Affiliation weighted networks with a differentially private degree sequence

Affiliation network is one kind of two-mode social network with two different sets of nodes (namely, a set of actors and a set of social events) and edges representing the affiliation of the actors with the social events. The asymptotic theorem of a differentially private estimator of the parameter in the private p0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p_{0}$$\end{document} model has been established. However, the p0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p_{0}$$\end{document} model only focuses on binary edges for one-mode network. In many case, the connections in many affiliation networks (two-mode) could be weighted, taking a set of finite discrete values. In this paper, we derive the consistency and asymptotic normality of the moment estimators of parameters in affiliation finite discrete weighted networks with a differentially private degree sequence. Simulation studies and a real data example demonstrate our theoretical results.