# 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} }

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…

## One Citation

Exact spectral norm error of sample covariance

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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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