# Differentially Private Maximal Information Coefficients

arXiv: https://arxiv.org/abs/2206.10685 · HTML: https://mlsanity.com/paper/2206.10685/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 31 references that are in the map.
- First posted on arXiv 21 Jun 2022.

## Builds on (most cited first, 9 of 9)

- [Private Mean Estimation of Heavy-Tailed Distributions](https://mlsanity.com/paper/2002.09464/) (2020)
- [Private Hypothesis Selection](https://mlsanity.com/paper/1905.13229/) (2019)
- [Equitability, mutual information, and the maximal information coefficient](https://mlsanity.com/paper/1301.7745/) (2013)
- [The Randomized Dependence Coefficient](https://mlsanity.com/paper/1304.7717/) (2013)
- [Differentially Private Quantiles](https://mlsanity.com/paper/2102.08244/) (2021)
- [Measuring dependence powerfully and equitably](https://mlsanity.com/paper/1505.02213/) (2015)
- [PAPRIKA: Private Online False Discovery Rate Control](https://mlsanity.com/paper/2002.12321/) (2020)
- [Equitability, interval estimation, and statistical power](https://mlsanity.com/paper/1505.02212/) (2015)
- [Consistency of the Maximal Information Coefficient Estimator](https://mlsanity.com/paper/2107.03836/) (2021)

## Abstract (arXiv)

The Maximal Information Coefficient (MIC) is a powerful statistic to identify dependencies between variables. However, it may be applied to sensitive data, and publishing it could leak private information. As a solution, we present algorithms to approximate MIC in a way that provides differential privacy. We show that the natural application of the classic Laplace mechanism yields insufficient accuracy. We therefore introduce the MICr statistic, which is a new MIC approximation that is more compatible with differential privacy. We prove MICr is a consistent estimator for MIC, and we provide two differentially private versions of it. We perform experiments on a variety of real and synthetic datasets. The results show that the private MICr statistics significantly outperform direct application of the Laplace mechanism. Moreover, experiments on real-world datasets show accuracy that is usable when the sample size is at least moderately large.