A study of logistic classifier: uniform consistency in finite-dimensional linear spaces

A study of logistic classifier: uniform consistency in finite-dimensional linear spaces
Title:
A study of logistic classifier: uniform consistency in finite-dimensional linear spaces
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Journal of Mathematics, Statistics and Operations Research
DOI:
10.5176/2251-1911_CMCGS16.8
Publication Date:
29 August 2016
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Abstract:
Let X be a random variable taking values in a finite dimensional linear space and Y ∈ {0, 1} its associated label. We study the case, where conditional distribution p(x) = P(Y = 1 | X = x) depends on x through some linear form θx. We show that in this case, under a mild assumption on the distribution µ of X, a maximum-likelihood estimator pˆ, as well as the induced class of logistic classifiers, are uniformly (w.r.t. p) consistent.
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