Learning with Square Loss: Localization through Offset Rademacher Complexity

02/21/2015

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by   Tengyuan Liang, et al.

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We consider regression with square loss and general classes of functions without the boundedness assumption. We introduce a notion of offset Rademacher complexity that provides a transparent way to study localization both in expectation and in high probability. For any (possibly non-convex) class, the excess loss of a two-step estimator is shown to be upper bounded by this offset complexity through a novel geometric inequality. In the convex case, the estimator reduces to an empirical risk minimizer. The method recovers the results of RakSriTsy15 for the bounded case while also providing guarantees without the boundedness assumption.