These lecture notes synthesize robust statistical learning theory, showing how median-of-means, minimax, homogeneity, and small-ball principles yield oracle inequalities for both ERM and robust estimators.
Robust multivariate mean estimation: the optimality of trimmed mean
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abstract
We consider the problem of estimating the mean of a random vector based on i.i.d. observations and adversarial contamination. We introduce a multivariate extension of the trimmed-mean estimator and show its optimal performance under minimal conditions.
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2019 1verdicts
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Lecture Notes: Selected topics on robust statistical learning theory
These lecture notes synthesize robust statistical learning theory, showing how median-of-means, minimax, homogeneity, and small-ball principles yield oracle inequalities for both ERM and robust estimators.