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. Expectation Error Bounds for Transfer Learning in Linear Regression and Linear Neural Networks

    Mar 30, 2026Meitong Liu, Christopher Jung, Rui Li +2Transfer LearningGeneralization Bounds

    University of Illinois Urbana-Champaign · Meta

  2. Refining time-space traffic diagrams: A neighborhood-adaptive linear regression method

    Mar 25, 2026Zhihong Yao, Yi Yu, Yunxia Wu +3Intelligent Transportation SystemsTraffic Flow Estimation

    National Engineering Laboratory of Integrated Transportation Big Data Application Technology, National United Engineering Laboratory of Integrated and Intelligent Transportation, School of Transportation and Logistics, Southwest Jiaotong University, Sichuan 610031, China · School of Transportation, Changsha University of Science and Technology, Changsha, China · Faculty of Science and Engineering, University of Nottingham Ningbo China, Ningbo, China

  3. High-dimensional estimation with missing data: Statistical and computational limits

    Mar 17, 2026Kabir Aladin Verchand, Ankit Pensia, Saminul Haque +1Learning with Missing DataCovariance Estimation

    Department of Data Sciences and Operations, University of Southern California · Department of Statistics and Data Science, Carnegie Mellon University · Department of Computer Science, Stanford University

  4. Intelligent Materials Modelling: Large Language Models Versus Partial Least Squares Regression for Predicting Polysulfone Membrane Mechanical Performance

    Mar 14, 2026Dingding Cao, Mieow Kee Chan, Wan Sieng Yeo +2Materials Property PredictionPolymer Property Prediction

    School of Big Data, Baoshan University, Baoshan, 678000, Yunnan Province, China. · Centre for Water Research, Faculty of Engineering, Built Environment and Information Technology, SEGi University. Jalan Teknologi, Kota Damansara, 47810 Petaling Jaya, Selangor Darul Ehsan, Malaysia. · School of Energy and Chemical Engineering, Xiamen University Malaysia, Jalan Sunsuria, Bandar Sunsuria, 43900 Sepang, Selangor, Malaysia. +3

  5. Locally Linear Continual Learning for Time Series based on VC-Theoretical Generalization Bounds

    Mar 14, 2026Yan V. G. Ferreira, Igor B. Lima, Pedro H. G. Mapa S. +2Explainable Time Series ForecastingNon-Stationary Time Series Forecasting

    Department of Electronic Engineering, Universidade Federal de Minas Gerais, UFMG, Belo Horizonte 31270-901, Brazil · Department of Computing Science, University of Alberta, Edmonton, Alberta, Canada · Graduate Program in Electrical Engineering, Universidade Federal de Minas Gerais, UFMG, Belo Horizonte 31270-901, Brazil

  6. Denoising the US Census: Succinct Block Hierarchical Regression

    Mar 10, 2026Badih Ghazi, Pritish Kamath, Ravi Kumar +2Linear RegressionDifferential Privacy

    Google Research

  7. Scaling Laws of SignSGD in Linear Regression: When Does It Outperform SGD?

    Mar 2, 2026Jihwan Kim, Dogyoon Song, Chulhee YunSign-Based OptimizationRandom Feature Methods

    Seoul National University & KAIST InnoCORE LLM · University of California, Davis · KAIST

  8. Learning with the Nash-Sutcliffe loss

    Mar 1, 2026Hristos Tyralis, Georgia PapacharalampousMultivariate Time Series ForecastingTime Series Forecasting

    1Support Command, Hellenic Air Force, Elefsina Air Base, 19 200, Elefsina, Greece · Department of Land, Environment, Agriculture and Forestry, University of Padova, Viale dell'Università 16, 35020, Legnaro, Italy

  9. Mathematical Foundations of Poisoning Attacks on Linear Regression over Cumulative Distribution Functions

    Feb 28, 2026Atsuki Sato, Martin Aumüller, Yusuke MatsuiData Poisoning AttacksLinear Regression

    Graduate School of Information Science and Technology, The University of Tokyo, Tokyo, Japan · Algorithms Group, IT University of Copenhagen, Copenhagen, Denmark

  10. Scaling Laws for Precision in High-Dimensional Linear Regression

    Feb 22, 2026Dechen Zhang, Xuan Tang, Yingyu Liang +1High-Dimensional Linear RegressionScaling Laws

    Institute of Data Science, The University of Hong Kong · School of Computing & Data Science, The University of Hong Kong · Institute of Data Science and School of Computing & Data Science, The University of Hong Kong +1

  11. Transfer Learning of Linear Regression with Multiple Pretrained Models: Benefiting from More Pretrained Models via Overparameterization Debiasing

    Feb 18, 2026Daniel Boharon, Yehuda DarOverparameterizationTransfer Learning

    Faculty of Computer and Information Science, Ben-Gurion University.

  12. 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

  13. Ordinary Least Squares as an Attention Mechanism

    Apr 13, 2025Philippe Goulet CoulombeTransformer AttentionLinear Regression

    Département des Sciences Économiques, Université du Québec à Montréal

  14. Can SGD Select Good Fishermen? Local Convergence under Self-Selection Biases

    Apr 6, 2025Alkis Kalavasis, Anay Mehrotra, Felix ZhouLinear RegressionStochastic Optimization Convergence

    Yale University

  15. On Regularization via Early Stopping for Least Squares Regression

    Jun 6, 2024Rishi Sonthalia, Jackie Lok, Elizaveta RebrovaEarly StoppingLinear Regression

    Department of Mathematics, Boston College · ORFE Department, Princeton University

  16. Efficient Cross-Validation for Sparse Linear Regression

    Jun 26, 2023Ryan Cory-Wright, Andrés GómezModel SelectionCross-Validation

    Department of Analytics, Marketing and Operations, Imperial Business School, London, UK · Department of Industrial and Systems Engineering, Viterbi School of Engineering, University of Southern California, CA

  17. 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