Edge differentially private estimation in the β-model via jittering and method of moments

Chang, Jinyuan, Hu, Qiao, Kolaczyk, Eric D., Yao, Qiwei ORCID: 0000-0003-2065-8486 and Yi, Fengting (2024) Edge differentially private estimation in the β-model via jittering and method of moments. Annals of Statistics. ISSN 0090-5364 (In Press)

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Abstract

A standing challenge in data privacy is the trade-off between the level of privacy and the efficiency of statistical inference. Here we conduct an in-depth study of this trade-off for parameter estimation in the β-model (Chatterjee, Diaconis and Sly, 2011) for edge differentially private network data re-leased via jittering (Karwa, Krivitsky and Slavkovi´c, 2017). Unlike most previous approaches based on maximum likelihood estimation for this network model, we proceed via method of moments. This choice facilitates our exploration of a substantially broader range of privacy levels – corresponding to stricter privacy – than has been to date. Over this new range we discover our proposed estimator for the parameters exhibits an interesting phase transition, with both its convergence rate and asymptotic variance following one of three different regimes of behavior depending on the level of privacy. Because identification of the operable regime is difficult to impossible in practice, we devise a novel adaptive bootstrap procedure to construct uniform inference across different phases. In fact, leveraging this bootstrap we are able to provide for simultaneous inference of all parameters in the β-model (i.e., equal to the number of vertices), which would appear to be the first result of its kind. Numerical experiments confirm the competitive and reliable finite sample performance of the proposed inference methods, next to a comparable maximum likelihood method, as well as significant advantages in terms of computational speed and memory.

Item Type:	Article
Additional Information:	© 2024 Institute of Mathematical Statistics
Divisions:	Statistics
Subjects:	H Social Sciences > HA Statistics
Date Deposited:	23 Feb 2024 17:12
Last Modified:	25 Apr 2024 09:33
URI:	http://eprints.lse.ac.uk/id/eprint/122099

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