2 A ug 2 01 6 Risk minimization by median - of - means tournaments ∗
نویسندگان
چکیده
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 variableX . Given a class of functions F and a sample of independent copies of (X,Y ), one needs to choose a function f̂ from F such that f̂(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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