Private Protocols for U-Statistics in the Local Model and Beyond

James Bell*, Aurelien Bellet, Adria Gascon, Tejas Kulkarni

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review

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Abstract

In this paper, we study the problem of computing U-statistics of degree 2, i.e., quantities that come in the form of averages over pairs of data points, in the local model of differential privacy (LDP). The class of U-statistics covers many statistical estimates of interest, including Gini mean difference, Kendall's tau coefficient and Area under the ROC Curve (AUC), as well as empirical risk measures for machine learning problems such as ranking, clustering and metric learning. We first introduce an LDP protocol based on quantizing the data into bins and applying randomized response, which guarantees an epsilon-LDP estimate with a Mean Squared Error (MSE) of O(1/root n epsilon) under regularity assumptions on the U-statistic or the data distribution. We then propose a specialized protocol for AUC based on a novel use of hierarchical histograms that achieves MSE of O (alpha(3)/n epsilon(2)) for arbitrary data distribution. We also show that 2-party secure computation allows to design a protocol with MSE of O(1/n epsilon(2)), without any assumption on the kernel function or data distribution and with total communication linear in the number of users n. Finally, we evaluate the performance of our protocols through experiments on synthetic and real datasets.

Original languageEnglish
Title of host publicationINTERNATIONAL CONFERENCE ON ARTIFICIAL INTELLIGENCE AND STATISTICS, VOL 108
EditorsS Chiappa, R Calandra
PublisherADDISON-WESLEY
Pages1573-1582
Number of pages10
Publication statusPublished - 2020
MoE publication typeA4 Article in a conference publication
EventInternational Conference on Artificial Intelligence and Statistics - Palermo, Italy
Duration: 3 Jun 20205 Jun 2020
Conference number: 23

Publication series

NameProceedings of Machine Learning Research
PublisherADDISON-WESLEY PUBL CO
Volume108
ISSN (Print)2640-3498

Conference

ConferenceInternational Conference on Artificial Intelligence and Statistics
Abbreviated titleAISTATS
CountryItaly
CityPalermo
Period03/06/202005/06/2020

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