Linear Regression

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Overview

Linear regression estimates relationships between features and outcomes, from ordinary least squares to sparse and functional models, and remains a useful baseline for prediction and scientific inference. Common approaches include ridge and Lasso regularization, principal component regression, early stopping with gradient descent, and robust losses or distributionally robust optimization. Theory and experiments study high-dimensional and overparameterized data, missing or corrupted observations, distribution shift, and practical settings such as time-series forecasting and tabular prediction. A central tension is that methods that improve prediction or robustness can make computation, uncertainty estimates, or interpretation more difficult, while correlated features can make even simple model coefficients unstable.

Latest papers

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77 papers11 papers in the last four weeks, up 83% on the four weeks before. 0.1% of all new papers.

  1. Crop Yield Prediction Using Regression Models: A Comparative Evaluation of Model Performance

    Oct 27, 2026Saptak Das, Arijit Sarkar, Soumik Neogi +1Crop Yield PredictionTabular Regression

    Indian Institute of Science Education and Research Thiruvananthapuram, Kerala, India · Department of Information Technology, MCKV Institute of Engineering, Howrah, West Bengal, India

  2. LLM knowledge for improved Out-of-Distribution Tabular Prediction - A Cross-Validated Regularisation Approach

    Oct 27, 2026Sølve Langseth, Kristoffer Herland Hellton, Hugo L. HammerOOD GeneralizationTabular Prediction

    Department of Computer Science, Oslo Metropolitan University, Oslo, Norway · Department of Holistic Systems, SimulaMet, Oslo, Norway · Department of Plastic and Reconstructive Surgery, Oslo University Hospital, Oslo, Norway

  3. On the Limits of Sparse Linear Model with Shuffled Differential Privacy

    Oct 23, 2026Yan Zhang, Jiong Tuo, Meng Ding +2High-Dimensional Linear RegressionDifferential Privacy

    Provable Responsible AI and Data Analytics Lab · Nankai University · King Abdullah University of Science and Technology (KAUST) +3

  4. Score-Preserving Continual Lasso under Task Shift

    Oct 23, 2026Jingyi Guo, Runze Li, Lingzhou XueContinual LearningRegularization-Based Continual Learning

    Pennsylvania State University

  5. Asymptotic Risk of Learning-Rate Schedules for Least-Squares Regression with Discretely Distributed Features

    Oct 12, 2026Noé Colomban, Francis Bach, Fabian SchaippLearning Rate SchedulingStochastic Gradient Descent

    Inria - École Normale Supérieure PSL Research University

  6. Why Linear Models Can Still Work in a Complex and Changing World

    Oct 9, 2026Fangzhou Lin, Dengzhe Hou, Yinxing Li +1Model SelectionLinear Regression

    Texas A&M University, USA · Tohoku University, Japan

  7. New Lower Bound and Upper Bounds on the Regret for Online Sparse Linear Regression

    Oct 8, 2026Xiaofeng Cao, Junfan Li, Langzhang Liang +2Linear RegressionMinimax Regret

    School of Computer Science and Technology, Tongji University, Shanghai, China · School of Computing and Artificial Intelligence, Shanghai University of Finance and Economics, Shanghai, China · AI3 Institute, Fudan University and Shanghai Innovation Institute +2

  8. Asymptotic Analysis of Empirical Risk Minimization on Entry-wise i.i.d. Heavy-Tailed Data

    Oct 6, 2026Kaito Takanami, Takashi Takahashi, Yoshiyuki KabashimaStatistical Physics of LearningHigh-Dimensional Asymptotics

    Graduate School of Science, The University of Tokyo · Institute for Physics of Intelligence, The University of Tokyo · Trans-Scale Quantum Science Institute, The University of Tokyo

  9. LinearPFN: Amortized Variable Selection for Linear Models with Interactions

    Oct 5, 2026Louis Schiekiera, Max Zimmer, Christophe Roux +3Model SelectionPrior-Data Fitted Networks

    Institute of Psychology, Humboldt-Universität zu Berlin, Berlin, Germany · Department of Education and Psychology, Freie Universität Berlin, Berlin, Germany · Department for AI in Society, Science, and Technology, Zuse Institute Berlin, Germany +1

  10. Least Squares for Time Series Forecasting

    Oct 1, 2026Weiu-qiou Ciang, Yuzhou Hong, Sherry ChenTime Series ForecastingLinear Regression

  11. 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

  12. Principal Component Regression Dominates all Monotone Spectral Filters for Linear Regression

    Sep 30, 2026Juno Kim, Hengyu Fu, Peter Bartlett +2Spectral RegularizationLinear Regression

    University of California, Berkeley · Google DeepMind

  13. Statistical Benefits of Fine-Tuning from Pretrained Initialization in Diagonal Linear Networks

    Sep 28, 2026Alexandre Declèves, Etienne Boursier, Nicolas FlammarionFine-TuningDeep Linear Networks

    TML, EPFL, Lausanne, Switzerland · INRIA, LMO, Université Paris-Saclay, Orsay, France

  14. 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.

  15. Learning with Synthetic Data via SGD in High-Dimensional Linear Regression

    Sep 9, 2026Jichu li, Difan ZouSynthetic Data PretrainingHigh-Dimensional Linear Regression

    Renmin University of China · The University of Hong Kong

  16. Weighted Data Selection: Sharp Upper-Half and Five-Dimensional Laws

    Sep 8, 2026Zhongxuan Liu, Hongzhi WangData SelectionTraining Data Selection

    Faculty of Computing, Harbin Institute of Technology

  17. Optimal estimation for Functional Linear Regression with Noisy Discretized Data

    Sep 8, 2026Sixtine SphabmixayNonparametric RegressionMinimax Estimation

    Université Paris Cité, CNRS, MAP5, F-75006 Paris, France

  18. Optimal Rates for Agentic Networked Information Aggregation

    Sep 4, 2026MohammadHossein Bateni, Zahra Hadizadeh, MohammadTaghi Hajiaghayi +2Statistical Learning TheoryDecentralized Learning

    Google Research · University of California, Irvine · University of Maryland

  19. Exact Recovery Thresholds for Weighted Data Selection in Vector-Valued Linear Regression

    Aug 31, 2026Guangjian ZhangData SelectionTraining Data Selection

  20. Exact Risk Ratios for Weighted Data Selection in Linear Regression

    Aug 28, 2026Guangjian ZhangTraining Data SelectionLinear Regression

    University of New South Wales

  21. Contact Geometry and Covariance Deficits in Volume-Sampled Least Squares

    Aug 27, 2026Kihun Rhee, Hanjoon Byun, Junpyo SeoRandomized SketchingLinear Regression

  22. Hadamard Flattening and Gaussian Pooling Sketch for Least Squares with Coordinate-wise Guarantee

    Aug 27, 2026Zhao Song, Lichen ZhangRandomized SketchingLinear Regression

    Independent Researcher. · Massachusetts Institute of Technology.

  23. Functional linear regression from sparse to dense designs: a pooling-ridge method and minimax optimality

    Aug 26, 2026Shunxing Yan, Fang YaoLinear RegressionMinimax Estimation

    Department of Statistics and Data Science, Tsinghua University · School of Mathematical Sciences, Center for Statistical Science, Peking University

  24. A Data-dependent Early Stopping Rule using Rademacher Complexity with L1-norm

    Aug 25, 2026Duy Hoang, Bastien Berret, Olivier Bruneau +1Early StoppingNeural Network Generalization

    Universit´e Paris-Saclay, CNRS, ENS Paris-Saclay, LMF Gif-sur-Yvette, 91190, France · Universit´e Paris-Saclay, Inria, CIAMS Gif-sur-Yvette, 91190, France · Universit´e Paris-Saclay, ENS Paris-Saclay, LURPA Gif-sur-Yvette, 91190, France

  25. Regularised Iterative Generalised Least Squares with Optimal Selection of the Hyper-Parameter for Identifying Nonlinear Phenomenological Models

    Aug 19, 2026Mark Cary, Charles BokorNonlinear System IdentificationRidge Regression

    Department of Aeronautical and Automotive Engineering, Loughborough University, Loughborough, LE11 3TU, UK · School of Engineering, Computing and Mathematics, Oxford Brookes University, Oxford OX33 1HX, UK

  26. Algorithms for adaptive and heteroskedastic linear regression at the computational threshold

    Aug 19, 2026Spencer Compton, Tselil SchrammMinimax EstimationHeteroscedastic Regression

    Stanford University

  27. Feature Priming in Online Linear Regression: Sparse-Regret Lower Bounds and Tight Coordinatewise Rates

    Aug 18, 2026Huibo Xu, Shi Fu, Qixin Zhang +1Linear RegressionStatistical Learning Theory

    Nanyang Technological University, Singapore

  28. The Fourth Quadrant: A Stylized View of Benign Misfitting

    Aug 2, 2026Gireeja Ranade, Anant SahaiBenign OverfittingLinear Regression

    University of California, Berkeley

  29. The Zero Pattern of a Design Matrix Drives Multiple Descent in Over-parameterized Regression

    Jul 27, 2026Kevin Han Huang, Haoyu Ye, Somak Laha +1Double DescentLinear Regression

    University of Warwick · Harvard University

  30. Beyond Negative-Ridge Endpoints: Mixed-Sign Spectral Regularization via Negative-Shifted Gradient Descent

    Jul 24, 2026Peng ZhaoSpectral RegularizationEarly Stopping

    Department of Applied Economics and Statistics · University of Delaware