# Fast Conditional Independence Test for Vector Variables with Large Sample Sizes

arXiv: https://arxiv.org/abs/1804.02747 · HTML: https://mlsanity.com/paper/1804.02747/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Apr 2018.

## Built on by (most cited first, 16 of 16)

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- [BECAUSE: Bilinear Causal Representation for Generalizable Offline Model-based Reinforcement Learning](https://mlsanity.com/paper/2407.10967/) (2024)
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- [Facing Asymmetry -- Uncovering the Causal Link between Facial Symmetry and Expression Classifiers using Synthetic Interventions](https://mlsanity.com/paper/2409.15927/) (2024)
- [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)
- [Fast Nonparametric Conditional Independence Testing via Two-Stage Regression](https://mlsanity.com/paper/2606.18011/) (2026)
- [Evaluating Independence and Conditional Independence Measures](https://mlsanity.com/paper/2205.07253/) (2022)
- [Evaluating LLP Methods: Challenges and Approaches](https://mlsanity.com/paper/2310.19065/) (2023)

## Abstract (arXiv)

We present and evaluate the Fast (conditional) Independence Test (FIT) -- a nonparametric conditional independence test. The test is based on the idea that when P(X mid Y, Z) = P(X mid Y), Z is not useful as a feature to predict X, as long as Y is also a regressor. On the contrary, if P(X mid Y, Z) neq P(X mid Y), Z might improve prediction results. FIT applies to thousand-dimensional random variables with a hundred thousand samples in a fraction of the time required by alternative methods. We provide an extensive evaluation that compares FIT to six extant nonparametric independence tests. The evaluation shows that FIT has low probability of making both Type I and Type II errors compared to other tests, especially as the number of available samples grows. Our implementation of FIT is publicly available.