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Related papers: Robust Mean Estimation in High Dimensions: An Outl…

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We study the robust mean estimation problem in high dimensions, where $\alpha <0.5$ fraction of the data points can be arbitrarily corrupted. Motivated by compressive sensing, we formulate the robust mean estimation problem as the…

Machine Learning · Statistics 2020-08-24 Jing Liu , Aditya Deshmukh , Venugopal V. Veeravalli

We study the problem of robustly estimating the mean of a $d$-dimensional distribution given $N$ examples, where most coordinates of every example may be missing and $\varepsilon N$ examples may be arbitrarily corrupted. Assuming each…

Data Structures and Algorithms · Computer Science 2021-05-04 Lunjia Hu , Omer Reingold

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 Theory · Mathematics 2021-03-17 Ilias Diakonikolas , Daniel M. Kane , Ankit Pensia

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 dimensions. In particular, even for the task of robust…

Data Structures and Algorithms · Computer Science 2019-11-15 Ilias Diakonikolas , Daniel M. Kane

Robust statistics aims to compute quantities to represent data where a fraction of it may be arbitrarily corrupted. The most essential statistic is the mean, and in recent years, there has been a flurry of theoretical advancement for…

Machine Learning · Statistics 2025-02-18 Cullen Anderson , Jeff M. Phillips

We study high-dimensional sparse estimation tasks in a robust setting where a constant fraction of the dataset is adversarially corrupted. Specifically, we focus on the fundamental problems of robust sparse mean estimation and robust sparse…

Data Structures and Algorithms · Computer Science 2019-11-20 Ilias Diakonikolas , Sushrut Karmalkar , Daniel Kane , Eric Price , Alistair Stewart

Robust estimation is much more challenging in high dimensions than it is in one dimension: Most techniques either lead to intractable optimization problems or estimators that can tolerate only a tiny fraction of errors. Recent work in…

Machine Learning · Computer Science 2018-03-14 Ilias Diakonikolas , Gautam Kamath , Daniel M. Kane , Jerry Li , Ankur Moitra , Alistair Stewart

We study the problem of high-dimensional robust mean estimation in the presence of a constant fraction of adversarial outliers. A recent line of work has provided sophisticated polynomial-time algorithms for this problem with…

Machine Learning · Computer Science 2020-05-05 Yu Cheng , Ilias Diakonikolas , Rong Ge , Mahdi Soltanolkotabi

Robust mean estimation is the problem of estimating the mean $\mu \in \mathbb{R}^d$ of a $d$-dimensional distribution $D$ from a list of independent samples, an $\epsilon$-fraction of which have been arbitrarily corrupted by a malicious…

Computational Complexity · Computer Science 2019-06-05 Samuel B. Hopkins , Jerry Li

We introduce new estimators for robust machine learning based on median-of-means (MOM) estimators of the mean of real valued random variables. These estimators achieve optimal rates of convergence under minimal assumptions on the dataset.…

Statistics Theory · Mathematics 2017-12-04 Guillaume Lecué , Matthieu Lerasle

We study two problems in high-dimensional robust statistics: \emph{robust mean estimation} and \emph{outlier detection}. In robust mean estimation the goal is to estimate the mean $\mu$ of a distribution on $\mathbb{R}^d$ given $n$…

Data Structures and Algorithms · Computer Science 2019-06-28 Yihe Dong , Samuel B. Hopkins , Jerry Li

We revisit the problem of estimating the mean of a high-dimensional distribution in the presence of an $\varepsilon$-fraction of adversarial outliers. When $\varepsilon$ is at most some sufficiently small constant, previous works can…

Data Structures and Algorithms · Computer Science 2024-11-22 Hongjie Chen , Deepak Narayanan Sridharan , David Steurer

We study the fundamental problem of high-dimensional mean estimation in a robust model where a constant fraction of the samples are adversarially corrupted. Recent work gave the first polynomial time algorithms for this problem with…

Machine Learning · Computer Science 2018-11-26 Yu Cheng , Ilias Diakonikolas , Rong Ge

We study the problem of high-dimensional robust mean estimation in an online setting. Specifically, we consider a scenario where $n$ sensors are measuring some common, ongoing phenomenon. At each time step $t=1,2,\ldots,T$, the $i^{th}$…

Machine Learning · Computer Science 2023-10-26 Daniel M. Kane , Ilias Diakonikolas , Hanshen Xiao , Sihan Liu

Many modern datasets are collected automatically and are thus easily contaminated by outliers. This led to a regain of interest in robust estimation, including new notions of robustness such as robustness to adversarial contamination of the…

Statistics Theory · Mathematics 2023-05-05 Pierre Alquier , Mathieu Gerber

Outliers widely occur in big-data applications and may severely affect statistical estimation and inference. In this paper, a framework of outlier-resistant estimation is introduced to robustify an arbitrarily given loss function. It has a…

Methodology · Statistics 2023-04-20 Yiyuan She , Zhifeng Wang , Jiahui Shen

The best subset selection (or "best subsets") estimator is a classic tool for sparse regression, and developments in mathematical optimization over the past decade have made it more computationally tractable than ever. Notwithstanding its…

Methodology · Statistics 2022-01-11 Ryan Thompson

We explore why many recently proposed robust estimation problems are efficiently solvable, even though the underlying optimization problems are non-convex. We study the loss landscape of these robust estimation problems, and identify the…

Machine Learning · Statistics 2020-05-29 Banghua Zhu , Jiantao Jiao , Jacob Steinhardt

We study the algorithmic problem of robust mean estimation of an identity covariance Gaussian in the presence of mean-shift contamination. In this contamination model, we are given a set of points in $\mathbb{R}^d$ generated i.i.d. via the…

Data Structures and Algorithms · Computer Science 2025-02-21 Ilias Diakonikolas , Giannis Iakovidis , Daniel M. Kane , Thanasis Pittas

We study the problem of robust mean estimation and introduce a novel Hamming distance-based measure of distribution shift for coordinate-level corruptions. We show that this measure yields adversary models that capture more realistic…

Machine Learning · Computer Science 2021-06-14 Zifan Liu , Jongho Park , Theodoros Rekatsinas , Christos Tzamos
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