mlsanityData to 14 Oct 2026

Operator-valued Kernels for Learning from Functional Response Data

arXiv 1510.08231 ↗First posted 28 Oct 2015cs.LG stat.MLcited by 60

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Abstract (arXiv)

In this paper we consider the problems of supervised classification and regression in the case where attributes and labels are functions: a data is represented by a set of functions, and the label is also a function. We focus on the use of reproducing kernel Hilbert space theory to learn from such functional data. Basic concepts and properties of kernel-based learning are extended to include the estimation of function-valued functions. In this setting, the representer theorem is restated, a set of rigorously defined infinite-dimensional operator-valued kernels that can be valuably applied when the data are functions is described, and a learning algorithm for nonlinear functional data analysis is introduced. The methodology is illustrated through speech and audio signal processing experiments.

Key facts. Cited by 60 papers in the map (data through 14 Oct 2026). First posted on arXiv 28 Oct 2015.

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Citing papers per year: 2021: 9; 2022: 11; 2023: 6; 2024: 10; 2025: 16; 2026: 8.

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  1. 2021Learning the solution operator of parametric partial differential equations with physics-informed DeepOnetscited by 540
  2. 2022Learning Operators with Coupled Attentioncited by 90
  3. 2021Improved architectures and training algorithms for deep operator networkscited by 86
  4. 2023Kernel Methods are Competitive for Operator Learningcited by 50
  5. 2021Conditional Distributional Treatment Effect with Kernel Conditional Mean Embeddings and U-Statistic Regressioncited by 40
  6. 2022Learning linear operators: Infinite-dimensional regression as a well-behaved non-compact inverse problemcited by 28
  7. 2022Transformer Meets Boundary Value Inverse Problemscited by 22
  8. 2023Koopman Kernel Regressioncited by 22
  9. 2023Towards Optimal Sobolev Norm Rates for the Vector-Valued Regularized Least-Squares Algorithmcited by 22
  10. 2024Operator Learning Using Random Features: A Tool for Scientific Computingcited by 21
  11. 2025Operator Learning: A Statistical Perspectivecited by 17
  12. 2025ProKeR: A Kernel Perspective on Few-Shot Adaptation of Large Vision-Language Modelscited by 15
38 more
  1. 2024Optimal Rates for Vector-Valued Spectral Regularization Learning Algorithmscited by 12
  2. 2024Linearization Turns Neural Operators into Function-Valued Gaussian Processescited by 12
  3. 2023A foundational neural operator that continuously learns without forgettingcited by 11
  4. 2021Reproducing kernel Hilbert C*-module and kernel mean embeddingscited by 10
  5. 2022Nonparametric learning of kernels in nonlocal operatorscited by 10
  6. 2022Learning "best" kernels from data in Gaussian process regression. With application to aerodynamicscited by 9
  7. 2022Data adaptive RKHS Tikhonov regularization for learning kernels in operatorscited by 8
  8. 2021Entangled Kernels -- Beyond Separabilitycited by 7
  9. 2022Learning in RKHM: a C^*-Algebraic Twist for Kernel Machinescited by 7
  10. 2024Nonlinear functional regression by functional deep neural network with kernel embeddingcited by 7
  11. 2024Hyperparameter Optimization for Randomized Algorithms: A Case Study on Random Featurescited by 7
  12. 2025Operator Learning at Machine Precisioncited by 7
  13. 2021Statistical Depth Meets Machine Learning: Kernel Mean Embeddings and Depth in Functional Data Analysiscited by 6
  14. 2021Koopman Spectrum Nonlinear Regulators and Efficient Online Learningcited by 5
  15. 2022Vector-Valued Least-Squares Regression under Output Regularity Assumptionscited by 5
  16. 2024Kernel Methods for the Approximation of the Eigenfunctions of the Koopman Operatorcited by 5
  17. 2021Handling Hard Affine SDP Shape Constraints in RKHSscited by 4
  18. 2024Diffeomorphic Measure Matching with Kernels for Generative Modelingcited by 4
  19. 2022A Fourier representation of kernel Stein discrepancy with application to Goodness-of-Fit tests for measures on infinite dimensional Hilbert spacescited by 3
  20. 2025Kernel-based estimators for functional causal effectscited by 3
  21. 2025Continuum Transformers Perform In-Context Learning by Operator Gradient Descentcited by 3
  22. 2026Fluids You Can Trust: Property-Preserving Operator Learning for Incompressible Flowscited by 3
  23. 2022Error-in-variables modelling for operator learningcited by 2
  24. 2022Functional Output Regression with Infimal Convolution: Exploring the Huber and ε-insensitive Lossescited by 1
  25. 2024C^*-Algebraic Machine Learning: Moving in a New Directioncited by 1
  26. 2024Spectral Truncation Kernels: Noncommutativity in C^*-algebraic Kernel Machinescited by 1
  27. 2024Learning signals defined on graphs with optimal transport and Gaussian process regressioncited by 1
  28. 2025Position: Quantum Kernel Machines Should Move Beyond Scalar-Valued Kernels to Realize Their Potentialcited by 1
  29. 2025A Kernel-based Stochastic Approximation Framework for Nonlinear Operator Learningcited by 1
  30. 2025Learning Paths for Dynamic Measure Transport: A Control Perspectivecited by 1
  31. 2025Function-on-Function Bayesian Optimizationcited by 1
  32. 2026Bayesian Optimization with Structured Measurements: A Vector-Valued RKHS Frameworkcited by 1
  33. 2026Kernel-based Operator Learning: Error Analysis, Budget Allocation, and a Physics-Informed Extensioncited by 1
  34. 2021Emotion Transfer Using Vector-Valued Infinite Task Learningcited by 0
  35. 2023Localisation of Regularised and Multiview Support Vector Machine Learningcited by 0
  36. 2023Convergence analysis of online algorithms for vector-valued kernel regressioncited by 0
  37. 2025Learning convolution operators on compact Abelian groupscited by 0
  38. 2025Transfer Learning Across Fixed-Income Product Classescited by 0

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