Recently, the paper “Edge differentially private estimation in the β-model via jittering and method of moments”, jointly completed by Professor 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, Professor Eric D. Kolaczyk from McGill University in Canada, Professor Qiwei Yao from the London School of Economics and Political Science in the UK, and Assistant Professor Fengting Yi from Yunnan University, has been officially accepted by the top international academic journal “Annals 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, Executive Director of the Joint Laboratory of Data Science and Business Intelligence at Southwestern University of Finance and Economics, Guanghua Distinguished Professor, and recipient of the National Science Fund for Distinguished Young Scholars of China. Mainly engaged in two research fields: ultra-high dimensional data analysis and high-frequency financial data analysis. Hu Qiao, a 2021 doctoral student majoring in statistics at the School of Statistics, Southwestern University of Finance and Economics, with Professor Jinyuan Chang as his supervisor. Mainly engaged in research in the fields of high-dimensional time series analysis, empirical likelihood, and network data analysis.
Eric D. Kolaczyk, Professor at McGill University in Canada. Mainly engaged in research in the fields of dynamic network modeling, machine learning, and artificial intelligence.
Qiwei Yao, Chair Professor at the London School of Economics. Mainly engaged in research in the fields of time series analysis, dimensionality reduction, factor modeling, dynamic network modeling, spatiotemporal modeling, financial econometrics, and non parametric regression.
Fengting Yi, Assistant Professor at Yunnan University. Mainly engaged in research in the fields of longitudinal data analysis, survival data analysis, network data analysis, etc.
