# Covariance Estimation: Optimal Dimension-free Guarantees for Adversarial Corruption and Heavy Tails

@article{Abdalla2022CovarianceEO,
title={Covariance Estimation: Optimal Dimension-free Guarantees for Adversarial Corruption and Heavy Tails},
author={Pedro Abdalla and Nikita Zhivotovskiy},
journal={ArXiv},
year={2022},
volume={abs/2205.08494}
}
• Published 17 May 2022
• Computer Science, Mathematics
• ArXiv
We provide an estimator of the covariance matrix that achieves the optimal rate of convergence (up to constant factors) in the operator norm under two standard notions of data contamination: We allow the adversary to corrupt an η -fraction of the sample arbitrarily, while the distribution of the remaining data points only satisﬁes that the L p marginal moment with some p > 4 is equivalent to the corresponding L 2 -marginal moment. Despite requiring the existence of only a few moments, our…
1 Citations
Exact spectral norm error of sample covariance
Gaussian widths over spherical slices of the standardized ellipsoid play the role of a ﬁrst-order analogue to the zeroth-order characteristic r ( Σ ). As an immediate application of the ﬁrst-order

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