mlsanityData to 7 Oct 2026

A Practical Introduction to Kernel Discrepancies: MMD, HSIC & KSD

arXiv 2503.04820 ↗First posted 4 Mar 2025stat.ML cs.LGcited by 9

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Abstract (arXiv)

This article provides a practical introduction to kernel discrepancies, focusing on the Maximum Mean Discrepancy (MMD), the Hilbert-Schmidt Independence Criterion (HSIC), and the Kernel Stein Discrepancy (KSD). Various estimators for these discrepancies are presented, including the commonly-used V-statistics and U-statistics, as well as several forms of the more computationally-efficient incomplete U-statistics. The importance of the choice of kernel bandwidth is stressed, showing how it affects the behaviour of the discrepancy estimation. Adaptive estimators are introduced, which combine multiple estimators with various kernels, addressing the problem of kernel selection.

Key facts. Cited by 9 papers in the map (data through 7 Oct 2026). Builds on 21 of its 57 references that are in the map. First posted on arXiv 4 Mar 2025.

Builds on

21 of 57 references.

References · 21

  1. 2016Kernel Mean Embedding of Distributions: A Review and Beyondcited by 360
  2. 2016A Kernelized Stein Discrepancy for Goodness-of-fit Tests and Model Evaluationcited by 236
  3. 2016A Kernel Test of Goodness of Fitcited by 143
  4. 2020Learning Deep Kernels for Non-Parametric Two-Sample Testscited by 129
  5. 2017Measuring Sample Quality with Kernelscited by 119
  6. 2016Generative Models and Model Criticism via Optimized Maximum Mean Discrepancycited by 99
  7. 2015Measuring Sample Quality with Stein's Methodcited by 94
  8. 2021MMD Aggregated Two-Sample Testcited by 74
  9. 2023MMD-FUSE: Learning and Combining Kernels for Two-Sample Testing Without Data Splittingcited by 33
  10. 2016Large-Scale Kernel Methods for Independence Testingcited by 32
  11. 2022Efficient Aggregated Kernel Tests using Incomplete U-statisticscited by 27
  12. 2022KSD Aggregated Goodness-of-fit Testcited by 21
9 more
  1. 2022A Permutation-free Kernel Two-Sample Testcited by 21
  2. 2022Efficient Conditionally Invariant Representation Learningcited by 19
  3. 2022Targeted Separation and Convergence with Kernel Discrepanciescited by 15
  4. 2020Dimension-agnostic inference using cross U-statisticscited by 14
  5. 2024Practical Kernel Tests of Conditional Independencecited by 13
  6. 2022A Permutation-Free Kernel Independence Testcited by 11
  7. 2019Unbiased estimators for the variance of MMD estimatorscited by 10
  8. 2023Differentially Private Permutation Testscited by 10
  9. 2024Robust Kernel Hypothesis Testing under Data Corruptioncited by 7

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 5; 2026: 4.

9 papers.

  1. 2025DUAL: Learning Diverse Kernels for Aggregated Two-sample and Independence Testingcited by 6
  2. 2025A Unified View of Optimal Kernel Hypothesis Testingcited by 4
  3. 2026Regularized f-Divergence Kernel Testscited by 2
  4. 2025DISCO: Mitigating Bias in Deep Learning with Conditional Distance Correlationcited by 0
  5. 2025Incorporating Interventional Independence Improves Robustness against Interventional Distribution Shiftcited by 0
  6. 2025Linear cost mutual information estimation and independence test of similar performance as HSICcited by 0
  7. 2026Mixture Proportion Estimation and Weakly-supervised Kernel Test for Conditional Independencecited by 0
  8. 2026Nonparametric Deconvolution and Denoising using Simulation Based Inferencecited by 0
  9. 2026Unbounded Characteristic and Universal Kernelscited by 0