Revisiting differentially private linear regression: optimal and adaptive prediction & estimation in unbounded domain

Yu-Xiang Wang
Proceedings of the 34th Conference on Uncertainty in Artificial Intelligence, PMLR R16:92-102, 2018.

Abstract

We revisit the problem of linear regression un- der a differential privacy constraint. By con- solidating existing pieces in the literature, we clarify the correct dependence of the feature, la- bel and coefficient domains in the optimization error and estimation error, hence revealing the delicate price of differential privacy in statis- tical estimation and statistical learning. More- over, we propose simple modifications of two existing DP algorithms: (a) posterior sampling, (b) sufficient statistics perturbation, and show that they can be upgraded into adaptive algo- rithms that are able to exploit data-dependent quantities and behave nearly optimally for every instance. Extensive experiments are conducted on both simulated data and real data, which conclude that both ADAOPS and ADASSP out- perform the existing techniques on nearly all 36 data sets that we test on.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR16-wang18b, title = {Revisiting differentially private linear regression: optimal and adaptive prediction & estimation in unbounded domain}, author = {Wang, Yu-Xiang}, booktitle = {Proceedings of the 34th Conference on Uncertainty in Artificial Intelligence}, pages = {92--102}, year = {2018}, editor = {Globerson, Amir and Silva, Ricardo}, volume = {R16}, series = {Proceedings of Machine Learning Research}, month = {06--10 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r16/main/assets/wang18b/wang18b.pdf}, url = {https://proceedings.mlr.press/r16/wang18b.html}, abstract = {We revisit the problem of linear regression un- der a differential privacy constraint. By con- solidating existing pieces in the literature, we clarify the correct dependence of the feature, la- bel and coefficient domains in the optimization error and estimation error, hence revealing the delicate price of differential privacy in statis- tical estimation and statistical learning. More- over, we propose simple modifications of two existing DP algorithms: (a) posterior sampling, (b) sufficient statistics perturbation, and show that they can be upgraded into adaptive algo- rithms that are able to exploit data-dependent quantities and behave nearly optimally for every instance. Extensive experiments are conducted on both simulated data and real data, which conclude that both ADAOPS and ADASSP out- perform the existing techniques on nearly all 36 data sets that we test on.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Revisiting differentially private linear regression: optimal and adaptive prediction & estimation in unbounded domain %A Yu-Xiang Wang %B Proceedings of the 34th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2018 %E Amir Globerson %E Ricardo Silva %F pmlr-vR16-wang18b %I PMLR %P 92--102 %U https://proceedings.mlr.press/r16/wang18b.html %V R16 %X We revisit the problem of linear regression un- der a differential privacy constraint. By con- solidating existing pieces in the literature, we clarify the correct dependence of the feature, la- bel and coefficient domains in the optimization error and estimation error, hence revealing the delicate price of differential privacy in statis- tical estimation and statistical learning. More- over, we propose simple modifications of two existing DP algorithms: (a) posterior sampling, (b) sufficient statistics perturbation, and show that they can be upgraded into adaptive algo- rithms that are able to exploit data-dependent quantities and behave nearly optimally for every instance. Extensive experiments are conducted on both simulated data and real data, which conclude that both ADAOPS and ADASSP out- perform the existing techniques on nearly all 36 data sets that we test on. %Z Reissued by PMLR on 04 October 2026.
APA
Wang, Y.. (2018). Revisiting differentially private linear regression: optimal and adaptive prediction & estimation in unbounded domain. Proceedings of the 34th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R16:92-102 Available from https://proceedings.mlr.press/r16/wang18b.html. Reissued by PMLR on 04 October 2026.

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