Differentially Private Approximate Quantiles

In this work we study the problem of differentially private (DP) quantiles, in which given dataset X and quantiles q1, ..., qm ∈ [0, 1], we want to output m quantile estimations which are as close as possible to the true quantiles and preserve DP. We describe a simple recursive DP algorithm, which we call ApproximateQuantiles (AQ), for this task. We give a worst case upper bound on its error, and show that its error is much lower than of previous implementations on several different datasets. Furthermore, it gets this low error while running time two orders of magnitude faster that the best previous implementation.

[1]  Moni Naor,et al.  Differential privacy under continual observation , 2010, STOC '10.

[2]  Moni Naor,et al.  Our Data, Ourselves: Privacy Via Distributed Noise Generation , 2006, EUROCRYPT.

[3]  Ryan M. Rogers,et al.  Optimal Differential Privacy Composition for Exponential Mechanisms , 2020, ICML.

[4]  Elaine Shi,et al.  Private and Continual Release of Statistics , 2010, TSEC.

[5]  Kobbi Nissim,et al.  Differentially Private Release and Learning of Threshold Functions , 2015, 2015 IEEE 56th Annual Symposium on Foundations of Computer Science.

[6]  Alex Kulesza,et al.  Differentially Private Quantiles , 2021, ICML.

[7]  Haim Kaplan,et al.  Privately Learning Thresholds: Closing the Exponential Gap , 2019, COLT.

[8]  Amos Beimel,et al.  Private Learning and Sanitization: Pure vs. Approximate Differential Privacy , 2013, APPROX-RANDOM.

[9]  Aaron Roth,et al.  The Algorithmic Foundations of Differential Privacy , 2014, Found. Trends Theor. Comput. Sci..

[10]  Kunal Talwar,et al.  Mechanism Design via Differential Privacy , 2007, 48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07).

[11]  Thomas Steinke,et al.  Concentrated Differential Privacy: Simplifications, Extensions, and Lower Bounds , 2016, TCC.

[12]  Adam D. Smith,et al.  Privacy-preserving statistical estimation with optimal convergence rates , 2011, STOC '11.

[13]  Cynthia Dwork,et al.  Calibrating Noise to Sensitivity in Private Data Analysis , 2006, TCC.

[14]  Guy N. Rothblum,et al.  Boosting and Differential Privacy , 2010, 2010 IEEE 51st Annual Symposium on Foundations of Computer Science.