The paper “Edge Differentially Private Estimation in the β-Model via Jittering and Method of Moments”, co-authored by Prof. Jinyuan Chang and his doctoral student Qiao Hu from the Joint Laboratory of Data Science and Business Intelligence at Southwestern University of Finance and Economics, Prof. Eric D. Kolaczyk from McGill University (Canada), Prof. Qiwei Yao from the London School of Economics and Political Science (UK), and Assistant Prof. Fengting Yi from Yunnan University, has been officially accepted by the Annals of Statistics, one of the world’s leading journals in the field of statistics.
Abstract
In the field of data privacy protection, there has long been a challenge – how to improve the efficiency of statistical inference while maintaining privacy levels. This article considers adding noise to network data that follows the β model based on jitter mechanism, and then using the newly obtained noise data to estimate and statistically infer the parameters in the original β model. Unlike the traditional method of estimating parameters through maximum likelihood, we propose a moment estimation method. This method enables us to estimate the parameters in the β model under stricter privacy levels, thereby enhancing data privacy in practical applications. The parameter estimator proposed in this article has phase transition characteristics – its convergence speed and asymptotic variance will follow three different rules depending on the difference in privacy level. Considering the difficulty in determining data privacy levels in practice, we propose a novel adaptive bootstrap method for statistical inference of parameters at different privacy levels. Based on this method, we can simultaneously perform statistical inference on all parameters (i.e. the number of nodes in the network) in the β model. Numerical experiments show that our proposed inference method performs similarly to the maximum likelihood method in limited samples, and has significant advantages in computational speed and memory consumption.
Author Introduction
Jinyuan Chang is the Executive Director of the Joint Laboratory of Data Science and Business Intelligence at Southwestern University of Finance and Economics. He is a Guanghua Distinguished Professor and a recipient of the National Science Fund for Distinguished Young Scholars of China. His primary research interests include ultra-high dimensional data analysis and high-frequency financial data analysis.
Qiao Hu is a doctoral student in statistics at the School of Statistics, Southwestern University of Finance and Economics, under the supervision of Professor Jinyuan Chang. His research focuses on high-dimensional time series analysis, empirical likelihood, and network data analysis.
Eric D. Kolaczyk is a Professor at McGill University in Canada. His research spans dynamic network modeling, machine learning, and artificial intelligence.
Qiwei Yao is a Chair Professor at the London School of Economics. His research interests include time series analysis, dimensionality reduction, factor modeling, dynamic network modeling, spatiotemporal modeling, financial econometrics, and nonparametric regression.
Fengting Yi is an Assistant Professor at Yunnan University. Her work focuses on longitudinal data analysis, survival data analysis, and network data analysis.
