Adversarially robust estimators transfer to heavy-tailed estimation for free, but heavy-tailed estimators do not transfer back to adversarial contamination.
Covariance estimation: Optimal dimension-free guarantees for adversarial corruption and heavy tails
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Heavy-tailed Contamination is Easier than Adversarial Contamination
Adversarially robust estimators transfer to heavy-tailed estimation for free, but heavy-tailed estimators do not transfer back to adversarial contamination.