Reproducing Kernel Hilbert Spaces

Also known as RKHS

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Unbounded Characteristic and Universal Kernels
Oct 7, 2026Jose Cribeiro-Ramallo, Florian Kalinke, Zoltán SzabóKernel Methods Reproducing Kernel Hilbert Spaces
Karlsruhe Institute of Technology · London School of Economics
Bayesian Optimization on Function Spaces via Sparse RKHS Manifolds
Oct 5, 2026Davide Sartor, Meghan E. Huber, Donghyun Kim +1Bayesian Optimization Black-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
Deep kernel hedging
Sep 28, 2026Jean-Loup Dupret, Donatien Hainaut, Edouard MotteQuantitative Finance Reproducing Kernel Hilbert Spaces
University of Amsterdam, Amsterdam School of Economics · ETH Zurich, Department of Mathematics, RiskLab · Université Catholique de Louvain, LIDAM–ISBA
Optimization Geometry of Equivalent Brownian RKHS Representations
Sep 18, 2026Mahdi Mohammadigohari, Gustau Camps-VallsReproducing Kernel Hilbert Spaces Stochastic 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
Resolution-Independent Analysis of Encoder--Decoder Operator Learning via Limiting Kernels
Sep 12, 2026Lei Shi, Jia-Qi Yang, Ding-Xuan ZhouOperator Learning Kernel 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.
Common Covariance Geometry and Certification for Brownian Kernel Ladders
Aug 25, 2026Mahdi MohammadigohariKernel Methods Reproducing Kernel Hilbert Spaces
Faculty of Engineering, Free University of Bozen–Bolzano Via Bruno Buozzi 1, 39100 Bolzano, Italy
Operator-Theoretic Generalization Bounds for Multitask Deep Learning
Aug 17, 2026Mahdi Mohammadigohari, Thomas Borsani, Giuseppe Di FattaGeneralization Bounds Multi-Task Learning
Free University of Bozen–Bolzano, Italy
Variation Brownian Kernel Ladders
Aug 14, 2026Mahdi MohammadigohariKernel Methods Neural Network Approximation Theory
Faculty of Engineering, Free University of Bozen-Bolzano Bruno Buozzi 1, Bolzano, 39100, Italy
Constrained Learning with Universally Learnable Concept Classes
Aug 9, 2026Herlock SeyedAbolfazl Rahimi, Spyridon Pougkakiotis, Dionysis KalogeriasPrimal-Dual Optimization Reproducing Kernel Hilbert Spaces
1Yale University · 2King’s College London
Data eccentricity, asymptotics of Gaussian RBF reproducing kernel Hilbert space, and kernel PCA
Jul 23, 2026Sergio A. AlvarezPrincipal Component Analysis Reproducing Kernel Hilbert Spaces
Department of Computer Science, Boston College, Chestnut Hill, MA 02467 USA
Time Series Classification through Diffeomorphic Time Warping (DiffTW)
Jun 22, 2026Vicky Geneva Haney, Kamel Lahouel, Victor Rielly +1Dynamic Time Warping Time Series Classification
Department of Mathematics and Statistics, Portland State University, USA · The Translational Genomics Research Institute (TGen), USA
Generalized nonparametric regression in reproducing kernel Hilbert spaces: Consistency and rates of convergence
Jun 22, 2026Ioannis KalogridisNonparametric Regression Reproducing Kernel Hilbert Spaces
School of Mathematics and Statistics, University of Glasgow, United Kingdom
Subsampling for supervised learning in reproducing kernel Hilbert spaces
Jun 19, 2026Eyal Vayness, Maxime SangnierImportance Sampling Adaptive Sampling
Sorbonne Universit´e, LPSM, Paris, France
Brownian Kernel Ladders
Jun 14, 2026Mahdi Mohammadigohari, Giuseppe Di Fatta, Giuseppe Nicosia +1Hierarchical Representation Learning Reproducing 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
Wahkon: A Statistically Principled Deep RKHS Superposition Network
May 13, 2026Yongkai Chen, Wenxuan Zhong, Ping MaReproducing Kernel Hilbert Spaces Kernel Methods
Department of Statistics, Harvard University · Department of Statistics, University of Georgia
A Behavioral Framework for Data-Driven Modeling of Nonlinear Systems in Vector-Valued Reproducing Kernel Hilbert Spaces
May 8, 2026Boya Hou, Maxim RaginskyDynamical Systems Nonlinear 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
A Universal Reproducing Kernel Hilbert Space from Polynomial Alignment and IMQ Distance
May 5, 2026Taha BouhsineReproducing Kernel Hilbert Spaces Kernel Methods
Azetta AI
Dynamic Regret for Online Regression in RKHS via Discounted VAW and Subspace Approximation
Apr 27, 2026Dmitry B. Rokhlin, Georgiy A. KarapetyantsSequential Decision Making Reproducing Kernel Hilbert Spaces
Institute of Mathematics, Mechanics and Computer Sciences of the Southern Federal University
Explicit integral representations and quantitative bounds for two-layer ReLU networks
Apr 25, 2026Anthony LeeReLU Neural Networks Reproducing Kernel Hilbert Spaces
School of Mathematics, University of Bristol
Complex Stochastic Gradient Descent and Directional Bias in Reproducing Kernel Hilbert Spaces
Apr 24, 2026Natanael Alpay, Emeric BattagliaKernel Regression Reproducing Kernel Hilbert Spaces
A Kernel-based Stochastic Approximation Framework for Nonlinear Operator Learning
Sep 14, 2025Jia-Qi Yang, Lei ShiStochastic Approximation Reproducing Kernel Hilbert Spaces
School of Mathematical Sciences and Shanghai Key Laboratory for Contemporary Applied Mathematics, Fudan University, Shanghai 200433, China.
Gaussian Processes and Reproducing Kernel Hilbert Spaces: Connections and Equivalences
Jun 20, 2025Motonobu Kanagawa, Philipp Hennig, Dino Sejdinovic +1Gaussian Processes Reproducing Kernel Hilbert Spaces
EURECOM · University of Tübingen, Tübingen AI Center Max Planck Institute for Intelligent Systems · Adelaide University Australian Institute for Machine Learning +1
Which Spaces can be Embedded in $L_p$ -type Reproducing Kernel Banach Space? A Characterization via Metric Entropy
Oct 14, 2024Yiping Lu, Daozhe Lin, Qiang DuReproducing Kernel Hilbert Spaces Kernel Methods
Industrial Engineering & Management Sciences, Northwestern University · Department of Applied Physics & Applied Mathematics, Columbia University
DynaWeightPnP: Toward global real-time 3D-2D solver in PnP without correspondences
Sep 27, 2024Jingwei Song, Maani GhaffariCamera Pose Estimation Reproducing Kernel Hilbert Spaces
United Imaging Research Institute of Intelligent Imaging, Beijing 100144, China, Beijing, 100144, China · University of Michigan, Ann Arbor, 48109, MI, USA

Oct 7, 2026, math.STJ/K move · Enter open · S save

Unbounded Characteristic and Universal Kernels

Jose Cribeiro-Ramallo, Florian Kalinke, Zoltán Szabó

Karlsruhe Institute of Technology · London School of Economics

Kernel Methods Reproducing Kernel Hilbert Spaces

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Kernel methods are among the most powerful tools in machine learning and statistics, with a large number of successful applications. Their immense success stems from the flexible function class associated to each kernel---its reproducing kernel Hilbert space (RKHS)---which facilitates statistical analysis, as well as from their computational tractability and applicability to many domains. Multiple notions (such as characteristic,

L_p

-universal, and integrally strictly positive definite) capture the expressivity of kernels and their RKHSs and play a key role in understanding the statistical properties of kernel methods; these concepts and their relations are well-understood for bounded kernels. Even though unbounded kernels have received significant attention over the past decade (for instance, in the construction of kernel-based discrepancy and dependence measures such as the maximum mean discrepancy, the Hilbert-Schmidt independence criterion, and the kernel Stein discrepancy), surprisingly little is known about the relations of these notions in the unbounded case. In the present paper we tackle this severe bottleneck, establishing their relations under mild assumptions.