# An Asymptotic Test for Conditional Independence using Analytic Kernel Embeddings

arXiv: https://arxiv.org/abs/2110.14868 · HTML: https://mlsanity.com/paper/2110.14868/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 49 references that are in the map.
- First posted on arXiv 28 Oct 2021.

## Builds on (most cited first, 22 of 22)

- [Generalization Properties of Learning with Random Features](https://mlsanity.com/paper/1602.04474/) (2016)
- [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)
- [Conditional independence testing based on a nearest-neighbor estimator of conditional mutual information](https://mlsanity.com/paper/1709.01447/) (2017)
- [Interpretable Distribution Features with Maximum Testing Power](https://mlsanity.com/paper/1605.06796/) (2016)
- [Fast Two-Sample Testing with Analytic Representations of Probability Measures](https://mlsanity.com/paper/1506.04725/) (2015)
- [Model-Powered Conditional Independence Test](https://mlsanity.com/paper/1709.06138/) (2017)
- [A Linear-Time Kernel Goodness-of-Fit Test](https://mlsanity.com/paper/1705.07673/) (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)
- [Conditional Independence Testing using Generative Adversarial Networks](https://mlsanity.com/paper/1907.04068/) (2019)
- [Large-Scale Kernel Methods for Independence Testing](https://mlsanity.com/paper/1606.07892/) (2016)
- [Double Generative Adversarial Networks for Conditional Independence Testing](https://mlsanity.com/paper/2006.02615/) (2020)
- [Kernel Partial Correlation Coefficient -- a Measure of Conditional Dependence](https://mlsanity.com/paper/2012.14804/) (2020)
- [Fast Conditional Independence Test for Vector Variables with Large Sample Sizes](https://mlsanity.com/paper/1804.02747/) (2018)
- [An Adaptive Test of Independence with Analytic Kernel Embeddings](https://mlsanity.com/paper/1610.04782/) (2016)
- [Wasserstein Conditional Independence Testing](https://mlsanity.com/paper/2107.14184/) (2021)
- [Comparing distributions: ℓ1 geometry improves kernel two-sample testing](https://mlsanity.com/paper/1909.09264/) (2019)
- [On Distance and Kernel Measures of Conditional Independence](https://mlsanity.com/paper/1912.01103/) (2019)
- [Mimic and Classify : A meta-algorithm for Conditional Independence Testing](https://mlsanity.com/paper/1806.09708/) (2018)

## Built on by (most cited first, 12 of 12)

- [Practical Kernel Tests of Conditional Independence](https://mlsanity.com/paper/2402.13196/) (2024)
- [Conditional independence testing under misspecified inductive biases](https://mlsanity.com/paper/2307.02520/) (2023)
- [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)
- [Efficient Ensemble Conditional Independence Test Framework for Causal Discovery](https://mlsanity.com/paper/2509.21021/) (2025)
- [Deep Nonparametric Conditional Independence Tests for Images](https://mlsanity.com/paper/2411.06140/) (2024)
- [A Fast Kernel-based Conditional Independence test with Application to Causal Discovery](https://mlsanity.com/paper/2505.11085/) (2025)
- [Score-based Generative Modeling for Conditional Independence Testing](https://mlsanity.com/paper/2505.23309/) (2025)
- [Toward Scalable and Valid Conditional Independence Testing with Spectral Representations](https://mlsanity.com/paper/2512.19510/) (2025)
- [RFFNet: Large-Scale Interpretable Kernel Methods via Random Fourier Features](https://mlsanity.com/paper/2211.06410/) (2022)
- [Closing the Expression Gap in LLM Instructions via Socratic Questioning](https://mlsanity.com/paper/2510.27410/) (2025)
- [Fast Flow Matching based Conditional Independence Tests for Causal Discovery](https://mlsanity.com/paper/2602.08315/) (2026)

## Abstract (arXiv)

We propose a new conditional dependence measure and a statistical test for conditional independence. The measure is based on the difference between analytic kernel embeddings of two well-suited distributions evaluated at a finite set of locations. We obtain its asymptotic distribution under the null hypothesis of conditional independence and design a consistent statistical test from it. We conduct a series of experiments showing that our new test outperforms state-of-the-art methods both in terms of type-I and type-II errors even in the high dimensional setting.