One-bit Submission for Locally Private Quasi-MLE: Its Asymptotic Normality and Limitation

Hajime Ono, Kazuhiro Minami, Hideitsu Hino
Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, PMLR 151:2762-2783, 2022.

Abstract

Local differential privacy (LDP) is an information-theoretic privacy definition suitable for statistical surveys that involve an untrusted data curator. An LDP version of quasi-maximum likelihood estimator (QMLE) has been developed, but the existing method to build LDP QMLE is difficult to implement for a large-scale survey system in the real world due to long waiting time, expensive communication cost, and the boundedness assumption of derivative of a log-likelihood function. We provided alternative LDP protocols without those issues, which are potentially much easily deployable to a large-scale survey. We also provided sufficient conditions for the consistency and asymptotic normality and limitations of our protocol. Our protocol is less burdensome for the users, and the theoretical guarantees cover more realistic cases than those for the existing method.

Cite this Paper

BibTeX
@InProceedings{pmlr-v151-ono22a, title = { One-bit Submission for Locally Private Quasi-MLE: Its Asymptotic Normality and Limitation }, author = {Ono, Hajime and Minami, Kazuhiro and Hino, Hideitsu}, booktitle = {Proceedings of The 25th International Conference on Artificial Intelligence and Statistics}, pages = {2762--2783}, year = {2022}, editor = {Camps-Valls, Gustau and Ruiz, Francisco J. R. and Valera, Isabel}, volume = {151}, series = {Proceedings of Machine Learning Research}, month = {28--30 Mar}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v151/ono22a/ono22a.pdf}, url = {https://proceedings.mlr.press/v151/ono22a.html}, abstract = { Local differential privacy (LDP) is an information-theoretic privacy definition suitable for statistical surveys that involve an untrusted data curator. An LDP version of quasi-maximum likelihood estimator (QMLE) has been developed, but the existing method to build LDP QMLE is difficult to implement for a large-scale survey system in the real world due to long waiting time, expensive communication cost, and the boundedness assumption of derivative of a log-likelihood function. We provided alternative LDP protocols without those issues, which are potentially much easily deployable to a large-scale survey. We also provided sufficient conditions for the consistency and asymptotic normality and limitations of our protocol. Our protocol is less burdensome for the users, and the theoretical guarantees cover more realistic cases than those for the existing method. } }
Endnote
%0 Conference Paper %T One-bit Submission for Locally Private Quasi-MLE: Its Asymptotic Normality and Limitation %A Hajime Ono %A Kazuhiro Minami %A Hideitsu Hino %B Proceedings of The 25th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2022 %E Gustau Camps-Valls %E Francisco J. R. Ruiz %E Isabel Valera %F pmlr-v151-ono22a %I PMLR %P 2762--2783 %U https://proceedings.mlr.press/v151/ono22a.html %V 151 %X Local differential privacy (LDP) is an information-theoretic privacy definition suitable for statistical surveys that involve an untrusted data curator. An LDP version of quasi-maximum likelihood estimator (QMLE) has been developed, but the existing method to build LDP QMLE is difficult to implement for a large-scale survey system in the real world due to long waiting time, expensive communication cost, and the boundedness assumption of derivative of a log-likelihood function. We provided alternative LDP protocols without those issues, which are potentially much easily deployable to a large-scale survey. We also provided sufficient conditions for the consistency and asymptotic normality and limitations of our protocol. Our protocol is less burdensome for the users, and the theoretical guarantees cover more realistic cases than those for the existing method.
APA
Ono, H., Minami, K. & Hino, H.. (2022). One-bit Submission for Locally Private Quasi-MLE: Its Asymptotic Normality and Limitation . Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 151:2762-2783 Available from https://proceedings.mlr.press/v151/ono22a.html.

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