Revealing network structure, confidentially: improved rates for node-private graphon estimation
Files
Accepted manuscript
Date
2018-01-01
Authors
Borgs, Christian
Chayes, Jennifer
Smith, Adam
Zadik, Ilias
Version
Accepted manuscript
OA Version
Citation
Christian Borgs, Jennifer Chayes, Adam Smith, Ilias Zadik. 2018. "Revealing Network Structure, Confidentially: Improved Rates for Node-Private Graphon Estimation." 2018 IEEE 59TH ANNUAL SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE (FOCS). 59th IEEE Annual Symposium on Foundations of Computer Science (FOCS). Paris, FRANCE, 2018-10-07 - 2018-10-09. https://doi.org/10.1109/FOCS.2018.00057
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 [15], reducing their error quadratically and matching, in many regimes, the optimal nonprivate algorithm [37]. 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 1/ε 2 n 3 instead of 1/ε 2 n 2 . This result uses a new extension lemma for differentially private algorithms that we hope will be broadly useful.