The Adverse Effects of Omitting Records in Differential Privacy: How Sampling and Suppression Degrade the Privacy--Utility Tradeoff (Long Version)

Abstract

Sampling is renowned for its privacy amplification in differential privacy (DP), and is often assumed to improve the utility of a DP mechanism by allowing a noise reduction. In this paper, we further show that this last assumption is flawed: When measuring utility at equal privacy levels, sampling as preprocessing consistently yields penalties due to utility loss from omitting records over all canonical DP mechanisms -- Laplace, Gaussian, exponential, and report noisy max -- , as well as recent applications of sampling, such as clustering. Extending this analysis, we investigate suppression as a generalized method of choosing, or omitting, records. Developing a theoretical analysis of this technique, we derive privacy bounds for arbitrary suppression strategies under unbounded approximate DP. We find that our tested suppression strategy also fails to improve the privacy--utility tradeoff. Surprisingly, uniform sampling emerges as one of the best suppression methods -- despite its still degrading effect. Our results call into question common preprocessing assumptions in DP practice.