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In today's era of big data, robust least-squares regression becomes a more challenging problem when considering the adversarial corruption along with explosive growth of datasets. Traditional robust methods can handle the noise but suffer…

Data Structures and Algorithms · Computer Science 2017-10-04 Xuchao Zhang , Liang Zhao , Arnold P. Boedihardjo , Chang-Tien Lu

We study multivariate linear regression under Gaussian covariates in two settings, where data may be erased or corrupted by an adversary under a coordinate-wise budget. In the incomplete data setting, an adversary may inspect the dataset…

Data Structures and Algorithms · Computer Science 2025-09-24 Ilias Diakonikolas , Jelena Diakonikolas , Daniel M. Kane , Jasper C. H. Lee , Thanasis Pittas

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

Convex and penalized robust regression methods often suffer from a persistent bias induced by large outliers, limiting their effectiveness in adversarial or heavy-tailed settings. In this work, we study a smooth redescending non-convex…

Statistics Theory · Mathematics 2025-12-01 Ilyes Hammouda , Mohamed Ndaoud , Abd-Krim Seghouane

Contaminations are a key concern in modern statistical learning, as small but systematic perturbations of all datapoints can substantially alter estimation results. Here, we study Wasserstein-$r$ contaminations ($r\ge 1$) in an $\ell_q$…

Machine Learning · Statistics 2025-11-24 Patrick Chao , Edgar Dobriban

In this paper, we propose a novel approach to fit a functional linear regression in which both the response and the predictor are functions of a common variable such as time. We consider the case that the response and the predictor…

Methodology · Statistics 2017-11-15 Behdad Mostafaiy , MohammadReza FaridRohani , Shojaeddin Chenouri

Identifying anomalies and contamination in datasets is important in a wide variety of settings. In this paper, we describe a new technique for estimating contamination in large, discrete valued datasets. Our approach considers the normal…

Information Theory · Computer Science 2015-06-16 Matthew L. Malloy , Scott Alfeld , Paul Barford

The Gaussian cluster-weighted model (CWM) is a mixture of regression models with random covariates that allows for flexible clustering of a random vector composed of response variables and covariates. In each mixture component, it adopts a…

Methodology · Statistics 2014-09-23 Antonio Punzo , Paul D. McNicholas

We study high-dimensional least-squares regression within a subgaussian statistical learning framework with heterogeneous noise. It includes $s$-sparse and $r$-low-rank least-squares regression when a fraction $\epsilon$ of the labels are…

Statistics Theory · Mathematics 2023-11-01 Philip Thompson

We study Gaussian sparse estimation tasks in Huber's contamination model with a focus on mean estimation, PCA, and linear regression. For each of these tasks, we give the first sample and computationally efficient robust estimators with…

Machine Learning · Computer Science 2024-03-18 Ilias Diakonikolas , Daniel M. Kane , Sushrut Karmalkar , Ankit Pensia , Thanasis Pittas

The advent of large-scale inference has spurred reexamination of conventional statistical thinking. In a Gaussian model for $n$ many $z$-scores with at most $k < \frac{n}{2}$ nonnulls, Efron suggests estimating the location and scale…

Statistics Theory · Mathematics 2025-01-15 Subhodh Kotekal , Chao Gao

We introduce one-sided versions of Huber's contamination model, in which corrupted samples tend to take larger values than uncorrupted ones. Two intertwined problems are addressed: estimation of the mean of uncorrupted samples (minimum…

Statistics Theory · Mathematics 2018-09-25 Alexandra Carpentier , Sylvain Delattre , Etienne Roquain , Nicolas Verzelen

We develop a method to generate prediction sets with a guaranteed coverage rate that is robust to corruptions in the training data, such as missing or noisy variables. Our approach builds on conformal prediction, a powerful framework to…

Machine Learning · Computer Science 2025-01-10 Shai Feldman , Yaniv Romano

We consider a variant of regression problem, where the correspondence between input and output data is not available. Such shuffled data is commonly observed in many real world problems. Taking flow cytometry as an example, the measuring…

Machine Learning · Computer Science 2021-02-12 Yujia Xie , Yixiu Mao , Simiao Zuo , Hongteng Xu , Xiaojing Ye , Tuo Zhao , Hongyuan Zha

Distributionally robust optimisation (DRO) minimises the worst-case expected loss over an ambiguity set that can capture distributional shifts in out-of-sample environments. While Huber (linear-vacuous) contamination is a classical…

Machine Learning · Statistics 2026-01-30 Mengqi Chen , Thomas B. Berrett , Theodoros Damoulas , Michele Caprio

We provide a new computationally-efficient class of estimators for risk minimization. We show that these estimators are robust for general statistical models: in the classical Huber epsilon-contamination model and in heavy-tailed settings.…

Machine Learning · Statistics 2018-04-23 Adarsh Prasad , Arun Sai Suggala , Sivaraman Balakrishnan , Pradeep Ravikumar

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 robust linear regression with response variable corruptions. We consider the oblivious adversary model, where the adversary corrupts a fraction of the responses in complete ignorance of the data. We provide a nearly…

Machine Learning · Computer Science 2019-03-21 Arun Sai Suggala , Kush Bhatia , Pradeep Ravikumar , Prateek Jain

Robust estimation under Huber's $\epsilon$-contamination model has become an important topic in statistics and theoretical computer science. Statistically optimal procedures such as Tukey's median and other estimators based on depth…

Machine Learning · Statistics 2019-02-27 Chao Gao , Jiyi Liu , Yuan Yao , Weizhi Zhu

We obtain robust and computationally efficient estimators for learning several linear models that achieve statistically optimal convergence rate under minimal distributional assumptions. Concretely, we assume our data is drawn from a…

Machine Learning · Statistics 2020-12-07 Ainesh Bakshi , Adarsh Prasad