# A Distribution Free Conditional Independence Test with Applications to Causal Discovery

arXiv: https://arxiv.org/abs/2105.07555 · HTML: https://mlsanity.com/paper/2105.07555/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 May 2021.

## Built on by (most cited first, 11 of 11)

- [Doubly Robust Conditional Independence Testing with Generative Neural Networks](https://mlsanity.com/paper/2407.17694/) (2024)
- [Nearest-Neighbor Sampling Based Conditional Independence Testing](https://mlsanity.com/paper/2304.04183/) (2023)
- [Efficient Ensemble Conditional Independence Test Framework for Causal Discovery](https://mlsanity.com/paper/2509.21021/) (2025)
- [Lossless Transformations and Excess Risk Bounds in Statistical Inference](https://mlsanity.com/paper/2307.16735/) (2023)
- [From Conditional to Unconditional Independence: Testing Conditional Independence via Transport Maps](https://mlsanity.com/paper/2504.09567/) (2025)
- [Score-based Generative Modeling for Conditional Independence Testing](https://mlsanity.com/paper/2505.23309/) (2025)
- [Fr'echet Cumulative Covariance Net for Deep Nonlinear Sufficient Dimension Reduction with Random Objects](https://mlsanity.com/paper/2502.15374/) (2025)
- [Optimal Prediction-Augmented Algorithms for Testing Independence of Distributions](https://mlsanity.com/paper/2603.04635/) (2026)
- [Causal-TS: A Python Library for Causal Discovery in High-Dimensional and Nonstationary Time Series](https://mlsanity.com/paper/2607.24673/) (2026)
- [TSLiNGAM: DirectLiNGAM under heavy tails](https://mlsanity.com/paper/2308.05422/) (2023)
- [Differentially Private Sliced Inverse Regression: Minimax Optimality and Algorithm](https://mlsanity.com/paper/2401.08150/) (2024)

## Abstract (arXiv)

This paper is concerned with test of the conditional independence. We first establish an equivalence between the conditional independence and the mutual independence. Based on the equivalence, we propose an index to measure the conditional dependence by quantifying the mutual dependence among the transformed variables. The proposed index has several appealing properties. (a) It is distribution free since the limiting null distribution of the proposed index does not depend on the population distributions of the data. Hence the critical values can be tabulated by simulations. (b) The proposed index ranges from zero to one, and equals zero if and only if the conditional independence holds. Thus, it has nontrivial power under the alternative hypothesis. (c) It is robust to outliers and heavy-tailed data since it is invariant to conditional strictly monotone transformations. (d) It has low computational cost since it incorporates a simple closed-form expression and can be implemented in quadratic time. (e) It is insensitive to tuning parameters involved in the calculation of the proposed index. (f) The new index is applicable for multivariate random vectors as well as for discrete data. All these properties enable us to use the new index as statistical inference tools for various data. The effectiveness of the method is illustrated through extensive simulations and a real application on causal discovery.