mlsanityData to 7 Oct 2026

Practical Kernel Tests of Conditional Independence

arXiv 2402.13196 ↗First posted 20 Feb 2024cs.LGcited by 13

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Abstract (arXiv)

We describe a data-efficient, kernel-based approach to statistical testing of conditional independence. A major challenge of conditional independence testing is to obtain the correct test level (the specified upper bound on the rate of false positives), while still attaining competitive test power. Excess false positives arise due to bias in the test statistic, which is in our case obtained using nonparametric kernel ridge regression. We propose SplitKCI, an automated method for bias control for the Kernel-based Conditional Independence (KCI) test based on data splitting. We show that our approach significantly improves test level control for KCI without sacrificing test power, both theoretically and for synthetic and real-world data.

Key facts. Cited by 13 papers in the map (data through 7 Oct 2026). Builds on 30 of its 65 references that are in the map. First posted on arXiv 20 Feb 2024.

Builds on

30 of 65 references.

References · 30

  1. 2016Equality of Opportunity in Supervised Learningcited by 2,000
  2. 2019A Survey on Bias and Fairness in Machine Learningcited by 1,911
  3. 2020Learning Deep Kernels for Non-Parametric Two-Sample Testscited by 129
  4. 2016Panning for Gold: Model-X Knockoffs for High-dimensional Controlled Variable Selectioncited by 120
  5. 2017Sobolev Norm Learning Rates for Regularized Least-Squares Algorithmcited by 113
  6. 2020A Measure-Theoretic Approach to Kernel Conditional Mean Embeddingscited by 86
  7. 2017Approximate Kernel-based Conditional Independence Tests for Fast Non-Parametric Causal Discoverycited by 76
  8. 2021MMD Aggregated Two-Sample Testcited by 74
  9. 2021Proximal Causal Learning with Kernels: Two-Stage Estimation and Moment Restrictioncited by 54
  10. 2022Optimal Rates for Regularized Conditional Mean Embedding Learningcited by 50
  11. 2017Model-Powered Conditional Independence Testcited by 43
  12. 2017Characteristic and Universal Tensor Product Kernelscited by 41
18 more
  1. 2019A simple measure of conditional dependencecited by 38
  2. 2023MMD-FUSE: Learning and Combining Kernels for Two-Sample Testing Without Data Splittingcited by 33
  3. 2014A Wild Bootstrap for Degenerate Kernel Testscited by 28
  4. 2022Efficient Aggregated Kernel Tests using Incomplete U-statisticscited by 27
  5. 2021Local permutation tests for conditional independencecited by 23
  6. 2023Towards Optimal Sobolev Norm Rates for the Vector-Valued Regularized Least-Squares Algorithmcited by 22
  7. 2020Kernel Partial Correlation Coefficient -- a Measure of Conditional Dependencecited by 21
  8. 2022KSD Aggregated Goodness-of-fit Testcited by 21
  9. 2022Efficient Conditionally Invariant Representation Learningcited by 19
  10. 2021Composite Goodness-of-fit Tests with Kernelscited by 16
  11. 2022The Projected Covariance Measure for assumption-lean variable significance testingcited by 16
  12. 2021The Weighted Generalised Covariance Measurecited by 13
  13. 2021An Asymptotic Test for Conditional Independence using Analytic Kernel Embeddingscited by 12
  14. 2022A Permutation-Free Kernel Independence Testcited by 11
  15. 2023Differentially Private Permutation Testscited by 10
  16. 2015A simpler condition for consistency of a kernel independence testcited by 8
  17. 2023Conditional independence testing under misspecified inductive biasescited by 7
  18. 2022A general framework for the analysis of kernel-based testscited by 2

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 2; 2025: 8; 2026: 3.

13 papers.

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  1. 2025A Practical Introduction to Kernel Discrepancies: MMD, HSIC & KSDcited by 9
  2. 2024Doubly Robust Conditional Independence Testing with Generative Neural Networkscited by 6
  3. 2025DUAL: Learning Diverse Kernels for Aggregated Two-sample and Independence Testingcited by 6
  4. 2025On the Hardness of Conditional Independence Testing In Practicecited by 6
  5. 2025Efficient Ensemble Conditional Independence Test Framework for Causal Discoverycited by 5
  6. 2025A Unified View of Optimal Kernel Hypothesis Testingcited by 4
  7. 2024General Frameworks for Conditional Two-Sample Testingcited by 3
  8. 2025A Fast Kernel-based Conditional Independence test with Application to Causal Discoverycited by 2
  9. 2026The Generalised Kernel Covariance Measurecited by 2
  10. 2025Quantum-enhanced causal discovery for a small number of samplescited by 1
  11. 2025Toward Scalable and Valid Conditional Independence Testing with Spectral Representationscited by 1
  12. 2026Mixture Proportion Estimation and Weakly-supervised Kernel Test for Conditional Independencecited by 0
1 more
  1. 2026Structure-agnostic Causal Representation Learningcited by 0