Statistics and Its Interface

Volume 13 (2020)

Number 3

Asymptotic Theory for Differentially Private Generalized $\beta$-models with Parameters Increasing

Pages: 385 – 398

DOI: https://dx.doi.org/10.4310/SII.2020.v13.n3.a8

Authors

Yifan Fan (Department of Statistics, Central China Normal University, Wuhan, China)

Huiming Zhang (School of Mathematical Sciences and Center for Statistical Science, Peking University, Beijing, China)

Ting Yan (Department of Statistics, Central China Normal University, Wuhan, China)

Abstract

Modelling edge weights play a crucial role in the analysis of network data, which reveals the extent of relationships among individuals. Due to the diversity of weight information, sharing these data has become a complicated challenge in a privacy-preserving way. In this paper, we consider the case of the non-denoising process to achieve the trade-off between privacy and weight information in the generalized β-model. Under the edge differential privacy with a discrete Laplace mechanism, the Z-estimators from estimating equations for the model parameters are shown to be consistent and asymptotically normally distributed. The simulations and a real data example are given to further support the theoretical results.

Keywords

$\beta$-models, Discrete Laplace distribution, Edge differential privacy, Network data, Z-estimators

2010 Mathematics Subject Classification

Primary 62F12. Secondary 05C80, 62E20, 62F10.

Full Text (PDF format)

Yan is partially supported by the National Natural Science Foundation of China (No. 11771171) and the Fundamental Research Funds for the Central Universities (No. CCNU17TS0005). Fan is supported by Fundamental Research Funds for the Central Universities (Innovative Funding Project) (2019CX ZZ071).

Received 16 April 2019

Accepted 21 February 2020

Published 22 April 2020