A Bayes Empirical Bayes Decision Rule for Classification

• Published in: Communications in statistics. Theory and methods Vol. 34; no. 5; pp. 1137 - 1149
• Main Authors: Li, Tze Fen, Yen, Tseng-Chang
• Format: Journal Article
• Language: English
• Published: Philadelphia, PA Taylor & Francis Group 01.05.2005; Taylor & Francis
• Subjects: Bayes decision rule; Classification; Decision theory; Distribution theory; Empirical Bayes decision rule; Exact sciences and technology; General topics; Mathematics; Multivariate analysis; Probability and statistics; Sciences and techniques of general use; Statistics; Unsupervised learning; Monte Carlo method; 68T10; 68T05; Probability; Probability distribution; Statistical simulation; Bayes decision rule; Decision rule; Learning; Statistical method; Statistical test; Classification; Empirical Bayes decision rule; 62H30; Unsupervised learning. 62C12; Bayes decision; Recognition
• ISSN: 0361-0926; 1532-415X
• DOI: 10.1081/STA-200056853

For classification, it is known that the Bayes decision rule is the best decision rule, which gives the minimum probability of misclassification. It is difficult to use the Bayes decision rule, since it contains unknown parameters from each class. In this study, a set of unidentified samples (patterns) is used to establish an optimal classifier such that (1) it only contains the observations of unclassified samples (testing samples), (2) no other classifier is strictly better than our optimal classifier, and (3) when the number of unidentified samples increases, the recognition rate of our classifier converges to the rate of the Bayes decision rule. A Monte Carlo simulation study is presented to demonstrate the favorable recognition rates obtained from our optimal classifier, which quickly converge to the highest rates obtained from the real Bayes decision rule, where the parameters in each class are known.