# Private independence testing across two parties

arXiv: https://arxiv.org/abs/2207.03652 · HTML: https://mlsanity.com/paper/2207.03652/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 33 references that are in the map.
- First posted on arXiv 8 Jul 2022.

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

- [CoinPress: Practical Private Mean and Covariance Estimation](https://mlsanity.com/paper/2006.06618/) (2020)
- [A Linear-Time Kernel Goodness-of-Fit Test](https://mlsanity.com/paper/1705.07673/) (2017)
- [Large-Scale Kernel Methods for Independence Testing](https://mlsanity.com/paper/1606.07892/) (2016)
- [Differentially Private Testing of Identity and Closeness of Discrete Distributions](https://mlsanity.com/paper/1707.05128/) (2017)
- [Differentially Private Chi-Squared Hypothesis Testing: Goodness of Fit and Independence Testing](https://mlsanity.com/paper/1602.03090/) (2016)
- [An Adaptive Test of Independence with Analytic Kernel Embeddings](https://mlsanity.com/paper/1610.04782/) (2016)
- [Inference under Information Constraints III: Local Privacy Constraints](https://mlsanity.com/paper/2101.07981/) (2021)
- [Locally Private Hypothesis Testing](https://mlsanity.com/paper/1802.03441/) (2018)
- [Towards practical differentially private causal graph discovery](https://mlsanity.com/paper/2006.08598/) (2020)
- [The Chi-Square Test of Distance Correlation](https://mlsanity.com/paper/1912.12150/) (2019)
- [Supervised Dimensionality Reduction via Distance Correlation Maximization](https://mlsanity.com/paper/1601.00236/) (2016)
- [Consistent distribution-free K-sample and independence tests for univariate random variables](https://mlsanity.com/paper/1410.6758/) (2014)
- [Testing mutual independence in high dimension via distance covariance](https://mlsanity.com/paper/1609.09380/) (2016)
- [Asymptotic Distributions of High-Dimensional Distance Correlation Inference](https://mlsanity.com/paper/1910.12970/) (2019)

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

- [Towards Practical Federated Causal Structure Learning](https://mlsanity.com/paper/2306.09433/) (2023)
- [Differentially Private Conditional Independence Testing](https://mlsanity.com/paper/2306.06721/) (2023)

## Abstract (arXiv)

We introduce π-test, a privacy-preserving algorithm for testing statistical independence between data distributed across multiple parties. Our algorithm relies on privately estimating the distance correlation between datasets, a quantitative measure of independence introduced in Sz'ekely et al. [2007]. We establish both additive and multiplicative error bounds on the utility of our differentially private test, which we believe will find applications in a variety of distributed hypothesis testing settings involving sensitive data.