Differentially Private Quantiles

Abstract

Quantiles are often used for summarizing and understanding data. If that data is sensitive, it may be necessary to compute quantiles in a way that is differentially private, providing theoretical guarantees that the result does not reveal private information. However, when multiple quantiles are needed, existing differentially private algorithms fare poorly: they either compute quantiles individually, splitting the privacy budget, or summarize the entire distribution, wasting effort. In either case the result is reduced accuracy. In this work we propose an instance of the exponential mechanism that simultaneously estimates exactly $m$ quantiles from $n$ data points while guaranteeing differential privacy. The utility function is carefully structured to allow for an efficient implementation that returns estimates of all $m$ quantiles in time $O(mn\log (n)+m^{2}n)$. Experiments show that our method significantly outperforms the current state of the art on both real and synthetic data while remaining efficient enough to be practical.

arXiv commentThis version corrects pseudocode typos and adds a note about perturbing data

References in corpus (5)

• Graphical-model based estimation and inference for differential privacy
• A Primer on Private Statistics
• Optimal Differential Privacy Composition for Exponential Mechanisms and the Cost of Adaptivity
• Optimal Private Median Estimation under Minimal Distributional Assumptions
• Duff: A Dataset-Distance-Based Utility Function Family for the Exponential Mechanism