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We study the problem of outlier robust high-dimensional mean estimation under a finite covariance assumption, and more broadly under finite low-degree moment assumptions. We consider a standard stability condition from the recent robust statistics literature and prove that, except with exponentially small failure probability, there exists a large fraction of the inliers satisfying this condition. As a corollary, it follows that a number of recently developed algorithms for robust mean estimation, including iterative filtering and non-convex gradient descent, give optimal error estimators with (near-)subgaussian rates. Previous analyses of these algorithms gave significantly suboptimal rates. As a corollary of our approach, we obtain the first computationally efficient algorithm with subgaussian rate for outlier-robust mean estimation in the strong contamination model under a finite covariance assumption.
In this paper, we develop a computational approach for estimating the mean value of a quantity in the presence of uncertainty. We demonstrate that, under some mild assumptions, the upper and lower bounds of the mean value are efficiently computable v
We develop efficient algorithms for estimating low-degree moments of unknown distributions in the presence of adversarial outliers. The guarantees of our algorithms improve in many cases significantly over the best previous ones, obtained in recent w
We revisit the problem of estimating the mean of a real-valued distribution, presenting a novel estimator with sub-Gaussian convergence: intuitively, our estimator, on any distribution, is as accurate as the sample mean is for the Gaussian distributi
We study the problem of {em list-decodable mean estimation} for bounded covariance distributions. Specifically, we are given a set $T$ of points in $mathbb{R}^d$ with the promise that an unknown $alpha$-fraction of points in $T$, where $0< alpha < 1/
We undertake a precise study of the non-asymptotic properties of vanilla generative adversarial networks (GANs) and derive theoretical guarantees in the problem of estimating an unknown $d$-dimensional density $p^*$ under a proper choice of the class