mlsanityData to 7 Oct 2026

Characteristic and Universal Tensor Product Kernels

arXiv 1708.08157 ↗First posted 28 Aug 2017stat.ML cs.IT math.ITcited by 41

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Abstract (arXiv)

Maximum mean discrepancy (MMD), also called energy distance or N-distance in statistics and Hilbert-Schmidt independence criterion (HSIC), specifically distance covariance in statistics, are among the most popular and successful approaches to quantify the difference and independence of random variables, respectively. Thanks to their kernel-based foundations, MMD and HSIC are applicable on a wide variety of domains. Despite their tremendous success, quite little is known about when HSIC characterizes independence and when MMD with tensor product kernel can discriminate probability distributions. In this paper, we answer these questions by studying various notions of characteristic property of the tensor product kernel.

Key facts. Cited by 41 papers in the map (data through 7 Oct 2026). First posted on arXiv 28 Aug 2017.

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Citing papers per year: 2021: 9; 2022: 5; 2023: 8; 2024: 5; 2025: 8; 2026: 6.

41 papers.

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  1. 2021Self-Supervised Learning with Kernel Dependence Maximizationcited by 77
  2. 2021RKHS-SHAP: Shapley Values for Kernel Methodscited by 30
  3. 2022Calibration tests beyond classificationcited by 20
  4. 2023Calibration by Distribution Matching: Trainable Kernel Calibration Metricscited by 20
  5. 2024Practical Kernel Tests of Conditional Independencecited by 13
  6. 2021An Asymptotic Test for Conditional Independence using Analytic Kernel Embeddingscited by 12
  7. 2022Learning Counterfactually Invariant Predictorscited by 10
  8. 2023Dynamic Flows on Curved Space Generated by Labeled Datacited by 10
  9. 2023Random Smoothing Regularization in Kernel Gradient Descent Learningcited by 6
  10. 2024Doubly Robust Conditional Independence Testing with Generative Neural Networkscited by 6
  11. 2025On the Hardness of Conditional Independence Testing In Practicecited by 6
  12. 2022Maximum Mean Discrepancy on Exponential Windows for Online Change Detectioncited by 5
29 more
  1. 2023Kernelized Cumulants: Beyond Kernel Mean Embeddingscited by 5
  2. 2023Nystr"om M-Hilbert-Schmidt Independence Criterioncited by 5
  3. 2021Exact Distribution-Free Hypothesis Tests for the Regression Function of Binary Classification via Conditional Kernel Mean Embeddingscited by 4
  4. 2021Human-in-the-loop Handling of Knowledge Driftcited by 4
  5. 2021Learning Invariant Representations with Missing Datacited by 4
  6. 2023Understanding Deep Generative Models with Generalized Empirical Likelihoodscited by 3
  7. 2025Amortized Linear-time Exact Shapley Value for Product-Kernel Methodscited by 3
  8. 2021Keep it Tighter -- A Story on Analytical Mean Embeddingscited by 2
  9. 2023Robust Bayesian Inference for Measurement Error Misspecification: The Berkson and Classical Casescited by 2
  10. 2024The Minimax Rate of HSIC Estimation for Translation-Invariant Kernelscited by 2
  11. 2024Learning Representations for Independence Testingcited by 2
  12. 2025All Models Are Miscalibrated, But Some Less So: Comparing Calibration with Conditional Mean Operatorscited by 2
  13. 2025The Minimax Lower Bound of Kernel Stein Discrepancy Estimationcited by 2
  14. 2025Sequence Modeling with Spectral Mean Flowscited by 2
  15. 2026The Generalised Kernel Covariance Measurecited by 2
  16. 2026Minimax Lower Bounds of Kernel Discrepancy Estimation: MMD, HSIC, KSDcited by 2
  17. 2021Bandits for Learning to Explain from Explanationscited by 1
  18. 2021Estimating R'enyi's α-Cross-Entropies in a Matrix-Based Waycited by 1
  19. 2022Non-Parametric Inference of Relational Dependencecited by 1
  20. 2024Disentangling Mean Embeddings for Better Diagnostics of Image Generatorscited by 1
  21. 2025When Bayesian Tensor Completion Meets Multioutput Gaussian Processes: Functional Universality and Rank Learningcited by 1
  22. 2022Discussion of `Multiscale Fisher's Independence Test for Multivariate Dependence'cited by 0
  23. 2023Returning The Favour: When Regression Benefits From Probabilistic Causal Knowledgecited by 0
  24. 2025Kernel-based Equalized Odds: A Quantification of Accuracy-Fairness Trade-off in Fair Representation Learningcited by 0
  25. 2025Bilateral Distribution Compression: Reducing Both Data Size and Dimensionalitycited by 0
  26. 2026Kernel Integrated R2: A Measure of Dependencecited by 0
  27. 2026A Joint-Distribution Route to Fair Representations with Continuous Sensitive Attributescited by 0
  28. 2026The Statistical Cost of Causal Discovery with Feedbackcited by 0
  29. 2026Structure-agnostic Causal Representation Learningcited by 0