Differentially Private Analysis for Binary Response Models: Optimality, Estimation, and Inference

Ce Zhang, Yixin Han, Yafei Wang, Xiaodong Yan, Linglong Kong, Ting Li, Bei Jiang
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:74923-74937, 2025.

Abstract

Randomized response (RR) mechanisms constitute a fundamental and effective technique for ensuring label differential privacy (LabelDP). However, existing RR methods primarily focus on the response labels while overlooking the influence of covariates and often do not fully address optimality. To address these challenges, this paper explores optimal LabelDP procedures using RR mechanisms, focusing on achieving optimal estimation and inference in binary response models. We first analyze the asymptotic behaviors of RR binary response models and then optimize the procedure by maximizing the trace of the Fisher Information Matrix within the $\varepsilon$- and $(\varepsilon,\delta)$-LabelDP constraints. Our theoretical results indicate that the proposed methods achieve optimal LabelDP guarantees while maintaining statistical accuracy in binary response models under mild conditions. Furthermore, we develop private confidence intervals with nominal coverage for statistical inference. Extensive simulation studies and real-world applications confirm that our methods outperform existing approaches in terms of precise estimation, privacy protection, and reliable inference.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-zhang25x, title = {Differentially Private Analysis for Binary Response Models: Optimality, Estimation, and Inference}, author = {Zhang, Ce and Han, Yixin and Wang, Yafei and Yan, Xiaodong and Kong, Linglong and Li, Ting and Jiang, Bei}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {74923--74937}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/zhang25x/zhang25x.pdf}, url = {https://proceedings.mlr.press/v267/zhang25x.html}, abstract = {Randomized response (RR) mechanisms constitute a fundamental and effective technique for ensuring label differential privacy (LabelDP). However, existing RR methods primarily focus on the response labels while overlooking the influence of covariates and often do not fully address optimality. To address these challenges, this paper explores optimal LabelDP procedures using RR mechanisms, focusing on achieving optimal estimation and inference in binary response models. We first analyze the asymptotic behaviors of RR binary response models and then optimize the procedure by maximizing the trace of the Fisher Information Matrix within the $\varepsilon$- and $(\varepsilon,\delta)$-LabelDP constraints. Our theoretical results indicate that the proposed methods achieve optimal LabelDP guarantees while maintaining statistical accuracy in binary response models under mild conditions. Furthermore, we develop private confidence intervals with nominal coverage for statistical inference. Extensive simulation studies and real-world applications confirm that our methods outperform existing approaches in terms of precise estimation, privacy protection, and reliable inference.} }
Endnote
%0 Conference Paper %T Differentially Private Analysis for Binary Response Models: Optimality, Estimation, and Inference %A Ce Zhang %A Yixin Han %A Yafei Wang %A Xiaodong Yan %A Linglong Kong %A Ting Li %A Bei Jiang %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-zhang25x %I PMLR %P 74923--74937 %U https://proceedings.mlr.press/v267/zhang25x.html %V 267 %X Randomized response (RR) mechanisms constitute a fundamental and effective technique for ensuring label differential privacy (LabelDP). However, existing RR methods primarily focus on the response labels while overlooking the influence of covariates and often do not fully address optimality. To address these challenges, this paper explores optimal LabelDP procedures using RR mechanisms, focusing on achieving optimal estimation and inference in binary response models. We first analyze the asymptotic behaviors of RR binary response models and then optimize the procedure by maximizing the trace of the Fisher Information Matrix within the $\varepsilon$- and $(\varepsilon,\delta)$-LabelDP constraints. Our theoretical results indicate that the proposed methods achieve optimal LabelDP guarantees while maintaining statistical accuracy in binary response models under mild conditions. Furthermore, we develop private confidence intervals with nominal coverage for statistical inference. Extensive simulation studies and real-world applications confirm that our methods outperform existing approaches in terms of precise estimation, privacy protection, and reliable inference.
APA
Zhang, C., Han, Y., Wang, Y., Yan, X., Kong, L., Li, T. & Jiang, B.. (2025). Differentially Private Analysis for Binary Response Models: Optimality, Estimation, and Inference. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:74923-74937 Available from https://proceedings.mlr.press/v267/zhang25x.html.

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