Four Extensions of the Universal Law of Robustness: Log-Concave Covariates, Heterogeneous Mixtures, Vector-Valued Predictors, and Markovian Data

arXiv:2611.03653v1 Announce Type: new Abstract: Bubeck and Sellke's universal law of robustness says that fitting $n$ noisy samples below the noise level with a class of $p$ real parameters forces a Lipschitz constant of order $\sqrt{nd/p}$, when the covariate distribution on $\mathbb{R}^d$ is isop…

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1. 2026-11-04 05:00 · arXiv cs.LG
   Four Extensions of the Universal Law of Robustness: Log-Concave Covariates, Heterogeneous Mixtures, Vector-Valued Predictors, and Markovian Data