Maximum Mean Discrepancy

Also known as MMD

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Overview

Maximum Mean Discrepancy (MMD) measures how different two distributions are by comparing their representations in a reproducing kernel Hilbert space. It is used in two-sample and drift tests, domain adaptation, generative modeling, and sampling, where detecting or reducing distribution mismatch matters. Common approaches include kernel mean embeddings, U-statistic estimators, random Fourier feature approximations, and gradient-based optimization; adaptive bandwidth and kernel-selection methods aim to improve sensitivity and power. Theory provides strong estimation and convergence guarantees, but choosing a kernel that detects the relevant differences while keeping tests valid and computation scalable remains a central challenge.

Latest papers

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33 papers4 papers in the last four weeks, against 1 the four weeks before. 0.0% of all new papers.

  1. A Jump-Modified Wasserstein Gradient Flow for Maximum Mean Discrepancy with Energy Kernels

    Oct 21, 2026Ansh Desai, Jason Liu, Srujan Roplekar +1Wasserstein Gradient FlowsMaximum Mean Discrepancy

  2. On the Optimisation Landscape of Overparameterised Weighted MMD

    Oct 14, 2026Tharrshann Jayan Logarajah, Jeremias Knoblauch, Louis SharrockOverparameterizationMaximum Mean Discrepancy

    University College London

  3. Beyond Marginal Monitoring: Distributed Joint-Distribution Testing for Data Concept Drift in Large Scale E-Commerce Operations

    Oct 6, 2026Cagdas Pullu, Mahmut Emir Arslan, Bugra Balkac +4Two-Sample TestingConcept Drift

    Data & Analytics, Trendyol Group, Istanbul, 34485, Istanbul, Türkiye. · Department of Data Science and Analytics, Istanbul Technical University, Maslak, Istanbul, 34469, Istanbul, Türkiye.

  4. Representation-Space MMD for Diffusion Language Models

    Oct 5, 2026Ilya Drobyshevskiy, Ilia Sudakov, Maksim Semenov +7Diffusion Model AlignmentMaximum Mean Discrepancy

    Yandex Research · HSE University · T-Tech +3

  5. M3-Score: Fidelity, Memorization and Coverage as Separate Axes for Evaluating Generative Radiology Image Models

    Sep 27, 2026Sathiyamohan Nishankar, Pubudu Sanjeewani, Asanka PereraMaximum Mean DiscrepancyMedical Image Synthesis

    Faculty of Engineering, University of Peradeniya, Sri Lanka · School of Computing Technologies, RMIT University, Melbourne, Australia · School of Engineering & Digital Technologies, University of Southern Queensland, Brisbane, Australia +1

  6. How fine a change can moments see? A scale law for detecting distribution shift, with a kernel calibration rule

    Aug 2, 2026Adel KalecheTwo-Sample TestingDistribution Shift

    Independent researcher, France

  7. Minimax Lower Bounds of Kernel Discrepancy Estimation: MMD, HSIC, KSD

    Jul 27, 2026Jose Cribeiro-Ramallo, Florian Kalinke, Zoltán SzabóMaximum Mean DiscrepancyMinimax Estimation

    Chair of Information Systems, Karlsruhe Institute of Technology, Am Fasanengarten 5, 76131 Karlsruhe, Germany · Department of Statistics, London School of Economics, Houghton Street, London, WC2A 2AE, UK

  8. Distributional Split Criteria for Random Forests: Extensions, Shrinkage, and the Robustness of Mean Splitting

    Jul 26, 2026Silas KoemenMaximum Mean DiscrepancyRandom Forest

  9. Online Variance Reduction for Domain Adaptation on Streaming Data

    Jul 22, 2026Andrea NapoliDomain AdaptationMaximum Mean Discrepancy

    Department of Electronics and Computer Science University of Southampton, UK

  10. Variance-reduced Domain Adaptation using Paired Sampling

    Jul 22, 2026Andrea NapoliUnsupervised Domain AdaptationMaximum Mean Discrepancy

    Department of Electronics and Computer Science University of Southampton, UK

  11. Directional Kernel Mean Difference: A Fast Signed Statistic for Univariate Distribution Comparison

    Jul 22, 2026Shijie Zhong, Jiangfeng FuTwo-Sample TestingMaximum Mean Discrepancy

    School of Power and Energy Northwestern Polytechnical University Xi’an, Shanxi 710129

  12. A Gradient Flow Perspective on Minimum MMD Estimation

    Jul 4, 2026Sophia Seulkee Kang, Louis Sharrock, Xiaoyuan Cheng +2Parameter EstimationMaximum Mean Discrepancy

    Independent Researcher · University College London

  13. Representation Distribution Matching for One-Step Visual Generation

    Jul 2, 2026Lan Feng, Wuyang Li, Eloi Zablocki +2Maximum Mean DiscrepancyOne-Step Generative Modeling

    1EPFL, Switzerland · 2Valeo.ai, France · 3Sorbonne Universit´e, France

  14. Difference of Convex Programming in the Wasserstein Space with Applications to MMD Optimization

    Jun 26, 2026Clément Bonet, Pierre-Cyril Aubin-Frankowski, Youssef MrouehMaximum Mean DiscrepancyNonconvex Optimization

    CMAP, CNRS, Ecole Polytechnique, IP Paris · CERMICS, CNRS, ENPC, IP Paris · IBM Research

  15. Enhancing Numerical Prediction in LLMs via Smooth MMD Alignment

    Jun 26, 2026Zhuo Zuo, Li Yue, Wenhao Zheng +2Numerical Reasoning in Language ModelsMaximum Mean Discrepancy

    College of Computer Science, Sichuan University, Chengdu, China · Dongfang Electric (Chengdu) Academy of Science and Technology Co., Ltd., Chengdu, China · Institute of Medical Information & Library, CAMS & PUMC, Beijing, China

  16. Expanding SPHERE-JEPA: A Family of Statistical Regularizers for the Hypersphere

    Jun 16, 2026Léo Nicollier, Enric Meinhardt-Llopis, Max Dunitz +3Maximum Mean DiscrepancyHyperspherical Representation Learning

    CB, ATT · Université Paris-Saclay, CNRS, ENS Paris-Saclay, Centre Borelli, France · CB +4

  17. Discrepancy Minimization Improves Cross-Hospital Robustness in Digital Pathology

    May 24, 2026Ben Vardi, Dana Schonberger, Yuval Friedmann +4Computational PathologyUnsupervised Domain Adaptation

    Reichman University, Herzliya, Israel · Institute of Pathology, Sheba Medical Center, Ramat-Gan, Israel · Technion - Israel Institute of Technology, Haifa, Israel

  18. A Martingale Kernel Independence Test

    May 21, 2026Felix Laumann, Zhaolu Liu, Mauricio BarahonaMaximum Mean DiscrepancyKernel Methods

    Imperial College London

  19. Asymptotically Optimal Ergodic Coverage on Generalized Motion Fields

    May 13, 2026Christian Hughes, Yilang Liu, Yanis Lahrach +6Maximum Mean DiscrepancyMobile Robotics

    Yale University · Université Catholique de Louvain · Rutgers University +2

  20. Sobolev Regularized MMD Gradient Flow

    May 12, 2026Chenyang Tian, Bharath K. Sriperumbudur, Arthur Gretton +1Maximum Mean DiscrepancySampling from Unnormalized Distributions

    Tsinghua University · Pennsylvania State University · University College London +1

  21. Kernel Selection is Model Selection: A Unified Complexity-Penalized Approach for MMD Two-Sample Tests

    May 7, 2026Yijin Ni, Xiaoming HuoModel SelectionTwo-Sample Testing

    H. Milton Stewart School of Industrial and Systems Engineering Georgia Institute of Technology Atlanta, GA 30332, USA

  22. A Robust Unsupervised Domain Adaptation Framework for Medical Image Classification Using RKHS-MMD

    May 5, 2026Sapna Sachan, Rakesh Kumar Sanodiya, Amulya Kumar MahtoChest X-Ray ClassificationUnsupervised Domain Adaptation

    Mehta Family School of Data Science and Artificial Intelligence, Indian Institute of Technology Guwahati, India · Indian Institute of Information Technology, Design and Manufacturing,2026 Jabalpur, India

  23. Measuring Differences between Conditional Distributions using Kernel Embeddings

    May 4, 2026Peter Moskvichev, Siu Lun Chau, Dino SejdinovicKernel Mean EmbeddingsMaximum Mean Discrepancy

    School of Mathematical Sciences, Adelaide University · College of Computing and Data Science, Nanyang Technological University

  24. Generalising maximum mean discrepancy: kernelised functional Bregman divergences

    Apr 27, 2026Russell Tsuchida, Frank NielsenKernel Mean EmbeddingsFunctional Bregman Divergences

    Department of Data Science and AI, Monash University, Australia. · Sony Computer Science Laboratories, Inc. Tokyo, Japan.

  25. Latent Dynamics-Aware OOD Monitoring for Trajectory Prediction with Provable Guarantees

    Mar 15, 2026Tongfei Guo, Lili SuOOD DetectionChange-Point Detection

    Department of Electrical and Computer Engineering, Northeastern University, Boston, MA, USA.

  26. Quantitative Convergence of Wasserstein Gradient Flows of Kernel Mean Discrepancies

    Mar 2, 2026Lénaïc Chizat, Maria Colombo, Roberto Colombo +1Wasserstein Gradient FlowsMaximum Mean Discrepancy

  27. Scalable Kernel-Based Distances for Statistical Inference and Integration

    Feb 25, 2026Masha NaslidnykNumerical IntegrationMaximum Mean Discrepancy

    Department of Computer Science University College London

  28. Finite-Sample Unbiased Variance of MMD under Unbalanced Sampling: Exact Estimation and Quasi-Linear Computation

    Jan 20, 2026Shijie Zhong, Yikun Yang, Da Gong +1Maximum Mean DiscrepancyKernel Methods

    School of Power and Energy, Northwestern Polytechnical University, 1 Dongxiang Road, Xi’an, 710129, Shanxi, China. · Advanced Power Research Institute, Northwestern Polytechnical University, 619 Jicui Road, Chengdu, 610299, Sichuan, China. · Taihang Laboratory, Chengdu, 610200, Sichuan, China. +1

  29. KerJEPA: Kernel Discrepancies for Euclidean Self-Supervised Learning

    Dec 22, 2025Eric Zimmermann, Harley Wiltzer, Justin Szeto +2Joint-Embedding Predictive ArchitectureSelf-Supervised Visual Representation Learning

    Microsoft Research, Cambridge, MA United States · Mila–Québec AI Institute, Montreal, Canada · McGill University, Montreal, Canada

  30. Maximum Mean Discrepancy with Unequal Sample Sizes via Generalized U-Statistics

    Dec 16, 2025Aaron Wei, Milad Jalali, Danica J. SutherlandTwo-Sample TestingMaximum Mean Discrepancy

    University of British Columbia · Independent researcher, Vancouver, Canada · Alberta Machine Intelligence Institute