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- W2608889590 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 $p(X)= mathsf {P}(Y=1 mid X)$ , 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 $hat p$ that is consistent uniformly in $pin P$ . We show that this holds if and only if $P$ is a totally bounded subset of $L^{1}(E,mu )$ , where $mu $ is the distribution of $X$ . In the case, where $E$ is countable, we give a complete characterization of classes $Pi $ , allowing consistent estimation of $p$ , uniform in $(mu ,p)in Pi $ ." @default.
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- W2608889590 date "2017-06-01" @default.
- W2608889590 modified "2023-09-23" @default.
- W2608889590 title "Conditions for Existence of Uniformly Consistent Classifiers" @default.
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- W2608889590 doi "https://doi.org/10.1109/tit.2017.2696961" @default.
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