mlsanityData to 7 Oct 2026

A Kernel Two-Sample Test for Functional Data

arXiv 2008.11095 ↗First posted 25 Aug 2020math.ST stat.ME stat.MLcited by 27

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Abstract (arXiv)

We propose a nonparametric two-sample test procedure based on Maximum Mean Discrepancy (MMD) for testing the hypothesis that two samples of functions have the same underlying distribution, using kernels defined on function spaces. This construction is motivated by a scaling analysis of the efficiency of MMD-based tests for datasets of increasing dimension. Theoretical properties of kernels on function spaces and their associated MMD are established and employed to ascertain the efficacy of the newly proposed test, as well as to assess the effects of using functional reconstructions based on discretised function samples. The theoretical results are demonstrated over a range of synthetic and real world datasets.

Key facts. Cited by 27 papers in the map (data through 7 Oct 2026). First posted on arXiv 25 Aug 2020.

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Citing papers per year: 2021: 4; 2022: 5; 2023: 5; 2024: 4; 2025: 6; 2026: 3.

27 papers.

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  1. 2021MMD Aggregated Two-Sample Testcited by 74
  2. 2023Non-adversarial training of Neural SDEs with signature kernel scorescited by 36
  3. 2022Spectral Diffusion Processescited by 24
  4. 2023Variational Autoencoding Neural Operatorscited by 22
  5. 2022KSD Aggregated Goodness-of-fit Testcited by 21
  6. 2023Correspondence-Free Domain Alignment for Unsupervised Cross-Domain Image Retrievalcited by 11
  7. 2024Bayesian Neural Networks with Domain Knowledge Priorscited by 8
  8. 2021Kernel Two-Sample Tests for Manifold Datacited by 7
  9. 2022Characteristic kernels on Hilbert spaces, Banach spaces, and on sets of measurescited by 7
  10. 2021Statistical Depth Meets Machine Learning: Kernel Mean Embeddings and Depth in Functional Data Analysiscited by 6
  11. 2022Energy-Based Models for Functional Data using Path Measure Tiltingcited by 5
  12. 2023A High-dimensional Convergence Theorem for U-statistics with Applications to Kernel-based Testingcited by 5
15 more
  1. 2025Probability-Flow ODE in Infinite-Dimensional Function Spacescited by 5
  2. 2022A Fourier representation of kernel Stein discrepancy with application to Goodness-of-Fit tests for measures on infinite dimensional Hilbert spacescited by 3
  3. 2025Uncertainty Quantification for Regression: A Unified Framework based on kernel scorescited by 2
  4. 2026Minimax Lower Bounds of Kernel Discrepancy Estimation: MMD, HSIC, KSDcited by 2
  5. 2021A fast and effective kernel two-sample test for large-scale datacited by 1
  6. 2023Domain-knowledge Inspired Pseudo Supervision (DIPS) for Unsupervised Image-to-Image Translation Models to Support Cross-Domain Classificationcited by 1
  7. 2024Variable Selection for Comparing High-dimensional Time-Series Datacited by 1
  8. 2025Anchor-based Maximum Discrepancy for Relative Similarity Testingcited by 1
  9. 2024Log-PDE Methods for Rough Signature Kernelscited by 0
  10. 2024Efficient pooling of predictions via kernel embeddingscited by 0
  11. 2025The Stochastic Occupation Kernel (SOCK) Method for Learning Stochastic Differential Equationscited by 0
  12. 2025Are Two Datasets Close Enough With Statistical Significance? A Kernel Distributional Closeness Testing Approachcited by 0
  13. 2025Novelty detection on path spacecited by 0
  14. 2026Gaussian mixture models in Hilbert spaces via kernel methodscited by 0
  15. 2026Functional dynamic mode decomposition: Learning infinite-dimensional systems from datacited by 0