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The goal of this paper is to show that a single robust estimator of the mean of a multivariate Gaussian distribution can enjoy five desirable properties. First, it is computationally tractable in the sense that it can be computed in a time…

Statistics Theory · Mathematics 2022-10-28 Arnak S. Dalalyan , Arshak Minasyan

We study the fundamental task of outlier-robust mean estimation for heavy-tailed distributions in the presence of sparsity. Specifically, given a small number of corrupted samples from a high-dimensional heavy-tailed distribution whose mean…

Data Structures and Algorithms · Computer Science 2022-11-30 Ilias Diakonikolas , Daniel M. Kane , Jasper C. H. Lee , Ankit Pensia

We study the problem of robustly estimating the mean or location parameter without moment assumptions. We show that for a large class of symmetric distributions, the same error as in the Gaussian setting can be achieved efficiently. The…

Data Structures and Algorithms · Computer Science 2023-11-09 Gleb Novikov , David Steurer , Stefan Tiegel

We provide a unified treatment of a broad class of noisy structure recovery problems, known as structured normal means problems. In this setting, the goal is to identify, from a finite collection of Gaussian distributions with different…

Machine Learning · Statistics 2016-01-27 Akshay Krishnamurthy

Good robust estimators can be tuned to combine a high breakdown point and a specified asymptotic efficiency at a central model. This happens in regression with MM- and tau-estimators among others. However, the finite-sample efficiency of…

Statistics Theory · Mathematics 2013-11-21 Ricardo Maronna , Víctor Yohai

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 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 observe a $n$-sample, the distribution of which is assumed to belong, or at least to be close enough, to a given mixture model. We propose an estimator of this distribution that belongs to our model and possesses some robustness…

Statistics Theory · Mathematics 2025-02-06 Alexandre Lecestre

The problem of linear predictions has been extensively studied for the past century under pretty generalized frameworks. Recent advances in the robust statistics literature allow us to analyze robust versions of classical linear models…

Machine Learning · Statistics 2022-03-15 Saptarshi Chakraborty , Debolina Paul , Swagatam Das

The state-of-the-art methods for estimating high-dimensional covariance matrices all shrink the eigenvalues of the sample covariance matrix towards a data-insensitive shrinkage target. The underlying shrinkage transformation is either…

Machine Learning · Statistics 2025-11-25 Man-Chung Yue , Yves Rychener , Daniel Kuhn , Viet Anh Nguyen

We consider the problem of robust mean and location estimation w.r.t. any pseudo-norm of the form $x\in\mathbb{R}^d\to ||x||_S = \sup_{v\in S}<v,x>$ where $S$ is any symmetric subset of $\mathbb{R}^d$. We show that the deviation-optimal…

Statistics Theory · Mathematics 2021-02-02 Jules Depersin , Guillaume Lecué

Robust Bayesian inference is the calculation of posterior probability bounds given perturbations in a probabilistic model. This paper focuses on perturbations that can be expressed locally in Bayesian networks through convex sets of…

Artificial Intelligence · Computer Science 2013-02-08 Fabio Gagliardi Cozman

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

The aim of this paper is to present a new estimation procedure that can be applied in many statistical frameworks including density and regression and which leads to both robust and optimal (or nearly optimal) estimators. In density…

Statistics Theory · Mathematics 2017-01-23 Yannick Baraud , Lucien Birgé , Mathieu Sart

The rapid emergence of massive datasets in various fields poses a serious challenge to traditional statistical methods. Meanwhile, it provides opportunities for researchers to develop novel algorithms. Inspired by the idea of…

Computation · Statistics 2023-04-14 Yuan Gao , Weidong Liu , Hansheng Wang , Xiaozhou Wang , Yibo Yan , Riquan Zhang

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 developments in robust statistics have established efficient…

Data Structures and Algorithms · Computer Science 2021-01-20 Samuel B. Hopkins , Jerry Li , Fred Zhang

The problem of quickest detection of a change in the distribution of a sequence of independent observations is considered. It is assumed that the pre-change distribution is known (accurately estimated), while the only information about the…

Statistics Theory · Mathematics 2023-09-29 Liyan Xie , Yuchen Liang , Venugopal V. Veeravalli

We propose a robust and scalable procedure for general optimization and inference problems on manifolds leveraging the classical idea of `median-of-means' estimation. This is motivated by ubiquitous examples and applications in modern data…

Methodology · Statistics 2020-06-16 Lizhen Lin , Drew Lazar , Bayan Sarpabayeva , David B. Dunson

The inverse Gaussian (IG) is one of the most famous and considered distributions with positive support. We propose a convenient mode-based parameterization yielding the reparametrized IG (rIG) distribution; it allows/simplifies the use of…

Methodology · Statistics 2017-07-17 Antonio Punzo

There has been a surge of interest in developing robust estimators for models with heavy-tailed and bounded variance data in statistics and machine learning, while few works impose unbounded variance. This paper proposes two type of robust…

Machine Learning · Statistics 2022-10-12 Lihu Xu , Fang Yao , Qiuran Yao , Huiming Zhang