mlsanityData to 7 Oct 2026

Model-Powered Conditional Independence Test

arXiv 1709.06138 ↗First posted 18 Sep 2017stat.ML cs.AI cs.ITcited by 43

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Abstract (arXiv)

We consider the problem of non-parametric Conditional Independence testing (CI testing) for continuous random variables. Given i.i.d samples from the joint distribution f(x,y,z) of continuous random vectors X,Y and Z, we determine whether X perp Y | Z. We approach this by converting the conditional independence test into a classification problem. This allows us to harness very powerful classifiers like gradient-boosted trees and deep neural networks. These models can handle complex probability distributions and allow us to perform significantly better compared to the prior state of the art, for high-dimensional CI testing. The main technical challenge in the classification problem is the need for samples from the conditional product distribution fCI(x,y,z) = f(x|z)f(y|z)f(z) -- the joint distribution if and only if X perp Y | Z. -- when given access only to i.i.d. samples from the true joint distribution f(x,y,z). To tackle this problem we propose a novel nearest neighbor bootstrap procedure and theoretically show that our generated samples are indeed close to fCI in terms of total variational distance. We then develop theoretical results regarding the generalization bounds for classification for our problem, which translate into error bounds for CI testing. We provide a novel analysis of Rademacher type classification bounds in the presence of non-i.i.d near-independent samples. We empirically validate the performance of our algorithm on simulated and real datasets and show performance gains over previous methods.

Key facts. Cited by 43 papers in the map (data through 7 Oct 2026). First posted on arXiv 18 Sep 2017.

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Citing papers per year: 2021: 5; 2022: 8; 2023: 8; 2024: 11; 2025: 6; 2026: 5.

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  1. 2021D'ya like DAGs? A Survey on Structure Learning and Causal Discoverycited by 209
  2. 2023A Survey on Causal Discovery Methods for I.I.D. and Time Series Datacited by 35
  3. 2024Mutual Information Estimation via Normalizing Flowscited by 22
  4. 2023Information Bottleneck Analysis of Deep Neural Networks via Lossy Compressioncited by 19
  5. 2024Signature Kernel Conditional Independence Tests in Causal Discovery for Stochastic Processescited by 18
  6. 2024Practical Kernel Tests of Conditional Independencecited by 13
  7. 2021An Asymptotic Test for Conditional Independence using Analytic Kernel Embeddingscited by 12
  8. 2023Auditing for Human Expertisecited by 12
  9. 2021Out-of-Distribution Generalization Analysis via Influence Functioncited by 11
  10. 2022Composite Feature Selection using Deep Ensemblescited by 11
  11. 2022Diffeomorphic Information Neural Estimationcited by 10
  12. 2023Less is More: Mitigate Spurious Correlations for Open-Domain Dialogue Response Generation Models by Causal Discoverycited by 10
31 more
  1. 2024Demystifying amortized causal discovery with transformerscited by 10
  2. 2022Conditional Independence Testing via Latent Representation Learningcited by 9
  3. 2023High-Dimensional Smoothed Entropy Estimation via Dimensionality Reductioncited by 7
  4. 2025InfoBridge: Mutual Information estimation via Bridge Matchingcited by 7
  5. 2024Doubly Robust Conditional Independence Testing with Generative Neural Networkscited by 6
  6. 2025On the Hardness of Conditional Independence Testing In Practicecited by 6
  7. 2023Nearest-Neighbor Sampling Based Conditional Independence Testingcited by 5
  8. 2024Scalable and Flexible Causal Discovery with an Efficient Test for Adjacencycited by 5
  9. 2024CausalScore: An Automatic Reference-Free Metric for Assessing Response Relevance in Open-Domain Dialogue Systemscited by 5
  10. 2025Efficient Ensemble Conditional Independence Test Framework for Causal Discoverycited by 5
  11. 2024FairICP: Encouraging Equalized Odds via Inverse Conditional Permutationcited by 4
  12. 2022DIET: Conditional independence testing with marginal dependence measures of residual informationcited by 3
  13. 2022A survey of some recent developments in measures of associationcited by 3
  14. 2024A Conditional Independence Test in the Presence of Discretizationcited by 3
  15. 2024Deep Nonparametric Conditional Independence Tests for Imagescited by 3
  16. 2021PPFS: Predictive Permutation Feature Selectioncited by 2
  17. 2021Data-Driven Representations for Testing Independence: Modeling, Analysis and Connection with Mutual Information Estimationcited by 2
  18. 2022Empirical Bayesian Approaches for Robust Constraint-based Causal Discovery under Insufficient Datacited by 2
  19. 2025Score-based Generative Modeling for Conditional Independence Testingcited by 2
  20. 2022Improving the Efficiency of the PC Algorithm by Using Model-Based Conditional Independence Testscited by 1
  21. 2024Causal Adjacency Learning for Spatiotemporal Prediction Over Graphscited by 1
  22. 2025From Conditional to Unconditional Independence: Testing Conditional Independence via Transport Mapscited by 1
  23. 2025Toward Scalable and Valid Conditional Independence Testing with Spectral Representationscited by 1
  24. 2026Empirically Calibrated Conditional Independence Testscited by 1
  25. 2026Separating Covariate Shift from Mechanism Change with Two Discriminators: CJSD, a Conditional Discrepancy with an Exact Covariate-Concept Decompositioncited by 1
  26. 2022Evaluating Independence and Conditional Independence Measurescited by 0
  27. 2023A New Paradigm for Generative Adversarial Networks based on Randomized Decision Rulescited by 0
  28. 2023Evaluating LLP Methods: Challenges and Approachescited by 0
  29. 2026Causality-Encoded Diffusion Models for Interventional Sampling and Edge Inferencecited by 0
  30. 2026PAIR-CI: Calibrated Conditional Independence Testing for Causal Discovery with Incomplete Datacited by 0
  31. 2026seq2cause: One Autoregressive Backbone, Four Causal Discovery Tasks in Event Sequencescited by 0