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We give the first polynomial-time algorithm for performing linear or polynomial regression resilient to adversarial corruptions in both examples and labels. Given a sufficiently large (polynomial-size) training set drawn i.i.d. from…

Machine Learning · Computer Science 2020-06-05 Adam Klivans , Pravesh K. Kothari , Raghu Meka

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

This paper studies a tensor-structured linear regression model with a scalar response variable and tensor-structured predictors, such that the regression parameters form a tensor of order $d$ (i.e., a $d$-fold multiway array) in…

Machine Learning · Computer Science 2020-11-26 Talal Ahmed , Haroon Raja , Waheed U. Bajwa

We develop machinery to design efficiently computable and consistent estimators, achieving estimation error approaching zero as the number of observations grows, when facing an oblivious adversary that may corrupt responses in all but an…

Machine Learning · Computer Science 2021-11-05 Tommaso d'Orsi , Chih-Hung Liu , Rajai Nasser , Gleb Novikov , David Steurer , Stefan Tiegel

In modern large-scale observational studies, data collection constraints often result in partially labeled datasets, posing challenges for reliable causal inference, especially due to potential labeling bias and relatively small size of the…

Methodology · Statistics 2025-04-22 Yuqian Zhang , Abhishek Chakrabortty , Jelena Bradic

Recent developments on deep learning established some theoretical properties of deep neural networks estimators. However, most of the existing works on this topic are restricted to bounded loss functions or (sub)-Gaussian or bounded input.…

Machine Learning · Statistics 2024-05-09 William Kengne , Modou Wade

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

High-dimensional linear regression under heavy-tailed noise or outlier corruption is challenging, both computationally and statistically. Convex approaches have been proven statistically optimal but suffer from high computational costs,…

Statistics Theory · Mathematics 2023-05-11 Yinan Shen , Jingyang Li , Jian-Feng Cai , Dong Xia

For the sparse vector model, we consider estimation of the target vector, of its L2-norm and of the noise variance. We construct adaptive estimators and establish the optimal rates of adaptive estimation when adaptation is considered with…

Statistics Theory · Mathematics 2020-03-04 Laëtitia Comminges , Olivier Collier , Mohamed Ndaoud , Alexandre B. Tsybakov

Dynamical systems can confront one of two extreme types of disturbances: persistent zero-mean independent noise, and sparse nonzero-mean adversarial attacks, depending on the specific scenario being modeled. While mean-based estimators like…

Optimization and Control · Mathematics 2026-03-31 Jihun Kim , Javad Lavaei

We establish theoretical guarantees for the expected prediction error of the exponential weighting aggregate in the case of multivariate regression that is when the label vector is multidimensional. We consider the regression model with…

Statistics Theory · Mathematics 2018-06-26 Arnak S. Dalalyan

Robust regression techniques rely on least-squares optimization, which works well for Gaussian noise but fails in the presence of asymmetric structured noise. We propose a hybrid neural-symbolic architecture where a transformer encoder…

Machine Learning · Computer Science 2025-08-06 Roman Gutierrez , Tony Kai Tang , Isabel Gutierrez

The problem of structured matrix estimation has been studied mostly under strong noise dependence assumptions. This paper considers a general framework of noisy low-rank-plus-sparse matrix recovery, where the noise matrix may come from any…

Machine Learning · Statistics 2025-04-07 Jinhang Chai , Jianqing Fan

We study the fundamental problems of Gaussian mean estimation and linear regression with Gaussian covariates in the presence of Huber contamination. Our main contribution is the design of the first sample near-optimal and almost linear-time…

Data Structures and Algorithms · Computer Science 2023-12-05 Ilias Diakonikolas , Daniel M. Kane , Ankit Pensia , Thanasis Pittas

This paper investigates tradeoffs among optimization errors, statistical rates of convergence and the effect of heavy-tailed errors for high-dimensional robust regression with nonconvex regularization. When the additive errors in linear…

Statistics Theory · Mathematics 2021-01-01 Xiaoou Pan , Qiang Sun , Wen-Xin Zhou

This paper focuses on efficient computational approaches to compute approximate solutions of a linear inverse problem that is contaminated with mixed Poisson--Gaussian noise, and when there are additional outliers in the measured data. The…

Numerical Analysis · Mathematics 2018-01-22 Marie Kubínová , James G. Nagy

We consider estimating an unknown signal, both blocky and sparse, which is corrupted by additive noise. We study three interrelated least squares procedures and their asymptotic properties. The first procedure is the fused lasso, put…

Statistics Theory · Mathematics 2009-08-31 Alessandro Rinaldo

This paper proposes an estimation framework to assess the performance of sorting over perturbed/noisy data. In particular, the recovering accuracy is measured in terms of Minimum Mean Square Error (MMSE) between the values of the sorting…

Information Theory · Computer Science 2019-09-04 Alex Dytso , Martina Cardone , H. Vincent Poor

We investigate high-dimensional sparse regression when both the noise and the design matrix exhibit heavy-tailed behavior. Standard algorithms typically fail in this regime, as heavy-tailed covariates distort the empirical risk geometry. We…

Methodology · Statistics 2026-01-12 Kaiyuan Zhou , Xiaoyu Zhang , Wenyang Zhang , Di Wang

We study robust high-dimensional sparse regression under finite-variance heavy-tailed noise, epsilon-contamination, and alpha-mixing dependence via two subsampling estimators: Adaptive Importance Sampling (AIS) and Stratified Sub-sampling…

Statistics Theory · Mathematics 2026-03-11 Prateek Mittal , Joohi Chauhan