Risk minimization by median-of-means tournaments

Gábor Lugosi, Shahar Mendelson

    Research output: Contribution to journalArticlepeer-review

    34 Citations (Scopus)

    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.

    Original languageEnglish
    Pages (from-to)925-965
    Number of pages41
    JournalJournal of the European Mathematical Society
    Volume22
    Issue number3
    DOIs
    Publication statusPublished - 2020

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