Differentially private ratio statistics

TL;DR

This paper develops methods for differentially private ratio statistics, such as relative risk and odds ratios, ensuring privacy while maintaining accuracy and providing confidence intervals, addressing a significant gap in privacy-preserving statistical analysis.

Contribution

It introduces new differentially private estimators for ratio statistics, analyzes their properties, and offers practical tools for private hypothesis testing and decision-making.

Findings

Simple algorithms achieve good privacy, accuracy, and bias at small sample sizes.

The private estimator for relative risk is consistent.

Method for constructing valid confidence intervals under differential privacy.

Abstract

Ratio statistics--such as relative risk and odds ratios--play a central role in hypothesis testing, model evaluation, and decision-making across many areas of machine learning, including causal inference and fairness analysis. However, despite privacy concerns surrounding many datasets and despite increasing adoption of differential privacy, differentially private ratio statistics have largely been neglected by the literature and have only recently received an initial treatment by Lin et al. [1]. This paper attempts to fill this lacuna, giving results that can guide practice in evaluating ratios when the results must be protected by differential privacy. In particular, we show that even a simple algorithm can provide excellent properties concerning privacy, sample accuracy, and bias, not just asymptotically but also at quite small sample sizes. Additionally, we analyze a differentially private estimator for relative risk, prove its consistency, and develop a method for constructing valid confidence intervals. Our approach bridges a gap in the differential privacy literature and provides a practical solution for ratio estimation in private machine learning pipelines.