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Regularization, sparse recovery, and median-of-means tournaments · Around

2017

Regularization, sparse recovery, and median-of-means tournaments

Lugosi, Gábor, Mendelson, Shahar

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A regularized risk minimization procedure for regression function estimation is introduced that achieves near optimal accuracy and confidence under general conditions, including heavy-tailed predictor and response variables.

The procedure is based on median-of-means tournaments, introduced by the authors in [8].
It is shown that the new procedure outperforms standard regularized empirical risk minimization procedures such as lasso or slope in heavy-tailed problems.

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Approximate loss minimization with heavy tails
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D. Hsu and S. Sabato · 2013
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Empirical risk minimization for heavy-tailed losses
C. Brownlees, E. Joly, and G. Lugosi · 2015
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Learning without concentration
S. Mendelson · 2015
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