Reproducing Kernel Hilbert Spaces

Also known as RKHS

Ask about this topic

Overview

Reproducing kernel Hilbert spaces provide function spaces where evaluating a function is expressed through an inner product with a kernel, making flexible models amenable to mathematical analysis. Common approaches include kernel ridge regression and other regularized estimators, Mercer or random-feature approximations, Gaussian-process methods, and vector-valued or operator-valued kernels for structured outputs and dynamical systems. These tools support tasks ranging from nonparametric regression and time-series alignment to PDE operator learning, while linking prediction, interpolation, and uncertainty through shared kernel structure. A central tension is balancing expressive or data-adapted kernels with computation and statistical control, since performance and guarantees depend on approximation error, spectral decay, and how well the chosen RKHS matches the target.

Latest papers

CardsList

30 papers5 papers in the last four weeks, up 67% on the four weeks before. 0.0% of all new papers.

  1. Norm-optimal model order reduction in reproducing kernel Hilbert spaces

    Oct 20, 2026Tamás Dózsa, Andrea Angino, Rolf Krause +1Reduced-Order ModelingReproducing Kernel Hilbert Spaces

  2. Expressivity of IQP Feature-Map Quantum Kernels via Reproducing Kernel Hilbert Spaces

    Oct 16, 2026Valeria Repetto, Stefano Melchionna, Romina D'AurizioQuantum Kernel MethodsQuantum Feature Maps

    National Research Council of Italy (CNR), Institute of Informatics and Telematics (IIT), via Giuseppe Moruzzi 1, Pisa, Italy · Computational Biomedicine Unit, Department of Medical Sciences, University of Turin, via Santena 19, Torino, Italy · Kipu Quantum, Greifswalderstrasse 212, 10405 Berlin, Germany

  3. Hierarchical Time Series Forecasting with Operator-Valued Kernels

    Oct 13, 2026Junjie Yang, Adeline Fermanian, Claire Boyer +1Time Series ForecastingKernel Methods

    LPSM · LMO, IUF

  4. Unbounded Characteristic and Universal Kernels

    Oct 7, 2026Jose Cribeiro-Ramallo, Florian Kalinke, Zoltán SzabóKernel MethodsReproducing Kernel Hilbert Spaces

    Karlsruhe Institute of Technology · London School of Economics

  5. Bayesian Optimization on Function Spaces via Sparse RKHS Manifolds

    Oct 5, 2026Davide Sartor, Meghan E. Huber, Donghyun Kim +1Bayesian OptimizationBlack-Box Optimization

    Department of Mathematics and Statistics University of Massachusetts Amherst · Department of Mechanical and Industrial Engineering University of Massachusetts Amherst · Manning College of Information and Computer Sciences University of Massachusetts Amherst

  6. Deep kernel hedging

    Sep 28, 2026Jean-Loup Dupret, Donatien Hainaut, Edouard MotteDeep Kernel LearningQuantitative Finance

    University of Amsterdam, Amsterdam School of Economics · ETH Zurich, Department of Mathematics, RiskLab · Université Catholique de Louvain, LIDAM–ISBA

  7. Optimization Geometry of Equivalent Brownian RKHS Representations

    Sep 18, 2026Mahdi Mohammadigohari, Gustau Camps-VallsReproducing Kernel Hilbert SpacesStochastic Gradient Descent

    Faculty of Engineering Free University of Bozen-Bolzano Bruno Buozzi 1, Bolzano 39100, Italy · Image Processing Laboratory (IPL) Universitat de València Paterna, València 46980, Spain

  8. Resolution-Independent Analysis of Encoder--Decoder Operator Learning via Limiting Kernels

    Sep 12, 2026Lei Shi, Jia-Qi Yang, Ding-Xuan ZhouOperator LearningKernel Methods

    School of Mathematical Sciences and Shanghai Key Laboratory for Contemporary Applied Mathematics, Fudan University, Shanghai 200433, China. · School of Mathematics and Statistics, the University of Sydney, Sydney, New South Wales 2006, Australia.

  9. Common Covariance Geometry and Certification for Brownian Kernel Ladders

    Aug 25, 2026Mahdi MohammadigohariKernel MethodsReproducing Kernel Hilbert Spaces

    Faculty of Engineering, Free University of Bozen–Bolzano Via Bruno Buozzi 1, 39100 Bolzano, Italy

  10. Operator-Theoretic Generalization Bounds for Multitask Deep Learning

    Aug 17, 2026Mahdi Mohammadigohari, Thomas Borsani, Giuseppe Di FattaGeneralization BoundsMulti-Task Learning

    Free University of Bozen–Bolzano, Italy

  11. Variation Brownian Kernel Ladders

    Aug 14, 2026Mahdi MohammadigohariKernel MethodsNeural Network Approximation Theory

    Faculty of Engineering, Free University of Bozen-Bolzano Bruno Buozzi 1, Bolzano, 39100, Italy

  12. Constrained Learning with Universally Learnable Concept Classes

    Aug 9, 2026Herlock SeyedAbolfazl Rahimi, Spyridon Pougkakiotis, Dionysis KalogeriasPrimal-Dual OptimizationReproducing Kernel Hilbert Spaces

    1Yale University · 2King’s College London

  13. Data eccentricity, asymptotics of Gaussian RBF reproducing kernel Hilbert space, and kernel PCA

    Jul 23, 2026Sergio A. AlvarezPrincipal Component AnalysisReproducing Kernel Hilbert Spaces

    Department of Computer Science, Boston College, Chestnut Hill, MA 02467 USA

  14. Time Series Classification through Diffeomorphic Time Warping (DiffTW)

    Jun 22, 2026Vicky Geneva Haney, Kamel Lahouel, Victor Rielly +1Dynamic Time WarpingTime Series Classification

    Department of Mathematics and Statistics, Portland State University, USA · The Translational Genomics Research Institute (TGen), USA

  15. Generalized nonparametric regression in reproducing kernel Hilbert spaces: Consistency and rates of convergence

    Jun 22, 2026Ioannis KalogridisNonparametric RegressionReproducing Kernel Hilbert Spaces

    School of Mathematics and Statistics, University of Glasgow, United Kingdom

  16. Subsampling for supervised learning in reproducing kernel Hilbert spaces

    Jun 19, 2026Eyal Vayness, Maxime SangnierImportance SamplingAdaptive Sampling

    Sorbonne Universit´e, LPSM, Paris, France

  17. Brownian Kernel Ladders

    Jun 14, 2026Mahdi Mohammadigohari, Giuseppe Di Fatta, Giuseppe Nicosia +1Hierarchical Representation LearningReproducing Kernel Hilbert Spaces

    Faculty of Engineering, Free University of Bozen-Bolzano, Via Bruno Buozzi 1, Bolzano, 39100, Italy · Department of Biomedical and Biotechnological Sciences, University of Catania, Catania, 95123, Santa Sofia, 97, Italy · Center for Applied Optimization, Department of Industrial and Systems Engineering, University of Florida, FL 32611, Gainesville, USA

  18. Wahkon: A Statistically Principled Deep RKHS Superposition Network

    May 13, 2026Yongkai Chen, Wenxuan Zhong, Ping MaReproducing Kernel Hilbert SpacesKernel Methods

    Department of Statistics, Harvard University · Department of Statistics, University of Georgia

  19. A Behavioral Framework for Data-Driven Modeling of Nonlinear Systems in Vector-Valued Reproducing Kernel Hilbert Spaces

    May 8, 2026Boya Hou, Maxim RaginskyDynamical SystemsNonlinear System Identification

    Carl R. Woese Institute for Genomic Biology and the Coordinated Science Laboratory, University of Illinois Urbana-Champaign, Urbana, IL, 61801 USA · Department of Electrical and Computer Engineering and the Coordinated Science Laboratory, University of Illinois Urbana-Champaign, Urbana, IL, 61801 USA

  20. A Universal Reproducing Kernel Hilbert Space from Polynomial Alignment and IMQ Distance

    May 5, 2026Taha BouhsineReproducing Kernel Hilbert SpacesKernel Methods

    Azetta AI

  21. Dynamic Regret for Online Regression in RKHS via Discounted VAW and Subspace Approximation

    Apr 27, 2026Dmitry B. Rokhlin, Georgiy A. KarapetyantsSequential Decision MakingReproducing Kernel Hilbert Spaces

    Institute of Mathematics, Mechanics and Computer Sciences of the Southern Federal University

  22. Explicit integral representations and quantitative bounds for two-layer ReLU networks

    Apr 25, 2026Anthony LeeReLU Neural NetworksReproducing Kernel Hilbert Spaces

    School of Mathematics, University of Bristol

  23. Complex Stochastic Gradient Descent and Directional Bias in Reproducing Kernel Hilbert Spaces

    Apr 24, 2026Natanael Alpay, Emeric BattagliaKernel RegressionReproducing Kernel Hilbert Spaces

  24. KROM: Kernelized Reduced Order Modeling

    Feb 27, 2026Aras Bacho, Jonghyeon Lee, Houman OwhadiPDE Surrogate ModelingReduced-Order Modeling

    Department of Computing and Mathematical Sciences, Caltech, CA, USA.

  25. RKHS Representation of Algebraic Convolutional Filters with Integral Operators

    Feb 22, 2026Alejandro Parada-Mayorga, Alejandro Ribeiro, Juan BazerqueReproducing Kernel Hilbert SpacesGraph Signal Processing

    Dept. of Electrical Eng., Univ.of Colorado (Denver). USA · Dept. of Electrical and Systems Eng., Univ.of Pennsylvania. · Dept. of Electrical and Comput Eng., Univ.of Pittsburgh. USA

  26. No More DeLuLu: Physics-Inspired Kernel Networks for Geometrically-Grounded Neural Computation

    Feb 22, 2026Taha BouhsineKernel MethodsReproducing Kernel Hilbert Spaces

    Azetta AI.

  27. A Kernel-based Stochastic Approximation Framework for Nonlinear Operator Learning

    Sep 14, 2025Jia-Qi Yang, Lei ShiStochastic ApproximationReproducing Kernel Hilbert Spaces

    School of Mathematical Sciences and Shanghai Key Laboratory for Contemporary Applied Mathematics, Fudan University, Shanghai 200433, China.

  28. Gaussian Processes and Reproducing Kernel Hilbert Spaces: Connections and Equivalences

    Jun 20, 2025Motonobu Kanagawa, Philipp Hennig, Dino Sejdinovic +1Gaussian ProcessesReproducing Kernel Hilbert Spaces

    EURECOM · University of Tübingen, Tübingen AI Center Max Planck Institute for Intelligent Systems · Adelaide University Australian Institute for Machine Learning +1

  29. Which Spaces can be Embedded in LpL_p-type Reproducing Kernel Banach Space? A Characterization via Metric Entropy

    Oct 14, 2024Yiping Lu, Daozhe Lin, Qiang DuReproducing Kernel Hilbert SpacesKernel Methods

    Industrial Engineering & Management Sciences, Northwestern University · Department of Applied Physics & Applied Mathematics, Columbia University

  30. DynaWeightPnP: Toward global real-time 3D-2D solver in PnP without correspondences

    Sep 27, 2024Jingwei Song, Maani GhaffariCamera Pose EstimationReproducing Kernel Hilbert Spaces

    United Imaging Research Institute of Intelligent Imaging, Beijing 100144, China, Beijing, 100144, China · University of Michigan, Ann Arbor, 48109, MI, USA