Bounding the expectation of the supremum of an empirical process over a\n (weak) vc-major class

2014/11/20 by Yannick Baraud, Baraud, Yannick · 2 citations
Computer Science · Mathematics · #Machine Learning and Algorithms #Mathematical Approximation and Integration

paper · pdf · doi:10.48550/arxiv.1411.5571

Abstract

Given a bounded class of functions G and independent random variables X1, . .\n. , Xn, we provide an upper bound for the expectation of the supremum of the\nempirical process over elements of G having a small variance. Our bound applies\nin the cases where G is a VC-subgraph or a VC-major class and it is of smaller\norder than those one could get by using a universal entropy bound over the\nwhole class G . It also involves explicit constants and does not require the\nknowledge of the entropy of G\n

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