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In this paper, we develop connections between two seemingly disparate, but central, models in robust statistics: Huber's epsilon-contamination model and the heavy-tailed noise model. We provide conditions under which this connection…

Machine Learning · Statistics 2019-07-03 Adarsh Prasad , Sivaraman Balakrishnan , Pradeep Ravikumar

Today's data pose unprecedented challenges to statisticians. It may be incomplete, corrupted or exposed to some unknown source of contamination. We need new methods and theories to grapple with these challenges. Robust estimation is one of…

Statistics Theory · Mathematics 2017-01-17 Mengjie Chen , Chao Gao , Zhao Ren

Coarse data arise when learners observe only partial information about samples; namely, a set containing the sample rather than its exact value. This occurs naturally through measurement rounding, sensor limitations, and lag in economic…

Machine Learning · Computer Science 2026-02-27 Alkis Kalavasis , Anay Mehrotra , Manolis Zampetakis , Felix Zhou , Ziyu Zhu

We study the problem of high-dimensional linear regression in a robust model where an $\epsilon$-fraction of the samples can be adversarially corrupted. We focus on the fundamental setting where the covariates of the uncorrupted samples are…

Machine Learning · Computer Science 2018-06-04 Ilias Diakonikolas , Weihao Kong , Alistair Stewart

We study the problem of estimating the covariance matrix of a high-dimensional distribution when a small constant fraction of the samples can be arbitrarily corrupted. Recent work gave the first polynomial time algorithms for this problem…

Machine Learning · Computer Science 2019-06-12 Yu Cheng , Ilias Diakonikolas , Rong Ge , David Woodruff

We study high-dimensional mean estimation in a collaborative setting where data is contributed by $N$ users in batches of size $n$. In this environment, a learner seeks to recover the mean $\mu$ of a true distribution $P$ from a collection…

Machine Learning · Computer Science 2026-02-25 Maryam Aliakbarpour , Vladimir Braverman , Yuhan Liu , Junze Yin

We consider a robust estimation of linear regression coefficients. In this note, we focus on the case where the covariates are sampled from an $L$-subGaussian distribution with unknown covariance, the noises are sampled from a distribution…

Statistics Theory · Mathematics 2024-05-27 Takeyuki Sasai , Hironori Fujisawa

While there is a rich literature on robust methodologies for contamination in continuously distributed data, contamination in categorical data is largely overlooked. This is regrettable because many datasets are categorical and oftentimes…

Methodology · Statistics 2024-12-13 Max Welz

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

In data analysis, contamination caused by outliers is inevitable, and robust statistical methods are strongly demanded. In this paper, our concern is to develop a new approach for robust data analysis based on scoring rules. The scoring…

Statistics Theory · Mathematics 2013-11-22 Takafumi Kanamori , Hironori Fujisawa

Multivariate Gaussian is often used as a first approximation to the distribution of high-dimensional data. Determining the parameters of this distribution under various constraints is a widely studied problem in statistics, and is often…

Statistics Theory · Mathematics 2016-02-09 Samuel Balmand , Arnak Dalalyan

Large datasets are often affected by cell-wise outliers in the form of missing or erroneous data. However, discarding any samples containing outliers may result in a dataset that is too small to accurately estimate the covariance matrix.…

Statistics Theory · Mathematics 2023-11-13 Karim Lounici , Grégoire Pacreau

We study robust mean estimation in an online and distributed scenario in the presence of adversarial data attacks. At each time step, each agent in a network receives a potentially corrupted data point, where the data points were originally…

Cryptography and Security · Computer Science 2022-09-21 Tong Yao , Shreyas Sundaram

Change point detection is becoming increasingly popular in many application areas. On one hand, most of the theoretically-justified methods are investigated in an ideal setting without model violations, or merely robust against identical…

Methodology · Statistics 2021-10-26 Mengchu Li , Yi Yu

We consider robust location-scale estimators under contamination. We show that commonly used robust estimators such as the median and the Huber estimator are inconsistent under asymmetric contamination, while the Tukey estimator is…

Statistics Theory · Mathematics 2025-02-14 Jens Klooster , Bent Nielsen

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

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 algorithmic problem of sparse mean estimation in the presence of adversarial outliers. Specifically, the algorithm observes a \emph{corrupted} set of samples from $\mathcal{N}(\mu,\mathbf{I}_d)$, where the unknown mean $\mu \in…

Data Structures and Algorithms · Computer Science 2024-03-08 Ankit Pensia

We propose a robust Bayesian formulation of random feature (RF) regression that accounts explicitly for prior and likelihood misspecification via Huber-style contamination sets. Starting from the classical equivalence between…

Machine Learning · Computer Science 2026-02-24 Michele Caprio , Katerina Papagiannouli , Siu Lun Chau , Sayan Mukherjee

Robust estimation of a mean vector, a topic regarded as obsolete in the traditional robust statistics community, has recently surged in machine learning literature in the last decade. The latest focus is on the sub-Gaussian performance and…

Machine Learning · Statistics 2022-02-22 Yijun Zuo