Differentially Private Maximal Information Coefficients

TL;DR

This paper introduces a differentially private approximation of the Maximal Information Coefficient (MIC), called MICr, which improves accuracy over traditional methods and is practical for real-world datasets with sufficient sample sizes.

Contribution

The paper proposes MICr, a novel MIC approximation compatible with differential privacy, along with two private algorithms and theoretical guarantees of consistency.

Findings

MICr outperforms the Laplace mechanism in accuracy

Private MICr is effective on real and synthetic datasets

Usable accuracy achieved with moderately large sample sizes

Abstract

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.