Research map / Learning theory and algorithms / Kernels and regression theory
RKHS kernel methods
Analyze and accelerate kernel methods with Hilbert space theory, Nystrom and kernel thinning.
127 accepted papers at ICML, NeurIPS, ICLR, CVPR and AAAI (2016–2026) · an approach in Kernels and regression theory, keyword cluster “kernels · hilbert · reproducing”
State History Benchmarks Tried Checklist Preprints Who Export
Where it stands
Few recent reports None of the tracked benchmarks has a report from 2025–26.
21 papers in 2023–24 and 23 in 2025–26 (at ICML, NeurIPS, ICLR, CVPR and AAAI); its share of the topic held steady, from 8.5% to 9.3%.
No longer reported by papers here: MNIST (accuracy, last in 2021).
How this is decided
A benchmark is tracked when at least four papers of this approach report their own method on the same dataset and metric in at least two different years. Its record is the best number reported up to 2024 compared with the best reported in 2025–26: still improving means at least 1% better, flat means at most 0.2% better with at least two papers from 2025–26 trying. Numbers on a different scale from the rest (a fraction among percentages) and far outliers are left out. Results come from different papers with different setups, so they are signals, not head-to-head comparisons. The share of papers is counted at ICML, NeurIPS, ICLR, CVPR and AAAI.
How it got here
Most cited paper of each year
- 2016 · Fast Algorithms for Linear and Kernel SVM+ (CVPR 2016 · 51 citations)
- 2017 · Kernel Feature Selection via Conditional Covariance Minimization (NeurIPS 2017 · 61 citations)
- 2018 · Efficient High Dimensional Bayesian Optimization with Additivity and Quadrature Fourier Features (NeurIPS 2018 · 91 citations)
- 2019 · A Kernel Theory of Modern Data Augmentation (ICML 2019 · 100 citations)
- 2020 · Kernel Methods Through the Roof: Handling Billions of Points Efficiently (NeurIPS 2020 · 40 citations)
- 2021 · The Inductive Bias of Quantum Kernels (NeurIPS 2021 · 44 citations)
- 2022 · Optimal Rates for Regularized Conditional Mean Embedding Learning (NeurIPS 2022 · 8 citations)
- 2023 · The Exact Sample Complexity Gain from Invariances for Kernel Regression (NeurIPS 2023 · 3 citations)
- 2024 · Statistical and Geometrical properties of the Kernel Kullback-Leibler divergence (NeurIPS 2024 · 2 citations)
- 2025 · Regularized least squares learning with heavy-tailed noise is minimax optimal (NeurIPS 2025 · 1 citation)
- 2026 · Alignment-Sensitive Minimax Rates for Spectral Algorithms with Learned Kernels (ICML 2026 · 0 citations)
Earliest papers here
- Fast Algorithms for Linear and Kernel SVM+ (CVPR 2016 · 51 citations)
- Fast DPP Sampling for Nystrom with Application to Kernel Methods (ICML 2016 · 40 citations)
- Recycling Randomness with Structure for Sublinear time Kernel Expansions (ICML 2016 · 30 citations)
Benchmark records
The best number each year that beat every earlier one, among papers of this approach reporting their own method. Numbers are extracted by AI from each paper's text; check the paper before citing.
MNIST · accuracy (higher is better)
4 papers, 2016–2021 · not reported since 2021
| Year | Best so far | Set by |
|---|---|---|
| 2016 | 99.51 | Kernel Approximation via Empirical Orthogonal Decomposition for Unsupervised Feature Learning (CVPR 2016 · 8 citations) |
What has been tried
103 papers here report 802 measured changes (a component added, removed or swapped, compared with a baseline): helped 62%, no clear effect 12%, hurt 21%, mixed 5%. Papers mostly publish changes that helped, so "helped" is over-represented.
Ablations in recent papers
| What was changed | Measured on | Result | Effect | Paper |
|---|---|---|---|---|
| Use the NW supervised meta-kernel k(x1,x2) + k(x1,x2)y1y2 instead of the base input kernel | Simulated data · MSE | Helped | Supervised Kernel Thinning (NeurIPS 2024 · 1 citation) | |
| Use APD instead of Frank-Wolfe for early iterations | Convergence · convergence rate | Hurt | Efficient Convex Algorithms for Universal Kernel Learning (NeurIPS 2024 · 1 citation) | |
| Add the e-KQD term to the centered estimator | Gaussian vs. Laplace · rejection rate | Helped | Kernel Quantile Embeddings and Associated Probability Metrics (ICML 2025 · 0 citations) | |
| use only the nearest 10 training points instead of the full data set | Safe control for uncertain nonlinear systems · success rate | Mixed | Optimal kernel regression bounds under energy-bounded noise (NeurIPS 2025 · 0 citations) | |
| Add inducing clusters instead of standard inducing points | TADPOLEL · R2 (%) | 60.7±3.9 -> 63.1±1.8 | Helped | Inducing Clusters Deep Kernel Gaussian Process for Longitudinal Data (AAAI 2024 · 0 citations) |
| replace RBF kernel with Laplace kernel | Hopper-medium, Hopper-expert, Walker2d-medium, Walker2d-expert, Halfcheetah-medium, Halfcheetah-expert (D4RL) · normalized return | Mixed | Scalable Kernel Inverse Optimization (NeurIPS 2024 · 0 citations) |
What reviewers will expect
Datasets and baselines named in the 16 papers of this approach from 2025–2026 that have a full-text summary. Leaving out the common ones is a frequent review question.
Datasets
- CIFAR-10 · 2 of 16 papers
- MNIST · 2 of 16 papers
Baselines
- KRR · 2 of 16 papers
Recent preprints
Loading recent arXiv preprints…
Who publishes on it
Institutions on the most papers of this approach since 2023 (of 44 papers; from OpenAlex and the papers' affiliations).
- Google · 3 papers
- Massachusetts Institute of Technology · 3 papers
- Tsinghua University · 2 papers
- University of Oxford · 2 papers
- Cornell University · 2 papers
- University College London · 2 papers
- NTT · 2 papers
- London School of Economics · 2 papers
Use it
Download BibTeX of 40 key papersOpen the topic in the interactive map
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Related approaches
Same keyword cluster
- Neural tangent kernel analysis (109 papers)
- Kernel regression under shift (89 papers)
- Kernel two-sample testing (30 papers)
- Random feature approximation (36 papers)
Elsewhere in the topic
- Statistical perspectives on generalization (99 papers)
- Information-theoretic generalization bounds (94 papers)
- High-dimensional asymptotic generalization (82 papers)
- Generalization theory of deep networks (67 papers)
- Empirical generalization measures (61 papers)
- High-dimensional linear regression theory (61 papers)
- Kernel ridge regression analysis (57 papers)
- Double descent and overfitting (53 papers)
Benchmark numbers, ablations and baseline numbers are extracted by AI from each paper's full text and can be wrong; the paper is the authority. Data: results index of 2026-11-02, citation counts from OpenAlex (2026-10-09).