A Bayesian classifier
Authors:
B. A. Zalessky and P. V. Lukashevich
Translated by:
N. Semenov
Original publication:
Teoriya Imovirnostei ta Matematichna Statistika, tom 78 (2008).
Journal:
Theor. Probability and Math. Statist. 78 (2009), 2335
MSC (2000):
Primary 62C10; Secondary 90Bxx
Published electronically:
August 4, 2009
MathSciNet review:
2446846
Fulltext PDF
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Abstract: We consider a new Bayesian classifier for the classification of multidimensional observations of if the learning sample is known. We assume that the data are generated by two disjoint bounded sets and each vector of the sample is a result of the observation after one of the sets , , with a random error. In other words, we assume that a priori the Bayesian probability is given on the set and that every vector of observations has the density where the function is a probability density for all and . The maximum a posteriori probability estimators , , for the sets , , are constructed with the help of the learning sample. Under natural assumptions imposed on and , we show that the estimators converge to some sets (possibly different from and ). If the mean frequencies of observations of the classes are equal to , , then the estimators are consistent in the sense that , . We also discuss some results of numerical experiments showing the applicability of our classifier for solving the problems of the statistical classification.
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Additional Information
B. A. Zalessky
Affiliation:
United Institute of Informatics Problems, National Academy of Sciences, Surganova Street 6, Minsk, 220012, Belarus’
Email:
zalesky@newman.basnet.by
P. V. Lukashevich
Affiliation:
United Institute of Informatics Problems, National Academy of Sciences, Surganova Street 6, Minsk, 220012, Belarus’
DOI:
http://dx.doi.org/10.1090/S0094900009007595
PII:
S 00949000(09)007595
Received by editor(s):
October 23, 2006
Published electronically:
August 4, 2009
Additional Notes:
The first author was supported by the INTAS grant 04777036
Article copyright:
© Copyright 2009 American Mathematical Society
