 41-51
MSC (2000): Primary 60G60, 62H30; Secondary 90C27
Published electronically: August 5, 2005
MathSciNet review: 2109821
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Abstract | References | Similar Articles | Additional Information

Abstract: New statistical classifiers for dependent observations with Gibbs prior distributions of the exponential or Gaussian type are presented. It is assumed that the observations are characterized by feature functions that assume values in finite sets of rational numbers. The distributions of observations are either Gibbs exponential or Gibbs Gaussian. Arbitrary neighborhoods on a completely connected graph are considered instead of local neighborhoods of the nearest observation.

The models studied in this paper can be used for some problems of the classification of random fields, in statistical physics, and for image processing.

A method of finding an optimal Bayes decision rule is described. The method is based on the reduction of the problem to the evaluation of the minimal cut of an appropriate graph. The method can be used for the fast evaluation of optimal Bayes decision rules for large samples.

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Additional Information

B. A. Zalesky
Affiliation: Joint Institute of Problems in Informatics, National Academy of Sciences, Surganov Street 6, Minsk 220012, Belarus

Received by editor(s): April 4, 2002
Published electronically: August 5, 2005
Additional Notes: Supported by a grant of MNTC B–517.
Article copyright: © Copyright 2005 American Mathematical Society

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