Conditions for Existence of Uniformly Consistent Classifiers

Conditions for Existence of Uniformly Consistent Classifiers
Title:
Conditions for Existence of Uniformly Consistent Classifiers
Other Titles:
IEEE Transactions on Information Theory
DOI:
10.1109/TIT.2017.2696961
Publication Date:
01 April 2017
Citation:
A. Kazakeviciute, V. Kazakevicius and M. Olivo, "Conditions for Existence of Uniformly Consistent Classifiers," in IEEE Transactions on Information Theory, vol. 63, no. 6, pp. 3425-3432, June 2017. doi: 10.1109/TIT.2017.2696961
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 p̂ that is consistent uniformly in p ∈ P. We show that this holds if and only if P is a totally bounded subset of L 1 (E, μ), 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) ∈ Π.
License type:
PublisherCopyrights
Funding Info:
Description:
© 2017 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
ISSN:
0018-9448
1557-9654
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