mlsanityData to 7 Oct 2026

Kernel Two-Sample Tests in High Dimension: Interplay Between Moment Discrepancy and Dimension-and-Sample Orders

arXiv 2201.00073 ↗First posted 31 Dec 2021math.ST stat.ML stat.THcited by 5

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Abstract (arXiv)

Motivated by the increasing use of kernel-based metrics for high-dimensional and large-scale data, we study the asymptotic behavior of kernel two-sample tests when the dimension and sample sizes both diverge to infinity. We focus on the maximum mean discrepancy (MMD) using isotropic kernel, including MMD with the Gaussian kernel and the Laplace kernel, and the energy distance as special cases. We derive asymptotic expansions of the kernel two-sample statistics, based on which we establish the central limit theorem (CLT) under both the null hypothesis and the local and fixed alternatives. The new non-null CLT results allow us to perform asymptotic exact power analysis, which reveals a delicate interplay between the moment discrepancy that can be detected by the kernel two-sample tests and the dimension-and-sample orders. The asymptotic theory is further corroborated through numerical studies.

Key facts. Cited by 5 papers in the map (data through 7 Oct 2026). Builds on 20 of its 48 references that are in the map. First posted on arXiv 31 Dec 2021.

Builds on

20 of 48 references.

References · 20

  1. 2018Demystifying MMD GANscited by 1,268
  2. 2016Deep Transfer Learning with Joint Adaptation Networkscited by 609
  3. 2015Generative Moment Matching Networkscited by 252
  4. 2016A Kernelized Stein Discrepancy for Goodness-of-fit Tests and Model Evaluationcited by 236
  5. 2015The Variational Fair Autoencodercited by 223
  6. 2018Just Interpolate: Kernel "Ridgeless" Regression Can Generalizecited by 190
  7. 2019Linearized two-layers neural networks in high dimensioncited by 155
  8. 2017Mind the Class Weight Bias: Weighted Maximum Mean Discrepancy for Unsupervised Domain Adaptationcited by 151
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  12. 2016Support pointscited by 39
8 more
  1. 2013A Nonparametric Approach for Multiple Change Point Analysis of Multivariate Datacited by 28
  2. 2013A new graph-based two-sample test for multivariate and object datacited by 24
  3. 2015Adaptivity and Computation-Statistics Tradeoffs for Kernel and Distance based High Dimensional Two Sample Testingcited by 14
  4. 2019A New Framework for Distance and Kernel-based Metrics in High Dimensionscited by 6
  5. 2019Distance-based and RKHS-based Dependence Metrics in High Dimensioncited by 4
  6. 2019Asymptotic Distributions of High-Dimensional Distance Correlation Inferencecited by 3
  7. 2021High-dimensional Change-point Detection Using Generalized Homogeneity Metricscited by 3
  8. 2019Interpoint Distance Based Two Sample Tests in High Dimensioncited by 1

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Cited by year

Citing papers per year: 2022: 1; 2023: 0; 2024: 1; 2025: 3.

5 papers.

  1. 2022Distance and Kernel-Based Measures for Global and Local Two-Sample Conditional Distribution Testingcited by 5
  2. 2024A Unified Data Representation Learning for Non-parametric Two-sample Testingcited by 5
  3. 2025A Two-Sample Test of Text Generation Similaritycited by 0
  4. 2025Moment Expansions of the Energy Distancecited by 0
  5. 2025Machine-Learning-Assisted Comparison of Regression Functionscited by 0