mlsanityData to 7 Oct 2026

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

arXiv 2205.08494 ↗First posted 17 May 2022math.ST cs.DS math.PRcited by 14

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Abstract (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 Lp-marginal moment with some p ≥ 4 is equivalent to the corresponding L2-marginal moment. Despite requiring the existence of only a few moments, our estimator achieves the same tail estimates as if the underlying distribution were Gaussian. As a part of our analysis, we prove a dimension-free Bai-Yin type theorem in the regime p > 4.

Key facts. Cited by 14 papers in the map (data through 7 Oct 2026). First posted on arXiv 17 May 2022.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 1; 2023: 2; 2024: 4; 2025: 2; 2026: 5.

14 papers.

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  1. 2024Sharp bounds for max-sliced Wasserstein distancescited by 10
  2. 2024Adaptive Gradient Clipping for Robust Federated Learningcited by 10
  3. 2026Robust Mean Estimation under Quantizationcited by 4
  4. 2023Statistically Optimal Robust Mean and Covariance Estimation for Anisotropic Gaussianscited by 3
  5. 2024Minimax Linear Regression under the Quantile Riskcited by 3
  6. 2026Power-Law Spectrum of the Random Feature Modelcited by 3
  7. 2023A Parameter-Free Two-Bit Covariance Estimator with Improved Operator Norm Error Ratecited by 2
  8. 2024Robust Gradient Descent for Phase Retrievalcited by 2
  9. 2025Do we really need the Rademacher complexities?cited by 1
  10. 2025Robust Estimation in metric spaces: Achieving Exponential Concentration with a Fr'echet Mediancited by 1
  11. 2026The Decision Geometry of Covariance Estimation for the Global Minimum-Variance Portfolio under Heavy Tailscited by 1
  12. 2022Robustifying Markowitzcited by 0
2 more
  1. 2026Computable Bernstein Certificates for Cross-Fitted Clipped Covariance Estimationcited by 0
  2. 2026Precise sample covariance spectral norm error -- an RDT viewcited by 0