# Differentially Private Conditional Independence Testing

arXiv: https://arxiv.org/abs/2306.06721 · HTML: https://mlsanity.com/paper/2306.06721/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 56 references that are in the map.
- First posted on arXiv 11 Jun 2023.

## Builds on (most cited first, 17 of 17)

- [Just Interpolate: Kernel "Ridgeless" Regression Can Generalize](https://mlsanity.com/paper/1808.00387/) (2018)
- [Panning for Gold: Model-X Knockoffs for High-dimensional Controlled Variable Selection](https://mlsanity.com/paper/1610.02351/) (2016)
- [Approximate Kernel-based Conditional Independence Tests for Fast Non-Parametric Causal Discovery](https://mlsanity.com/paper/1702.03877/) (2017)
- [Private Selection from Private Candidates](https://mlsanity.com/paper/1811.07971/) (2018)
- [Differentially Private Chi-Squared Hypothesis Testing: Goodness of Fit and Independence Testing](https://mlsanity.com/paper/1602.03090/) (2016)
- [Permute-and-Flip: A new mechanism for differentially private selection](https://mlsanity.com/paper/2010.12603/) (2020)
- [The Permute-and-Flip Mechanism is Identical to Report-Noisy-Max with Exponential Noise](https://mlsanity.com/paper/2105.07260/) (2021)
- [The Weighted Generalised Covariance Measure](https://mlsanity.com/paper/2111.04361/) (2021)
- [Differentially private significance tests for regression coefficients](https://mlsanity.com/paper/1705.09561/) (2017)
- [Differentially Private Nonparametric Hypothesis Testing](https://mlsanity.com/paper/1903.09364/) (2019)
- [Private Causal Inference](https://mlsanity.com/paper/1512.05469/) (2015)
- [Towards practical differentially private causal graph discovery](https://mlsanity.com/paper/2006.08598/) (2020)
- [Improved Differentially Private Analysis of Variance](https://mlsanity.com/paper/1903.00534/) (2019)
- [The Test of Tests: A Framework For Differentially Private Hypothesis Testing](https://mlsanity.com/paper/2302.04260/) (2023)
- [Differentially Private Hypothesis Testing with the Subsampled and Aggregated Randomized Response Mechanism](https://mlsanity.com/paper/2208.06803/) (2022)
- [Differentially Private ANOVA Testing](https://mlsanity.com/paper/1711.01335/) (2017)
- [Private independence testing across two parties](https://mlsanity.com/paper/2207.03652/) (2022)

## Abstract (arXiv)

Conditional independence (CI) tests are widely used in statistical data analysis, e.g., they are the building block of many algorithms for causal graph discovery. The goal of a CI test is to accept or reject the null hypothesis that X perp !!! perp Y mid Z, where X ∈ ℝ, Y ∈ ℝ, Z ∈ ℝd. In this work, we investigate conditional independence testing under the constraint of differential privacy. We design two private CI testing procedures: one based on the generalized covariance measure of Shah and Peters (2020) and another based on the conditional randomization test of Cand`es et al. (2016) (under the model-X assumption). We provide theoretical guarantees on the performance of our tests and validate them empirically. These are the first private CI tests with rigorous theoretical guarantees that work for the general case when Z is continuous.