Learning without Concentration

Shahar Mendelson

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arXiv · 1401.0304

Learning without Concentration

Shahar Mendelson

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Abstract

We obtain sharp bounds on the performance of Empirical Risk Minimization performed in a convex class and with respect to the squared loss, without assuming that class members and the target are bounded functions or have rapidly decaying tails. Rather than resorting to a concentration-based argument, the method used here relies on a `small-ball' assumption and thus holds for classes consisting of heavy-tailed functions and for heavy-tailed targets. The resulting estimates scale correctly with the `noise level' of the problem, and when applied to the classical, bounded scenario, always improve the known bounds.

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Shahar Mendelson. 2014-01-01. Learning without Concentration. https://arxiv.org/abs/1401.0304

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