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

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

*Tämän työn vastaava kirjoittaja

Tutkimustuotos: Artikkeli kirjassa/konferenssijulkaisussaConference contributionScientificvertaisarvioitu

8 Lataukset (Pure)

Abstrakti

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.

AlkuperäiskieliEnglanti
OtsikkoINTERNATIONAL CONFERENCE ON ARTIFICIAL INTELLIGENCE AND STATISTICS, VOL 108
ToimittajatS Chiappa, R Calandra
KustantajaADDISON-WESLEY
Sivut1573-1582
Sivumäärä10
TilaJulkaistu - 2020
OKM-julkaisutyyppiA4 Artikkeli konferenssijulkaisuussa
TapahtumaInternational Conference on Artificial Intelligence and Statistics - Palermo, Italia
Kesto: 3 kesäk. 20205 kesäk. 2020
Konferenssinumero: 23

Julkaisusarja

NimiProceedings of Machine Learning Research
KustantajaADDISON-WESLEY PUBL CO
Vuosikerta108
ISSN (painettu)2640-3498

Conference

ConferenceInternational Conference on Artificial Intelligence and Statistics
LyhennettäAISTATS
Maa/AlueItalia
KaupunkiPalermo
Ajanjakso03/06/202005/06/2020

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