Differentially Private Maximal Information Coefficients

John Lazarsfeld, Aaron Johnson, Emmanuel Adeniran
Proceedings of the 39th International Conference on Machine Learning, PMLR 162:12126-12163, 2022.

Abstract

The Maximal Information Coefficient (MIC) is a powerful statistic to identify dependencies between variables. However, it may be applied to sensitive data, and publishing it could leak private information. As a solution, we present algorithms to approximate MIC in a way that provides differential privacy. We show that the natural application of the classic Laplace mechanism yields insufficient accuracy. We therefore introduce the MICr statistic, which is a new MIC approximation that is more compatible with differential privacy. We prove MICr is a consistent estimator for MIC, and we provide two differentially private versions of it. We perform experiments on a variety of real and synthetic datasets. The results show that the private MICr statistics significantly outperform direct application of the Laplace mechanism. Moreover, experiments on real-world datasets show accuracy that is usable when the sample size is at least moderately large.

Cite this Paper

BibTeX
@InProceedings{pmlr-v162-lazarsfeld22a, title = {Differentially Private Maximal Information Coefficients}, author = {Lazarsfeld, John and Johnson, Aaron and Adeniran, Emmanuel}, booktitle = {Proceedings of the 39th International Conference on Machine Learning}, pages = {12126--12163}, 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/lazarsfeld22a/lazarsfeld22a.pdf}, url = {https://proceedings.mlr.press/v162/lazarsfeld22a.html}, abstract = {The Maximal Information Coefficient (MIC) is a powerful statistic to identify dependencies between variables. However, it may be applied to sensitive data, and publishing it could leak private information. As a solution, we present algorithms to approximate MIC in a way that provides differential privacy. We show that the natural application of the classic Laplace mechanism yields insufficient accuracy. We therefore introduce the MICr statistic, which is a new MIC approximation that is more compatible with differential privacy. We prove MICr is a consistent estimator for MIC, and we provide two differentially private versions of it. We perform experiments on a variety of real and synthetic datasets. The results show that the private MICr statistics significantly outperform direct application of the Laplace mechanism. Moreover, experiments on real-world datasets show accuracy that is usable when the sample size is at least moderately large.} }
Endnote
%0 Conference Paper %T Differentially Private Maximal Information Coefficients %A John Lazarsfeld %A Aaron Johnson %A Emmanuel Adeniran %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-lazarsfeld22a %I PMLR %P 12126--12163 %U https://proceedings.mlr.press/v162/lazarsfeld22a.html %V 162 %X The Maximal Information Coefficient (MIC) is a powerful statistic to identify dependencies between variables. However, it may be applied to sensitive data, and publishing it could leak private information. As a solution, we present algorithms to approximate MIC in a way that provides differential privacy. We show that the natural application of the classic Laplace mechanism yields insufficient accuracy. We therefore introduce the MICr statistic, which is a new MIC approximation that is more compatible with differential privacy. We prove MICr is a consistent estimator for MIC, and we provide two differentially private versions of it. We perform experiments on a variety of real and synthetic datasets. The results show that the private MICr statistics significantly outperform direct application of the Laplace mechanism. Moreover, experiments on real-world datasets show accuracy that is usable when the sample size is at least moderately large.
APA
Lazarsfeld, J., Johnson, A. & Adeniran, E.. (2022). Differentially Private Maximal Information Coefficients. Proceedings of the 39th International Conference on Machine Learning, in Proceedings of Machine Learning Research 162:12126-12163 Available from https://proceedings.mlr.press/v162/lazarsfeld22a.html.

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