Recent advances in algorithmic high-dimensional robust statistics

I Diakonikolas, DM Kane - arxiv preprint arxiv:1911.05911, 2019 - arxiv.org
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 …

Mean estimation and regression under heavy-tailed distributions: A survey

G Lugosi, S Mendelson - Foundations of Computational Mathematics, 2019 - Springer
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 …

Efficient mean estimation with pure differential privacy via a sum-of-squares exponential mechanism

SB Hopkins, G Kamath, M Majid - Proceedings of the 54th Annual ACM …, 2022 - dl.acm.org
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 …

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 …

Private mean estimation of heavy-tailed distributions

G Kamath, V Singhal, J Ullman - Conference on Learning …, 2020 - proceedings.mlr.press
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 …

Robust and heavy-tailed mean estimation made simple, via regret minimization

S Hopkins, J Li, F Zhang - Advances in Neural Information …, 2020 - proceedings.neurips.cc
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 …

Privacy induces robustness: Information-computation gaps and sparse mean estimation

K Georgiev, S Hopkins - Advances in neural information …, 2022 - proceedings.neurips.cc
We establish a simple connection between robust and differentially-private algorithms:
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

J Depersin, G Lecué - The Annals of Statistics, 2022 - projecteuclid.org
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 …

Outlier robust mean estimation with subgaussian rates via stability

I Diakonikolas, DM Kane… - Advances in Neural …, 2020 - proceedings.neurips.cc
We study the problem of outlier robust high-dimensional mean estimation under a bounded
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 …