Research map / Learning theory and algorithms / Kernels and regression theory
Kernel two-sample testing
Learn and combine kernels for MMD-based two-sample and independence tests.
30 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 Tried Checklist Preprints Who Export
Where it stands
Not enough benchmark data Fewer than four papers report the same benchmark, so there is no record to follow.
2 papers in 2023–24 and 13 in 2025–26 (at ICML, NeurIPS, ICLR, CVPR and AAAI); its share of the topic grew, from 0.8% to 5.3%.
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 · Minimax Estimation of Maximum Mean Discrepancy with Radial Kernels (NeurIPS 2016 · 61 citations)
- 2017 · An Adaptive Test of Independence with Analytic Kernel Embeddings (ICML 2017 · 16 citations)
- 2018 · Early Stopping for Nonparametric Testing (NeurIPS 2018 · 4 citations)
- 2019 · Linear Kernel Tests via Empirical Likelihood for High-Dimensional Data (AAAI 2019 · 10 citations)
- 2020 · Learning Deep Kernels for Non-Parametric Two-Sample Tests (ICML 2020 · 75 citations)
- 2021 · A Kernel-based Test of Independence for Cluster-correlated Data (NeurIPS 2021 · 4 citations)
- 2022 · Efficient Aggregated Kernel Tests using Incomplete $U$-statistics (NeurIPS 2022 · 6 citations)
- 2023 · MMD-Fuse: Learning and Combining Kernels for Two-Sample Testing Without Data Splitting (NeurIPS 2023 · 4 citations)
- 2025 · DUAL: Learning Diverse Kernels for Aggregated Two-sample and Independence Testing (NeurIPS 2025 · 0 citations)
- 2026 · Are Two Datasets Close Enough With Statistical Significance? A Kernel Distributional Closeness Testing Approach (ICML 2026 · 0 citations)
Earliest papers here
- Minimax Estimation of Maximum Mean Discrepancy with Radial Kernels (NeurIPS 2016 · 61 citations)
- An Adaptive Test of Independence with Analytic Kernel Embeddings (ICML 2017 · 16 citations)
- A Linear-Time Kernel Goodness-of-Fit Test (NeurIPS 2017)
What has been tried
21 papers here report 199 measured changes (a component added, removed or swapped, compared with a baseline): helped 59%, no clear effect 14%, hurt 21%, mixed 6%. Papers mostly publish changes that helped, so "helped" is over-represented.
Ablations in recent papers
| What was changed | Measured on | Result | Effect | Paper |
|---|---|---|---|---|
| Add selection inference to diverse-kernel aggregation | BLOB · test power | Helped | DUAL: Learning Diverse Kernels for Aggregated Two-sample and Independence Testing (NeurIPS 2025 · 0 citations) | |
| Add augmentation during kernel estimation | MNIST · test power | AMD vs AMD-NA: .277 ± .043 vs .224 ± .038 (m=130); .409 ± .036 vs .353 ± .041 (m=160); .604 ± .049 vs .517 ± .049 (m=190 | Helped | Anchor-based Maximum Discrepancy for Relative Similarity Testing (NeurIPS 2025 · 0 citations) |
| Select the conditioning kernel to maximize approximate test power rather than use a regression kernel for dependence measurement | Synthetic CI, alternative · test power | Helped | On the Hardness of Conditional Independence Testing In Practice (NeurIPS 2025 · 0 citations) | |
| Use analytical rather than bootstrapped thresholds | Controlled type I and type II error experiments · type I error calibration | Hurt | Kernel conditional tests from learning-theoretic bounds (NeurIPS 2025 · 0 citations) |
What reviewers will expect
Datasets and baselines named in the 8 papers of this approach from 2025–2026 that have a full-text summary. Leaving out the common ones is a frequent review question.
Datasets
- MNIST · 2 of 8 papers
- ImageNet · 2 of 8 papers
- CIFAR-10 · 2 of 8 papers
Baselines
- MMD-Agg · 2 of 8 papers
- MMD-D · 2 of 8 papers
- MMD-FUSE · 2 of 8 papers
Recent preprints
Loading recent arXiv preprints…
Who publishes on it
Institutions on the most papers of this approach since 2023 (of 15 papers; from OpenAlex and the papers' affiliations).
- University of Melbourne · 3 papers
- University College London · 2 papers
- Carnegie Mellon University · 2 papers
Use it
Download BibTeX of 29 key papersOpen the topic in the interactive map
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Related approaches
Same keyword cluster
- RKHS kernel methods (127 papers)
- Neural tangent kernel analysis (109 papers)
- Kernel regression under shift (89 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).