Privacy utility trade offs for parameter estimation in degree heterogeneous higher order networks

TL;DR

This paper investigates the fundamental limits of estimating parameters in degree-heterogeneous higher-order networks under privacy constraints, providing optimal estimators and finite sample bounds for privacy-utility trade-offs.

Contribution

It offers the first comprehensive finite sample analysis of privacy-utility trade-offs for parameter estimation in $eta$ models and hypergraph extensions, with optimal estimators under differential privacy.

Findings

Finite sample minimax bounds derived for privacy-utility trade-offs.

Proposed estimators achieve bounds up to constants and logarithmic factors.

Experimental validation on synthetic and real-world data demonstrates effectiveness.

Abstract

In sensitive applications involving relational datasets, protecting information about individual links from adversarial queries is of paramount importance. In many such settings, the available data are summarized solely through the degrees of the nodes in the network. We adopt the $\beta$ model, which is the prototypical statistical model adopted for this form of aggregated relational information, and study the problem of minimax-optimal parameter estimation under both local and central differential privacy constraints. We establish finite sample minimax lower bounds that characterize the precise dependence of the estimation risk on the network size and the privacy parameters, and we propose simple estimators that achieve these bounds up to constants and logarithmic factors under both local and central differential privacy frameworks. Our results provide the first comprehensive finite sample characterization of privacy utility trade offs for parameter estimation in $\beta$ models, addressing the classical graph case and extending the analysis to higher order hypergraph models. We further demonstrate the effectiveness of our methods through experiments on synthetic data and a real world communication network.