Private frequency estimation via projective geometry

Vitaly Feldman, Jelani Nelson, Huy Nguyen, Kunal Talwar
Proceedings of the 39th International Conference on Machine Learning, PMLR 162:6418-6433, 2022.

Abstract

In this work, we propose a new algorithm ProjectiveGeometryResponse (PGR) for locally differentially private (LDP) frequency estimation. For universe size of k and with n users, our eps-LDP algorithm has communication cost ceil(log_2 k) and computation cost O(n + k\exp(eps) log k) for the server to approximately reconstruct the frequency histogram, while achieve optimal privacy-utility tradeoff. In many practical settings this is a significant improvement over the O (n+k^2) computation cost that is achieved by the recent PI-RAPPOR algorithm (Feldman and Talwar; 2021). Our empirical evaluation shows a speedup of over 50x over PI-RAPPOR while using approximately 75x less memory. In addition, the running time of our algorithm is comparable to that of HadamardResponse (Acharya, Sun, and Zhang; 2019) and RecursiveHadamardResponse (Chen, Kairouz, and Ozgur; 2020) which have significantly worse reconstruction error. The error of our algorithm essentially matches that of the communication- and time-inefficient but utility-optimal SubsetSelection (SS) algorithm (Ye and Barg; 2017). Our new algorithm is based on using Projective Planes over a finite field to define a small collection of sets that are close to being pairwise independent and a dynamic programming algorithm for approximate histogram reconstruction for the server.

Cite this Paper

BibTeX
@InProceedings{pmlr-v162-feldman22a, title = {Private frequency estimation via projective geometry}, author = {Feldman, Vitaly and Nelson, Jelani and Nguyen, Huy and Talwar, Kunal}, booktitle = {Proceedings of the 39th International Conference on Machine Learning}, pages = {6418--6433}, year = {2022}, editor = {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan}, volume = {162}, series = {Proceedings of Machine Learning Research}, month = {17--23 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v162/feldman22a/feldman22a.pdf}, url = {https://proceedings.mlr.press/v162/feldman22a.html}, abstract = {In this work, we propose a new algorithm ProjectiveGeometryResponse (PGR) for locally differentially private (LDP) frequency estimation. For universe size of k and with n users, our eps-LDP algorithm has communication cost ceil(log_2 k) and computation cost O(n + k\exp(eps) log k) for the server to approximately reconstruct the frequency histogram, while achieve optimal privacy-utility tradeoff. In many practical settings this is a significant improvement over the O (n+k^2) computation cost that is achieved by the recent PI-RAPPOR algorithm (Feldman and Talwar; 2021). Our empirical evaluation shows a speedup of over 50x over PI-RAPPOR while using approximately 75x less memory. In addition, the running time of our algorithm is comparable to that of HadamardResponse (Acharya, Sun, and Zhang; 2019) and RecursiveHadamardResponse (Chen, Kairouz, and Ozgur; 2020) which have significantly worse reconstruction error. The error of our algorithm essentially matches that of the communication- and time-inefficient but utility-optimal SubsetSelection (SS) algorithm (Ye and Barg; 2017). Our new algorithm is based on using Projective Planes over a finite field to define a small collection of sets that are close to being pairwise independent and a dynamic programming algorithm for approximate histogram reconstruction for the server.} }
Endnote
%0 Conference Paper %T Private frequency estimation via projective geometry %A Vitaly Feldman %A Jelani Nelson %A Huy Nguyen %A Kunal Talwar %B Proceedings of the 39th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2022 %E Kamalika Chaudhuri %E Stefanie Jegelka %E Le Song %E Csaba Szepesvari %E Gang Niu %E Sivan Sabato %F pmlr-v162-feldman22a %I PMLR %P 6418--6433 %U https://proceedings.mlr.press/v162/feldman22a.html %V 162 %X In this work, we propose a new algorithm ProjectiveGeometryResponse (PGR) for locally differentially private (LDP) frequency estimation. For universe size of k and with n users, our eps-LDP algorithm has communication cost ceil(log_2 k) and computation cost O(n + k\exp(eps) log k) for the server to approximately reconstruct the frequency histogram, while achieve optimal privacy-utility tradeoff. In many practical settings this is a significant improvement over the O (n+k^2) computation cost that is achieved by the recent PI-RAPPOR algorithm (Feldman and Talwar; 2021). Our empirical evaluation shows a speedup of over 50x over PI-RAPPOR while using approximately 75x less memory. In addition, the running time of our algorithm is comparable to that of HadamardResponse (Acharya, Sun, and Zhang; 2019) and RecursiveHadamardResponse (Chen, Kairouz, and Ozgur; 2020) which have significantly worse reconstruction error. The error of our algorithm essentially matches that of the communication- and time-inefficient but utility-optimal SubsetSelection (SS) algorithm (Ye and Barg; 2017). Our new algorithm is based on using Projective Planes over a finite field to define a small collection of sets that are close to being pairwise independent and a dynamic programming algorithm for approximate histogram reconstruction for the server.
APA
Feldman, V., Nelson, J., Nguyen, H. & Talwar, K.. (2022). Private frequency estimation via projective geometry. Proceedings of the 39th International Conference on Machine Learning, in Proceedings of Machine Learning Research 162:6418-6433 Available from https://proceedings.mlr.press/v162/feldman22a.html.

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