Revealing Network Structure, Confidentially: Improved Rates for Node-Private Graphon Estimation
This addresses privacy concerns in social network analysis by providing improved algorithms for node-private graph estimation, though it is incremental as it builds on prior work with specific enhancements.
The paper tackles the problem of estimating network models like stochastic block models and graphons under node-differential privacy, achieving algorithms that reduce error quadratically compared to prior work and match optimal non-private rates in many regimes, with specific convergence rates such as 1/(ε^2 n^3) for simple models.
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 $\frac{1}{ε^2 n^{3}}$ instead of $\frac{1}{ε^2 n^2}$. This result uses a new extension lemma for differentially private algorithms that we hope will be broadly useful.