Robust subgaussian estimation with VC-dimension

Jules Depersin

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arXiv · 2004.11734

Robust subgaussian estimation with VC-dimension

Jules Depersin

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Abstract

Median-of-means (MOM) based procedures provide non-asymptotic and strong deviation bounds even when data are heavy-tailed and/or corrupted. This work proposes a new general way to bound the excess risk for MOM estimators. The core technique is the use of VC-dimension (instead of Rademacher complexity) to measure the statistical complexity. In particular, this allows to give the first robust estimators for sparse estimation which achieves the so-called subgaussian rate only assuming a finite second moment for the uncorrupted data. By comparison, previous works using Rademacher complexities required a number of finite moments that grows logarithmically with the dimension. With this technique, we derive new robust sugaussian bounds for mean estimation in any norm. We also derive a new robust estimator for covariance estimation that is the first to achieve subgaussian bounds without $L_4-L_2$ norm equivalence.

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BibTeX RIS

Jules Depersin. 2020-04-24. Robust subgaussian estimation with VC-dimension. https://arxiv.org/abs/2004.11734

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