# Practical Kernel Tests of Conditional Independence

arXiv: https://arxiv.org/abs/2402.13196 · HTML: https://mlsanity.com/paper/2402.13196/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 65 references that are in the map.
- First posted on arXiv 20 Feb 2024.

## Builds on (most cited first, 30 of 30)

- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [A Survey on Bias and Fairness in Machine Learning](https://mlsanity.com/paper/1908.09635/) (2019)
- [Learning Deep Kernels for Non-Parametric Two-Sample Tests](https://mlsanity.com/paper/2002.09116/) (2020)
- [Panning for Gold: Model-X Knockoffs for High-dimensional Controlled Variable Selection](https://mlsanity.com/paper/1610.02351/) (2016)
- [Sobolev Norm Learning Rates for Regularized Least-Squares Algorithm](https://mlsanity.com/paper/1702.07254/) (2017)
- [A Measure-Theoretic Approach to Kernel Conditional Mean Embeddings](https://mlsanity.com/paper/2002.03689/) (2020)
- [Approximate Kernel-based Conditional Independence Tests for Fast Non-Parametric Causal Discovery](https://mlsanity.com/paper/1702.03877/) (2017)
- [MMD Aggregated Two-Sample Test](https://mlsanity.com/paper/2110.15073/) (2021)
- [Proximal Causal Learning with Kernels: Two-Stage Estimation and Moment Restriction](https://mlsanity.com/paper/2105.04544/) (2021)
- [Optimal Rates for Regularized Conditional Mean Embedding Learning](https://mlsanity.com/paper/2208.01711/) (2022)
- [Model-Powered Conditional Independence Test](https://mlsanity.com/paper/1709.06138/) (2017)
- [Characteristic and Universal Tensor Product Kernels](https://mlsanity.com/paper/1708.08157/) (2017)
- [A simple measure of conditional dependence](https://mlsanity.com/paper/1910.12327/) (2019)
- [MMD-FUSE: Learning and Combining Kernels for Two-Sample Testing Without Data Splitting](https://mlsanity.com/paper/2306.08777/) (2023)
- [A Wild Bootstrap for Degenerate Kernel Tests](https://mlsanity.com/paper/1408.5404/) (2014)
- [Efficient Aggregated Kernel Tests using Incomplete U-statistics](https://mlsanity.com/paper/2206.09194/) (2022)
- [Local permutation tests for conditional independence](https://mlsanity.com/paper/2112.11666/) (2021)
- [Towards Optimal Sobolev Norm Rates for the Vector-Valued Regularized Least-Squares Algorithm](https://mlsanity.com/paper/2312.07186/) (2023)
- [Kernel Partial Correlation Coefficient -- a Measure of Conditional Dependence](https://mlsanity.com/paper/2012.14804/) (2020)
- [KSD Aggregated Goodness-of-fit Test](https://mlsanity.com/paper/2202.00824/) (2022)
- [Efficient Conditionally Invariant Representation Learning](https://mlsanity.com/paper/2212.08645/) (2022)
- [Composite Goodness-of-fit Tests with Kernels](https://mlsanity.com/paper/2111.10275/) (2021)
- [The Projected Covariance Measure for assumption-lean variable significance testing](https://mlsanity.com/paper/2211.02039/) (2022)
- [The Weighted Generalised Covariance Measure](https://mlsanity.com/paper/2111.04361/) (2021)
- [An Asymptotic Test for Conditional Independence using Analytic Kernel Embeddings](https://mlsanity.com/paper/2110.14868/) (2021)
- [A Permutation-Free Kernel Independence Test](https://mlsanity.com/paper/2212.09108/) (2022)
- [A simpler condition for consistency of a kernel independence test](https://mlsanity.com/paper/1501.06103/) (2015)
- [Differentially Private Permutation Tests](https://mlsanity.com/paper/2310.19043/) (2023)
- [Conditional independence testing under misspecified inductive biases](https://mlsanity.com/paper/2307.02520/) (2023)
- [A general framework for the analysis of kernel-based tests](https://mlsanity.com/paper/2209.00124/) (2022)

## Built on by (most cited first, 15 of 15)

- [A Practical Introduction to Kernel Discrepancies: MMD, HSIC & KSD](https://mlsanity.com/paper/2503.04820/) (2025)
- [Doubly Robust Conditional Independence Testing with Generative Neural Networks](https://mlsanity.com/paper/2407.17694/) (2024)
- [On the Hardness of Conditional Independence Testing In Practice](https://mlsanity.com/paper/2512.14000/) (2025)
- [DUAL: Learning Diverse Kernels for Aggregated Two-sample and Independence Testing](https://mlsanity.com/paper/2510.11140/) (2025)
- [A Unified View of Optimal Kernel Hypothesis Testing](https://mlsanity.com/paper/2503.07084/) (2025)
- [Efficient Ensemble Conditional Independence Test Framework for Causal Discovery](https://mlsanity.com/paper/2509.21021/) (2025)
- [General Frameworks for Conditional Two-Sample Testing](https://mlsanity.com/paper/2410.16636/) (2024)
- [A Fast Kernel-based Conditional Independence test with Application to Causal Discovery](https://mlsanity.com/paper/2505.11085/) (2025)
- [The Generalised Kernel Covariance Measure](https://mlsanity.com/paper/2604.03721/) (2026)
- [Quantum-enhanced causal discovery for a small number of samples](https://mlsanity.com/paper/2501.05007/) (2025)
- [Toward Scalable and Valid Conditional Independence Testing with Spectral Representations](https://mlsanity.com/paper/2512.19510/) (2025)
- [Structure-agnostic Causal Representation Learning](https://mlsanity.com/paper/2610.00968/) (2026)
- [Mixture Proportion Estimation and Weakly-supervised Kernel Test for Conditional Independence](https://mlsanity.com/paper/2604.07191/) (2026)
- [Semiparametrically Efficient Inference for Kernel Measures of Noise Heterogeneity](https://mlsanity.com/paper/2605.27526/) (2026)
- [Aggregation of Statistical Evidence under Exchangeability](https://mlsanity.com/paper/2607.15823/) (2026)

## 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.