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Empirical risk minimization for heavy-tailed losses

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In this talk we discuss empirical risk minimization when the losses are not necessarily bounded and may have a distribution with heavy tails. In such situations usual empirical averages may fail to give accurate risk estimates. However, some robust mean estimators proposed in the literature may be used to replace empirical means. We pay particular attention to empirical risk minimization based on a robust estimate proposed by Olivier Catoni. We develop performance bounds based on a chaining argument tailored to Catoni’s mean estimator. The results are illustrated on examples of regression function estimation and k-means clustering. Joint work with Christian Brownlees and Emilien Joly.

This talk is part of the Probability Theory and Statistics in High and Infinite Dimensions series.

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