Covariance Estimation

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Overview

Covariance estimation studies how to recover the relationships and uncertainty among variables from finite, often noisy observations, supporting tasks such as scientific inference, portfolio design, sensor fusion, and machine learning. Classical approaches include shrinkage and low-rank models, while robust likelihoods, Bayesian methods, and expectation-maximization address outliers and missing data. Newer methods use online estimators and structured neural models to track changing covariance or represent large matrices efficiently, sometimes with privacy or stability guarantees. A central challenge is balancing accuracy and reliable uncertainty estimates against limited data, computational cost, distribution shifts, and privacy constraints.

Latest papers

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61 papers7 papers in the last four weeks, down 22% on the four weeks before. 0.0% of all new papers.

  1. Semiparametrically Efficient Inference for Kernel Measures of Noise Heterogeneity

    May 26, 2026Jakub Wornbard, Zikai Shen, Dimitri Meunier +1Semiparametric InferenceKernel Methods

    University College London

  2. Gaussian Process-based learning with new MCMC-based implementation of Wishart prior on correlation matrix

    May 26, 2026Kane Warrior, Dalia ChakrabartyBayesian InferenceCovariance Estimation

    Department of Mathematics University of York

  3. Private Adaptive Covariance Estimation via Gaussian Graphical Models

    May 22, 2026Cecilia Ferrando, Miguel Fuentes, Brett Mullins +2Differential PrivacyCovariance Estimation

    Manning College of Information and Computer Sciences University of Massachusetts Amherst

  4. Self-Distillation is Optimal Among Spectral Shrinkage Estimators in Spiked Covariance Models

    May 18, 2026Radu Lecoiu, Debarghya Mukherjee, Pragya SurSelf-DistillationSpectral Methods

    Department of Statistics, Harvard University · Department of Mathematics & Statistics, Boston University

  5. A Hybrid Gaussian Process Regression Framework for Stable Volatility-Covariance Estimation: Evidence from Global Equity Indices

    May 17, 2026Ujjwala VadrevuQuantitative FinanceFinancial Time Series

  6. Covariance-aware sampling for Diffusion Models

    May 13, 2026Andrea Schioppa, Tim SalimansDiffusion Model SamplingDiffusion Sampling

    GDM - Amsterdam · work done at GDM - Amsterdam

  7. Online Segmented Beamforming via Dynamic Programming

    May 8, 2026Manan Mittal, Ryan M. Corey, Diego Cuji +2Dynamic ProgrammingCovariance Estimation

    Stony Brook University1 · University of Illinois Chicago2 · University of Massachusetts Darthmouth3

  8. Divergence is Uncertainty: A Closed-Form Posterior Covariance for Flow Matching

    May 1, 2026Jiarui Xing, Song Wang, Jian WangFlow MatchingUncertainty Quantification

    Yale University · Harvard Medical School

  9. Inference of Online Newton Methods with Nesterov's Accelerated Sketching

    Apr 25, 2026Haoxuan Wang, Xinchen Du, Sen NaStochastic ApproximationSecond-Order Optimization

    School of Industrial and Systems Engineering, Georgia Institute of Technology.

  10. Refining Covariance Matrix Estimation in Stochastic Gradient Descent Through Bias Reduction

    Apr 23, 2026Ziyang Wei, Wanrong Zhu, Jingyang Lyu +1Covariance EstimationStochastic Gradient Descent

    Department of Statistics University of Chicago Chicago, IL 60637, USA · Department of Statistics University of California, Irvine Irvine, CA 92617, USA · Department of Statistics University of Wisconsin–Madison Madison, WI 53706, USA

  11. On Higher-Order Geometric Refinements of Classical Covariance Asymptotics: An Approach via Intrinsic and Extrinsic Information Geometry

    Apr 14, 2026Malik Amir, Sourangshu GhoshInformation GeometryCovariance Estimation

  12. Online Covariance Estimation in Averaged SGD: Improved Batch-Mean Rates and Minimax Optimality via Trajectory Regression

    Apr 12, 2026Yijin Ni, Xiaoming HuoPolyak-Ruppert AveragingCovariance Estimation

    H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology

  13. Polynomial-Time Optimal Group Selection via the Double-Commutator Eigenvalue Problem

    Apr 4, 2026Mitchell A. ThorntonCovariance EstimationSpectral Methods

    Richardson, TX 75080 USA

  14. State estimations and noise identifications with intermittent corrupted observations via Bayesian variational inference

    Apr 3, 2026Peng Sun, Ruoyu Wang, Xue LuoRobust EstimationCovariance Estimation

    School of Mathematical Sciences, Beihang University, Beijing, P. R. China 102206. · School of Mathematical Sciences, Beihang University, Beijing, P. R. China 102206, and Key Laboratory of Mathematics, Informatics and Behavioral Semantics (LMIB), Beihang University, Beijing, P. R. China 100191.

  15. Model Merging via Data-Free Covariance Estimation

    Apr 1, 2026Marawan Gamal Abdel Hameed, Derek Tam, Pascal Jr Tikeng Notsawo +2Multi-Task LearningLanguage Model Merging

    Mila & DIRO, Universit´e de Montr´eal · University of Toronto & Vector Institute

  16. Machine Learning-Assisted High-Dimensional Matrix Estimation

    Mar 30, 2026Wan Tian, Hui Yang, Zhouhui Lian +2Learning to OptimizeAlternating Direction Method of Multipliers

    Advanced Institute of Information Technology, Peking University · Wangxuan Institute of Computer Technology, Peking University, China, 100871 · Guanghua School of Management, Peking University, Beijing, China, 100871 +3

  17. Minimax and Adaptive Covariance Matrix Estimation under Differential Privacy

    Mar 20, 2026T. Tony Cai, Yicheng LiCovariance EstimationParameter Estimation

    Department of Statistics and Data Science, The Wharton School, University of Pennsylvania · KLATASDS-MOE, School of Statistics, East China Normal University

  18. K-GMRF: Kinetic Gauss-Markov Random Field for First-Principles Covariance Tracking on Lie Groups

    Mar 20, 2026ZhiMing LiCovariance EstimationVisual Object Tracking

    School of Computer Science and Technology, Tianjin University

  19. Recovering Sparse Neural Connectivity from Partial Measurements: A Covariance-Based Approach with Granger-Causality Refinement

    Mar 19, 2026Quilee SimeonBrain Network AnalysisSparse Recovery

    Massachusetts Institute of Technology

  20. 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

  21. A Hybrid Neural-Assisted Unscented Kalman Filter for Unmanned Ground Vehicle Navigation

    Mar 12, 2026Gal Versano, Itzik KleinRobot NavigationUnscented Kalman Filtering

    Autonomous Navigation and Sensor Fusion Lab, Hatter Department of Marine Technologies, Charney School of Marine Sciences, University of Haifa, Israel.

  22. Heavy-Tailed Principal Component Analysis

    Mar 11, 2026Mario Sayde, Christopher Khater, Jihad Fahs +1Principal Component AnalysisRobust Estimation

    Electrical and Computer Engineering Department American University of Beirut Riad El-Solh, Beirut 1107 2020, Lebanon

  23. Outlier-robust Autocovariance Least Square Estimation via Iteratively Reweighted Least Square

    Mar 9, 2026Jiahong Li, Fang DengCovariance EstimationRobust Estimation

    College of Robotics, Beijing Union University, Beijing 100101, China · Key Laboratory of Intelligent Control and Decision of Complex Systems, and also with the School of Automation, Beijing Institute of Technology, Beijing 100081, China

  24. Joint Return and Risk Modeling with Deep Neural Networks for Portfolio Construction

    Mar 9, 2026Keonvin ParkQuantitative FinancePortfolio Optimization

    Interdisciplinary Program in Artificial Intelligence, Seoul National University, Seoul, 08829, South Korea

  25. ACE-Merging: Data-Free Model Merging with Adaptive Covariance Estimation

    Mar 3, 2026Bo Xu, Haotian Wu, Hehai Lin +4Model MergingLanguage Model Merging

    The Hong Kong University of Science and Technology (Guangzhou) · University of Science and Technology of China

  26. Environment-Aware Learning of Smooth GNSS Covariance Dynamics for Autonomous Racing

    Feb 24, 2026Y. Deemo Chen, Arion Zimmermann, Thomas A. Berrueta +1Contraction TheoryCovariance Estimation

    Department of Computing and Mathematical Sciences, California Institute of Technology, Pasadena, CA.

  27. Machine Learning Argument of Latitude Error Model for LEO Satellite Orbit and Covariance Correction

    Feb 18, 2026Alex Moody, Penina Axelrad, Rebecca RussellUncertainty PropagationCovariance Estimation

    University of Colorado Boulder Boulder, CO · The Charles Stark Draper Laboratory, Inc. Cambridge, MA

  28. The Optimization Landscape of Carathéodory Decomposition of Toeplitz Covariances

    Nov 3, 2025Daniel Busbib, Ami WieselNonconvex OptimizationMatrix Optimization

    School of Computer Science and Engineering, The Hebrew University of Jerusalem, Jerusalem 91904, Israel

  29. Non-asymptotic Estimation of Sparse Partial Correlation via Joint Partial Regression

    Feb 12, 2025Samuel Erickson, Tobias RydénCovariance Estimation

    Division of Decision and Control Systems KTH Royal Institute of Technology Stockholm, Sweden · Lynx Asset Management AB Stockholm, Sweden

  30. Conditional Moment Kernels: Joint Modeling of Expected Returns and Covariances in Unbalanced Panels

    Oct 29, 2024Damir Filipovic, Paul SchneiderQuantitative FinanceCovariance Estimation

    École Polytechnique Fédérale de Lausanne and Swiss Finance Institute · Università della Svizzera italiana and Swiss Finance Institute