Learning subgaussian classes : Upper and minimax bounds

Guillaume Lecué; Shahar Mendelson

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arXiv · 1305.4825

Learning subgaussian classes : Upper and minimax bounds

Guillaume Lecué·Shahar Mendelson

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Abstract

We obtain sharp oracle inequalities for the empirical risk minimization procedure in the regression model under the assumption that the target Y and the model F are subgaussian. The bound we obtain is sharp in the minimax sense if F is convex. Moreover, under mild assumptions on F, the error rate of ERM remains optimal even if the procedure is allowed to perform with constant probability. A part of our analysis is a new proof of minimax results for the gaussian regression model.

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Guillaume Lecué, Shahar Mendelson. 2013-05-21. Learning subgaussian classes : Upper and minimax bounds. https://arxiv.org/abs/1305.4825

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