Recent advances in algorithmic high-dimensional robust statistics
Learning in the presence of outliers is a fundamental problem in statistics. Until recently, all
known efficient unsupervised learning algorithms were very sensitive to outliers in high …
known efficient unsupervised learning algorithms were very sensitive to outliers in high …
Mean estimation and regression under heavy-tailed distributions: A survey
We survey some of the recent advances in mean estimation and regression function
estimation. In particular, we describe sub-Gaussian mean estimators for possibly heavy …
estimation. In particular, we describe sub-Gaussian mean estimators for possibly heavy …
Efficient mean estimation with pure differential privacy via a sum-of-squares exponential mechanism
We give the first polynomial-time algorithm to estimate the mean of ad-variate probability
distribution with bounded covariance from Õ (d) independent samples subject to pure …
distribution with bounded covariance from Õ (d) independent samples subject to pure …
Robust multivariate mean estimation: the optimality of trimmed mean
G Lugosi, S Mendelson - 2021 - projecteuclid.org
Robust multivariate mean estimation: The optimality of trimmed mean Page 1 The Annals of
Statistics 2021, Vol. 49, No. 1, 393–410 https://doi.org/10.1214/20-AOS1961 © Institute of …
Statistics 2021, Vol. 49, No. 1, 393–410 https://doi.org/10.1214/20-AOS1961 © Institute of …
Private mean estimation of heavy-tailed distributions
We give new upper and lower bounds on the minimax sample complexity of differentially
private mean estimation of distributions with bounded $ k $-th moments. Roughly speaking …
private mean estimation of distributions with bounded $ k $-th moments. Roughly speaking …
Robust and heavy-tailed mean estimation made simple, via regret minimization
We study the problem of estimating the mean of a distribution in high dimensions when
either the samples are adversarially corrupted or the distribution is heavy-tailed. Recent …
either the samples are adversarially corrupted or the distribution is heavy-tailed. Recent …
Privacy induces robustness: Information-computation gaps and sparse mean estimation
We establish a simple connection between robust and differentially-private algorithms:
private mechanisms which perform well with very high probability are automatically robust in …
private mechanisms which perform well with very high probability are automatically robust in …
Robust sub-Gaussian estimation of a mean vector in nearly linear time
We construct an algorithm for estimating the mean of a heavy-tailed random variable when
given an adversarial corrupted sample of N independent observations. The only assumption …
given an adversarial corrupted sample of N independent observations. The only assumption …
Outlier robust mean estimation with subgaussian rates via stability
We study the problem of outlier robust high-dimensional mean estimation under a bounded
covariance assumption, and more broadly under bounded low-degree moment …
covariance assumption, and more broadly under bounded low-degree moment …
Mean estimation with sub-Gaussian rates in polynomial time
SB Hopkins - The Annals of Statistics, 2020 - JSTOR
We study polynomial time algorithms for estimating the mean of a heavytailed multivariate
random vector. We assume only that the random vector X has finite mean and covariance. In …
random vector. We assume only that the random vector X has finite mean and covariance. In …