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arXiv · 1608.00757

Risk minimization by median-of-means tournaments

Gabor Lugosi·Shahar Mendelson
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Abstract

We consider the classical statistical learning/regression problem, when the value of a real random variable Y is to be predicted based on the observation of another random variable X. Given a class of functions F and a sample of independent copies of (X, Y ), one needs to choose a function f from F such that f(X) approximates Y as well as possible, in the mean-squared sense. We introduce a new procedure, the so-called median-of-means tournament, that achieves the optimal tradeoff between accuracy and confidence under minimal assumptions, and in particular outperforms classical methods based on empirical risk minimization.

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Gabor Lugosi, Shahar Mendelson. 2016-08-02. Risk minimization by median-of-means tournaments. https://arxiv.org/abs/1608.00757

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