Improving the Variance of Differentially Private Randomized Experiments through Clustering

TL;DR

This paper introduces Cluster-DP, a new differentially private mechanism that uses data clustering to reduce variance in causal effect estimation, balancing privacy and accuracy more effectively.

Contribution

The paper proposes Cluster-DP, a novel privacy mechanism leveraging data clustering to improve the privacy-variance trade-off in causal analysis.

Findings

Cluster-DP reduces variance compared to baseline methods.

Higher-quality clusters lead to better privacy-variance trade-offs.

Theoretical and empirical evaluations confirm the effectiveness of Cluster-DP.

Abstract

Estimating causal effects from randomized experiments is only possible if participants are willing to disclose their potentially sensitive responses. Differential privacy, a widely used framework for ensuring an algorithms privacy guarantees, can encourage participants to share their responses without the risk of de-anonymization. However, many mechanisms achieve differential privacy by adding noise to the original dataset, which reduces the precision of causal effect estimation. This introduces a fundamental trade-off between privacy and variance when performing causal analyses on differentially private data. In this work, we propose a new differentially private mechanism, "Cluster-DP", which leverages a given cluster structure in the data to improve the privacy-variance trade-off. While our results apply to any clustering, we demonstrate that selecting higher-quality clusters, according to a quality metric we introduce, can decrease the variance penalty without compromising privacy guarantees. Finally, we evaluate the theoretical and empirical performance of our Cluster-DP algorithm on both real and simulated data, comparing it to common baselines, including two special cases of our algorithm: its unclustered version and a uniform-prior version.