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

DOI: 10.5176/2251-1911_CMCGS16.8

Authors: Agne Kazakeviciute and Malini Olivo

Abstract: Let X be a random variable taking values in a finite dimensional linear space and Y 2 f0; 1g its associated label. We study the case, where conditional distribution p(x) = P(Y = 1 j X = x) depends on x through some linear form x. We show that in this case, under a mild assumption on the distribution  of X, a maximum-likelihood estimator ^p, as well as the induced class of logistic classifiers, are uniformly (w.r.t. p) consistent.

Keywords: Uniform consistency, logistic classifier, finitedimensional linear spaces