Revealing Network Structure, Confidentially: Improved Rates for Node-Private Graphon Estimation

TL;DR

This paper introduces improved node-private algorithms for estimating complex network models like graphons, achieving near-optimal accuracy and revealing insights into privacy-accuracy trade-offs in social network analysis.

Contribution

The authors develop new algorithms for node-differentially private estimation of network models, reducing error rates and extending the applicability of privacy-preserving network analysis.

Findings

Algorithms achieve quadratic error reduction over prior work.

Node-private algorithms are more accurate for simple random graph models.

New extension lemma for differentially private algorithms enhances analysis.

Abstract

Motivated by growing concerns over ensuring privacy on social networks, we develop new algorithms and impossibility results for fitting complex statistical models to network data subject to rigorous privacy guarantees. We consider the so-called node-differentially private algorithms, which compute information about a graph or network while provably revealing almost no information about the presence or absence of a particular node in the graph. We provide new algorithms for node-differentially private estimation for a popular and expressive family of network models: stochastic block models and their generalization, graphons. Our algorithms improve on prior work, reducing their error quadratically and matching, in many regimes, the optimal nonprivate algorithm. We also show that for the simplest random graph models ($G(n,p)$ and $G(n,m)$), node-private algorithms can be qualitatively more accurate than for more complex models---converging at a rate of $\frac{1}{\epsilon^2 n^{3}}$ instead of $\frac{1}{\epsilon^2 n^2}$. This result uses a new extension lemma for differentially private algorithms that we hope will be broadly useful.