Robust Regression

Ask about this topic

Overview

Robust regression studies how to estimate relationships between variables when data contain outliers, contamination, heavy-tailed noise, or distribution shifts. Common approaches include robust losses such as Huber and Welsch, trimming and median-of-means estimators, sparse thresholding, and distributionally robust optimization. The field also develops guarantees for settings such as adversarial corruption, missing features, and multi-task learning, alongside practical methods for uncertainty estimates and nonlinear models. A central tension is balancing protection against bad data with statistical efficiency and computational cost, since robust methods do not always outperform ordinary least squares when its assumptions are adequate.

Latest papers

CardsList

29 papers4 papers in the last four weeks, against 2 the four weeks before. 0.0% of all new papers.

  1. Partial Modal Tensor Regression

    Oct 25, 2026Jintao Han, Li Zhang, Xuejun MaRobust RegressionDimensionality Reduction

    Soochow University, School of Mathematical Sciences · Renmin University of China, School of Smart Governance

  2. GBTSVR: Twin Support Vector Regression via Granular Ball Computing

    Oct 14, 2026A. Quadir, M. TanveerRobust RegressionSupport Vector Machines

    Department of Mathematics, Indian Institute of Technology Indore, Simrol, Indore, 453552, Madhya Pradesh, India

  3. Robustly Reliable Learning for Regression

    Oct 12, 2026Avrim Blum, Anh Tuan NguyenRobust Regression

    TTIC · Carnegie Mellon University

  4. Distributionally robust linear regression through the lens of adversarial training

    Sep 30, 2026Elis Stefansson, David Vävinggren, Antônio H. RibeiroRobust RegressionDistributionally Robust Optimization

    Uppsala University, Sweden · Science for Life Laboratory, Sweden

  5. CVaR anchor regression protects against rare shifts

    Sep 22, 2026Malte LondschienDistribution Shift RobustnessRobust Regression

  6. Sparse Regression Distilled from a Single Robust Fit

    Sep 20, 2026Wooyoung Shin, Seunghwan ParkRobust RegressionLinear Regression

    Department of Information Statistics, Kangwon National University, 1, Kangwondaehak-gil, Chuncheon-si, Gangwon-do, 24341, Republic of Korea.

  7. When Does Dynamic Ensembling Pay Off? Diagnosing Regionwise Gains in Regression under Distribution Shift

    Aug 18, 2026Tianxin Zhou, Ruixi LinEnsemble LearningDistribution Shift Robustness

  8. Variational Outlier-Robust Gaussian Process Regression with Generative Modeling

    Aug 17, 2026Arslan Majal, Aamir Hussain ChughtaiGaussian Process RegressionRobust Regression

    Zunitech, LLC, Houston, USA · Institute of Data Science, University of Engineering and Technology, Lahore, Pakistan

  9. Higher-Order Certified Robustness for Regression

    Jul 6, 2026Jie Zhang, Natalie FrankRobust RegressionRandomized Smoothing

    University of Washington, USA

  10. Distributionally Robust Linear Regression With Block Lewis Weights

    Jun 30, 2026Naren Sarayu Manoj, Kumar Kshitij PatelRobust RegressionGroup Distributionally Robust Optimization

    TTIC · Institute for Foundations of Data Science, Yale University

  11. Adversarial Contamination Meets Hard Thresholding: An Iterative Algorithm with Signal Adaptivity and Minimax Optimality

    Jun 26, 2026Shixiang Liu, Hanming YangRobust RegressionSparse Recovery

    School of Statistics, Renmin University of China · Institute of Statistics and Big Data, Renmin University of China

  12. Alternate loss functions and regression models that achieve robustness to outliers by modulating the learning rate

    Jun 20, 2026Mathew Mithra Noel, Arindam Banerjee, Yug D. Oswal +2Robust RegressionRobust Loss Functions

    aSchool of Electrical Engineering, Vellore Institute of Technology, Vellore, 632 014, Tamil Nadu, India · bErnst and Young GDS, Godrej Waterside, Ring Rd, DP Block, Sector V, Bidhannagar, Kolkata, 700 091, West Bengal, India · cSchool of Computer Science and Engineering, Vellore Institute of Technology, Vellore, 632 014, Tamil Nadu, India

  13. Joint Model and Data Sparsification via the Marginal Likelihood

    May 28, 2026Alexander Timans, Thomas Möllenhoff, Christian A. Naesseth +2Dataset PruningRobust Regression

    1UvA-Bosch Delta Lab, University of Amsterdam · 2RIKEN Center for AI Project, Tokyo, Japan · Department of Computer Science, Johns Hopkins University.

  14. Algorithms with Polynomially-Improved Approximation Factors for the 2→q2 \rightarrow q Norm, and Applications

    May 24, 2026Samuel B. Hopkins, Stefan TiegelRobust RegressionRobust Mean Estimation

    MIT

  15. Multi-task Linear Regression without Eigenvalue Lower Bounds: Adaptivity, Robustness, and Safety

    May 16, 2026Seok-Jin KimRobust RegressionMulti-Task Learning

    Columbia IEOR

  16. Byzantine-Robust Distributed Sparse Learning Revisited

    May 13, 2026Yuxuan Wang, Lixin Zhang, Kangqiang LiDistributed TrainingDistributed Optimization

    School of Mathematical Sciences, Zhejiang University, Hangzhou, 310027, Zhejiang, China · School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou, 310018, Zhejiang, China · Information Center, Hubei Provincial Tobacco Monopoly Administration, Wuhan, 430030, Hubei, China

  17. SHIFT: Robust Double Machine Learning for Average Dose-Response Functions under Heavy-Tailed Contamination

    Apr 30, 2026Eichi UeharaDouble MLRobust Regression

    Independent researcher.

  18. Bayesian X-Learner: Calibrated Posterior Inference for Heterogeneous Treatment Effects under Heavy-Tailed Outcomes

    Apr 30, 2026Eichi UeharaRobust RegressionCausal Effect Estimation

    Independent researcher

  19. Meta Additive Model: Interpretable Sparse Learning With Auto Weighting

    Apr 22, 2026Xuelin Zhang, Xinyue Liu, Lingjuan Wu +1Robust RegressionAdaptive Loss Weighting

    College of Informatics, Huazhong Agricultural University, Wuhan, China

  20. Double descent for least-squares interpolation on contaminated data: A simulation study

    Apr 15, 2026Tino WernerDouble DescentLinear Regression

    Institute for Mathematics, Carl von Ossietzky University Oldenburg, Carl-von-Ossietzky-Straße 9-11, 26129 Oldenburg, Lower Saxony, Germany

  21. Computation of Least Trimmed Squares: A Branch-and-Bound framework with Hyperplane Arrangement Enhancements

    Apr 13, 2026Xiang Meng, Andrés Gómez, Rahul MazumderRobust RegressionRobust Statistics

    MIT Operations Research Center · USC Daniel J. Epstein Department of Industrial and Systems Engineering · MIT Sloan School of Management, Operations Research Center

  22. LEADER: Learning Reliable Local-to-Global Correspondences for LiDAR Relocalization

    Apr 13, 2026Jianshi Wu, Minghang Zhu, Dunqiang Liu +5LiDAR LocalizationPoint Cloud Learning

    Fujian Key Laboratory of Urban Intelligent Sensing and Computing · Key Laboratory of Multimedia Trusted Perception and Efficient Computing, Ministry of Education of China, School of Informatics, Xiamen University, China · School of Engineering Mathematics and Technology, University of Bristol

  23. Transformers Learn Robust In-Context Regression under Distributional Uncertainty

    Mar 19, 2026Hoang T. H. Cao, Hai D. V. Trinh, Tho Quan +1In-Context LearningTransformer

    Faculty of Computer Science and Engineering, Ho Chi Minh University of Technology (HCMUT), Vietnam National University Ho Chi Minh City (VNU-HCM), Vietnam

  24. Global Truncated Loss Minimization for Robust and Threshold-Resilient Geometric Estimation

    Mar 16, 2026Tianyu Huang, Liangzu Peng, Xinyue Zhang +5Robust Loss FunctionsBranch and Bound

    Hong Kong Centre For Logistics Robotics, The Chinese University of Hong Kong. · Center for Innovation in Data Engineering and Science (IDEAS), University of Pennsylvania. · Mobile Perception Lab of the School of Information and Technology, ShanghaiTech University. +1

  25. Towards a data-scale independent regulariser for robust sparse identification of non-linear dynamics

    Mar 5, 2026Jay Raut, Daniel N. Wilke, Stephan SchmidtSparse Identification of Nonlinear DynamicsNonlinear System Identification

    Department of Mechanical and Aeronautical Engineering, University of Pretoria, Pretoria, South Africa · School of Mechanical, Industrial and Aeronautical Engineering, University of the Witwatersrand, Johannesburg, South Africa

  26. Robust Predictive Uncertainty and Double Descent in Contaminated Bayesian Random Features

    Feb 22, 2026Michele Caprio, Katerina Papagiannouli, Siu Lun Chau +1Random Feature MethodsBayesian Inference

    The University of Manchester, UK · University of Pisa, Italy · Nanyang Technological University, Singapore +1

  27. CAIRO: Decoupling Order from Scale in Regression

    Feb 16, 2026Harri Vanhems, Yue Zhao, Peng Shi +1Robust RegressionTabular Regression

    McGill University and Mila · University of York · University of Wisconsin

  28. Linear Regression under Missing or Corrupted Coordinates

    Sep 23, 2025Ilias Diakonikolas, Jelena Diakonikolas, Daniel M. Kane +2Robust RegressionLearning with Missing Data

    University of Wisconsin-Madison · University of California, San Diego · University of California, Davis

  29. Robust Linear Predictions: Analyses of Uniform Concentration, Fast Rates and Model Misspecification

    Jan 6, 2022Saptarshi Chakraborty, Debolina Paul, Swagatam DasRobust RegressionModel Misspecification

    Department of Statistics, University of California, Berkeley · Department of Statistics, Stanford University · Electronics and Communication Sciences Unit, Indian Statistical Institute, Kolkata, India