mlsanityData to 7 Oct 2026

Conditional independence testing based on a nearest-neighbor estimator of conditional mutual information

arXiv 1709.01447 ↗First posted 5 Sep 2017stat.ML cs.IT math.ITcited by 70

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Abstract (arXiv)

Conditional independence testing is a fundamental problem underlying causal discovery and a particularly challenging task in the presence of nonlinear and high-dimensional dependencies. Here a fully non-parametric test for continuous data based on conditional mutual information combined with a local permutation scheme is presented. Through a nearest neighbor approach, the test efficiently adapts also to non-smooth distributions due to strongly nonlinear dependencies. Numerical experiments demonstrate that the test reliably simulates the null distribution even for small sample sizes and with high-dimensional conditioning sets. The test is better calibrated than kernel-based tests utilizing an analytical approximation of the null distribution, especially for non-smooth densities, and reaches the same or higher power levels. Combining the local permutation scheme with the kernel tests leads to better calibration, but suffers in power. For smaller sample sizes and lower dimensions, the test is faster than random fourier feature-based kernel tests if the permutation scheme is (embarrassingly) parallelized, but the runtime increases more sharply with sample size and dimensionality. Thus, more theoretical research to analytically approximate the null distribution and speed up the estimation for larger sample sizes is desirable.

Key facts. Cited by 70 papers in the map (data through 7 Oct 2026). First posted on arXiv 5 Sep 2017.

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Citing papers per year: 2021: 8; 2022: 10; 2023: 19; 2024: 12; 2025: 12; 2026: 9.

70 papers.

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  1. 2021Causal Influence Detection for Improving Efficiency in Reinforcement Learningcited by 70
  2. 2023Causal Discovery from Temporal Data: An Overview and New Perspectivescited by 43
  3. 2021Combining Human Predictions with Model Probabilities via Confusion Matrices and Calibrationcited by 40
  4. 2023A Survey on Causal Discovery Methods for I.I.D. and Time Series Datacited by 35
  5. 2021NTS-NOTEARS: Learning Nonparametric DBNs With Prior Knowledgecited by 33
  6. 2023Discovering Causal Relations and Equations from Datacited by 33
  7. 2023CUTS: Neural Causal Discovery from Irregular Time-Series Datacited by 32
  8. 2023Conditional Mutual Information for Disentangled Representations in Reinforcement Learningcited by 27
  9. 2022Achieving Long-Term Fairness in Sequential Decision Makingcited by 18
  10. 2021An Asymptotic Test for Conditional Independence using Analytic Kernel Embeddingscited by 12
  11. 2023Auditing for Human Expertisecited by 12
  12. 2022Composite Feature Selection using Deep Ensemblescited by 11
38 more
  1. 2022Diffeomorphic Information Neural Estimationcited by 10
  2. 2021Entropy-based Discovery of Summary Causal Graphs in Time Seriescited by 9
  3. 2022Conditional Independence Testing via Latent Representation Learningcited by 9
  4. 2023Local Discovery by Partitioning: Polynomial-Time Causal Discovery Around Exposure-Outcome Pairscited by 9
  5. 2023Conditional independence testing under misspecified inductive biasescited by 7
  6. 2021Semiparametric Bayesian Networkscited by 6
  7. 2023Conditional Independence Testing with Heteroskedastic Data and Applications to Causal Discoverycited by 6
  8. 2023Towards Causal Representations of Climate Model Datacited by 6
  9. 2024Local Causal Discovery for Structural Evidence of Direct Discriminationcited by 6
  10. 2023Nearest-Neighbor Sampling Based Conditional Independence Testingcited by 5
  11. 2024Scalable and Flexible Causal Discovery with an Efficient Test for Adjacencycited by 5
  12. 2024Causal Representation Learning in Temporal Data via Single-Parent Decodingcited by 5
  13. 2025Causal Additive Models with Unobserved Causal Paths and Backdoor Pathscited by 5
  14. 2025Efficient Ensemble Conditional Independence Test Framework for Causal Discoverycited by 5
  15. 2023Data AUDIT: Identifying Attribute Utility- and Detectability-Induced Bias in Task Modelscited by 4
  16. 2024Fast Computation of Leave-One-Out Cross-Validation for k-NN Regressioncited by 4
  17. 2025The Third Pillar of Causal Analysis? A Measurement Perspective on Causal Representationscited by 4
  18. 2022DIET: Conditional independence testing with marginal dependence measures of residual informationcited by 3
  19. 2022A survey of some recent developments in measures of associationcited by 3
  20. 2023Causal Discovery via Conditional Independence Testing with Proxy Variablescited by 3
  21. 2023Causal Feature Selection via Transfer Entropycited by 3
  22. 2024The Power of Properties: Uncovering the Influential Factors in Emotion Classificationcited by 3
  23. 2024Deep Nonparametric Conditional Independence Tests for Imagescited by 3
  24. 2021Data-Driven Representations for Testing Independence: Modeling, Analysis and Connection with Mutual Information Estimationcited by 2
  25. 2021Finding Regions of Heterogeneity in Decision-Making via Expected Conditional Covariancecited by 2
  26. 2022Trying to Outrun Causality with Machine Learning: Limitations of Model Explainability Techniques for Identifying Predictive Variablescited by 2
  27. 2022A Causal Research Pipeline and Tutorial for Psychologists and Social Scientistscited by 2
  28. 2024Facing Asymmetry -- Uncovering the Causal Link between Facial Symmetry and Expression Classifiers using Synthetic Interventionscited by 2
  29. 2025Locally Explaining Prediction Behavior via Gradual Interventions and Measuring Property Gradientscited by 2
  30. 2025Score-based Generative Modeling for Conditional Independence Testingcited by 2
  31. 2025Efficient Causal Discovery for Autoregressive Time Seriescited by 2
  32. 2023Hierarchical Topological Ordering with Conditional Independence Test for Limited Time Seriescited by 1
  33. 2023Non-parametric Conditional Independence Testing for Mixed Continuous-Categorical Variables: A Novel Method and Numerical Evaluationcited by 1
  34. 2024Causal Layering via Conditional Entropycited by 1
  35. 2024When Medical Imaging Met Self-Attention: A Love Story That Didn't Quite Work Outcited by 1
  36. 2024Interventional Causal Structure Discovery over Graphical Models with Convergence and Optimality Guaranteescited by 1
  37. 2025Amortized Conditional Independence Testingcited by 1
  38. 2025Learning Causal Response Representations through Direct Effect Analysiscited by 1

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