INSPECTRE: Privately Estimating the Unseen

TL;DR

This paper introduces differentially private methods for estimating distributional properties like support size and entropy, demonstrating that privacy costs are often negligible and providing tight bounds on sample complexity.

Contribution

It develops new privacy-preserving estimation techniques for distributional functionals with tight sample complexity bounds and minimal privacy costs.

Findings

Almost-tight bounds on sample size for private estimation

Privacy cost is negligible in many settings

Methods are based on sensitivity analysis of existing estimators

Abstract

We develop differentially private methods for estimating various distributional properties. Given a sample from a discrete distribution $p$, some functional $f$, and accuracy and privacy parameters $\alpha$ and $\varepsilon$, the goal is to estimate $f(p)$ up to accuracy $\alpha$, while maintaining $\varepsilon$-differential privacy of the sample. We prove almost-tight bounds on the sample size required for this problem for several functionals of interest, including support size, support coverage, and entropy. We show that the cost of privacy is negligible in a variety of settings, both theoretically and experimentally. Our methods are based on a sensitivity analysis of several state-of-the-art methods for estimating these properties with sublinear sample complexities.