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Title: Conditions for Existence of Uniformly Consistent Classifiers
Authors: Kazakeviciute, A
Kazakevicius, V
Olivo, M
Issue Date: 2017
Publisher: Institute of Electrical and Electronics Engineers
Citation: IEEE Transactions on Information Theory, 2017, 63 (6), pp. 3425 - 3432
Abstract: We consider the statistical problem of binary classification, which means attaching a random observation X from a separable metric space E to one of the two classes, 0 or 1. We prove that the consistent estimation of conditional probability p(X)= P(Y=1 X) , where Y is the true class of X, is equivalent to the consistency of a class of empirical classifiers. We then investigate for what classes P there exist an estimate p that is consistent uniformly in p P. We show that this holds if and only if P is a totally bounded subset of L1(Eμ), where μ is the distribution of X. In the case, where E is countable, we give a complete characterization of classes π, allowing consistent estimation of p, uniform in (μ,p)ϵπ.
ISSN: 0018-9448
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