# A Fast Kernel-based Conditional Independence test with Application to Causal Discovery

arXiv: https://arxiv.org/abs/2505.11085 · HTML: https://mlsanity.com/paper/2505.11085/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 37 references that are in the map.
- First posted on arXiv 16 May 2025.

## Builds on (most cited first, 14 of 14)

- [Causal Inference in the Presence of Latent Variables and Selection Bias](https://mlsanity.com/paper/1302.4983/) (2013)
- [Causal-learn: Causal Discovery in Python](https://mlsanity.com/paper/2307.16405/) (2023)
- [Approximate Kernel-based Conditional Independence Tests for Fast Non-Parametric Causal Discovery](https://mlsanity.com/paper/1702.03877/) (2017)
- [A Survey on Causal Discovery: Theory and Practice](https://mlsanity.com/paper/2305.10032/) (2023)
- [A fast PC algorithm for high dimensional causal discovery with multi-core PCs](https://mlsanity.com/paper/1502.02454/) (2015)
- [Conditional Independence Testing using Generative Adversarial Networks](https://mlsanity.com/paper/1907.04068/) (2019)
- [Local permutation tests for conditional independence](https://mlsanity.com/paper/2112.11666/) (2021)
- [textttcausalAssembly: Generating Realistic Production Data for Benchmarking Causal Discovery](https://mlsanity.com/paper/2306.10816/) (2023)
- [Practical Kernel Tests of Conditional Independence](https://mlsanity.com/paper/2402.13196/) (2024)
- [Causal Discovery with Fewer Conditional Independence Tests](https://mlsanity.com/paper/2406.01823/) (2024)
- [cuPC: CUDA-based Parallel PC Algorithm for Causal Structure Learning on GPU](https://mlsanity.com/paper/1812.08491/) (2018)
- [An Asymptotic Test for Conditional Independence using Analytic Kernel Embeddings](https://mlsanity.com/paper/2110.14868/) (2021)
- [Embarrassingly Parallel Inference for Gaussian Processes](https://mlsanity.com/paper/1702.08420/) (2017)
- [Partitioned hybrid learning of Bayesian network structures](https://mlsanity.com/paper/2103.12188/) (2021)

## Built on by (most cited first, 2 of 2)

- [Efficient Ensemble Conditional Independence Test Framework for Causal Discovery](https://mlsanity.com/paper/2509.21021/) (2025)
- [Fast Nonparametric Conditional Independence Testing via Two-Stage Regression](https://mlsanity.com/paper/2606.18011/) (2026)

## Abstract (arXiv)

Kernel-based conditional independence (KCI) testing is a powerful nonparametric method commonly employed in causal discovery tasks. Despite its flexibility and statistical reliability, cubic computational complexity limits its application to large datasets. To address this computational bottleneck, we propose textitFastKCI, a scalable and parallelizable kernel-based conditional independence test that utilizes a mixture-of-experts approach inspired by embarrassingly parallel inference techniques for Gaussian processes. By partitioning the dataset based on a Gaussian mixture model over the conditioning variables, FastKCI conducts local KCI tests in parallel, aggregating the results using an importance-weighted sampling scheme. Experiments on synthetic datasets and benchmarks on real-world production data validate that FastKCI maintains the statistical power of the original KCI test while achieving substantial computational speedups. FastKCI thus represents a practical and efficient solution for conditional independence testing in causal inference on large-scale data.