Differentially Private Bayesian Inference for Generalized Linear Models

Tejas Kulkarni, Joonas Jälkö, Antti Koskela, Samuel Kaski, Antti Honkela
Proceedings of the 38th International Conference on Machine Learning, PMLR 139:5838-5849, 2021.

Abstract

Generalized linear models (GLMs) such as logistic regression are among the most widely used arms in data analyst’s repertoire and often used on sensitive datasets. A large body of prior works that investigate GLMs under differential privacy (DP) constraints provide only private point estimates of the regression coefficients, and are not able to quantify parameter uncertainty. In this work, with logistic and Poisson regression as running examples, we introduce a generic noise-aware DP Bayesian inference method for a GLM at hand, given a noisy sum of summary statistics. Quantifying uncertainty allows us to determine which of the regression coefficients are statistically significantly different from zero. We provide a previously unknown tight privacy analysis and experimentally demonstrate that the posteriors obtained from our model, while adhering to strong privacy guarantees, are close to the non-private posteriors.

Cite this Paper

BibTeX
@InProceedings{pmlr-v139-kulkarni21a, title = {Differentially Private Bayesian Inference for Generalized Linear Models}, author = {Kulkarni, Tejas and J{\"a}lk{\"o}, Joonas and Koskela, Antti and Kaski, Samuel and Honkela, Antti}, booktitle = {Proceedings of the 38th International Conference on Machine Learning}, pages = {5838--5849}, year = {2021}, editor = {Meila, Marina and Zhang, Tong}, volume = {139}, series = {Proceedings of Machine Learning Research}, month = {18--24 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v139/kulkarni21a/kulkarni21a.pdf}, url = {https://proceedings.mlr.press/v139/kulkarni21a.html}, abstract = {Generalized linear models (GLMs) such as logistic regression are among the most widely used arms in data analyst’s repertoire and often used on sensitive datasets. A large body of prior works that investigate GLMs under differential privacy (DP) constraints provide only private point estimates of the regression coefficients, and are not able to quantify parameter uncertainty. In this work, with logistic and Poisson regression as running examples, we introduce a generic noise-aware DP Bayesian inference method for a GLM at hand, given a noisy sum of summary statistics. Quantifying uncertainty allows us to determine which of the regression coefficients are statistically significantly different from zero. We provide a previously unknown tight privacy analysis and experimentally demonstrate that the posteriors obtained from our model, while adhering to strong privacy guarantees, are close to the non-private posteriors.} }
Endnote
%0 Conference Paper %T Differentially Private Bayesian Inference for Generalized Linear Models %A Tejas Kulkarni %A Joonas Jälkö %A Antti Koskela %A Samuel Kaski %A Antti Honkela %B Proceedings of the 38th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2021 %E Marina Meila %E Tong Zhang %F pmlr-v139-kulkarni21a %I PMLR %P 5838--5849 %U https://proceedings.mlr.press/v139/kulkarni21a.html %V 139 %X Generalized linear models (GLMs) such as logistic regression are among the most widely used arms in data analyst’s repertoire and often used on sensitive datasets. A large body of prior works that investigate GLMs under differential privacy (DP) constraints provide only private point estimates of the regression coefficients, and are not able to quantify parameter uncertainty. In this work, with logistic and Poisson regression as running examples, we introduce a generic noise-aware DP Bayesian inference method for a GLM at hand, given a noisy sum of summary statistics. Quantifying uncertainty allows us to determine which of the regression coefficients are statistically significantly different from zero. We provide a previously unknown tight privacy analysis and experimentally demonstrate that the posteriors obtained from our model, while adhering to strong privacy guarantees, are close to the non-private posteriors.
APA
Kulkarni, T., Jälkö, J., Koskela, A., Kaski, S. & Honkela, A.. (2021). Differentially Private Bayesian Inference for Generalized Linear Models. Proceedings of the 38th International Conference on Machine Learning, in Proceedings of Machine Learning Research 139:5838-5849 Available from https://proceedings.mlr.press/v139/kulkarni21a.html.

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