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http://bura.brunel.ac.uk/handle/2438/17009
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. |
URI: | http://bura.brunel.ac.uk/handle/2438/17010 |
DOI: | http://dx.doi.org/10.1109/TIT.2017.2696961 |
ISSN: | 0018-9448 http://dx.doi.org/10.1109/TIT.2017.2696961 |
Appears in Collections: | Publications Publications |
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