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

Gábor Lugosi; Shahar Mendelson

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arXiv · 1701.04112

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

Gábor Lugosi·Shahar Mendelson

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Abstract

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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Gábor Lugosi, Shahar Mendelson. 2017-01-15. Regularization, sparse recovery, and median-of-means tournaments. https://arxiv.org/abs/1701.04112

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