TY - JOUR

T1 - Private graphon estimation for sparse graphs

AU - Borgs, Christian

AU - Chayes, Jennifer T.

AU - Smith, Adam

N1 - Funding Information:
A.S. was supported by NSF award IIS-1447700 and a Google Faculty Award. Part of this work was done while visiting Boston University's Hariri Institute for Computation and Harvard University's Center for Research on Computation and Society.

PY - 2015

Y1 - 2015

N2 - We design algorithms for fitting a high-dimensional statistical model to a large, sparse network without revealing sensitive information of individual members. Given a sparse input graph G, our algorithms output a node-differentially private nonparametric block model approximation. By node-differentially private, we mean that our output hides the insertion or removal of a vertex and all its adjacent edges. If G is an instance of the network obtained from a generative nonparametric model defined in terms of a graphon W, our model guarantees consistency: as the number of vertices tends to infinity, the output of our algorithm converges to W in an appropriate version of the L2 norm. In particular, this means we can estimate the sizes of all multi-way cuts in G. Our results hold as long as W is bounded, the average degree of G grows at least like the log of the number of vertices, and the number of blocks goes to infinity at an appropriate rate. We give explicit error bounds in terms of the parameters of the model; in several settings, our bounds improve on or match known nonprivate results.

AB - We design algorithms for fitting a high-dimensional statistical model to a large, sparse network without revealing sensitive information of individual members. Given a sparse input graph G, our algorithms output a node-differentially private nonparametric block model approximation. By node-differentially private, we mean that our output hides the insertion or removal of a vertex and all its adjacent edges. If G is an instance of the network obtained from a generative nonparametric model defined in terms of a graphon W, our model guarantees consistency: as the number of vertices tends to infinity, the output of our algorithm converges to W in an appropriate version of the L2 norm. In particular, this means we can estimate the sizes of all multi-way cuts in G. Our results hold as long as W is bounded, the average degree of G grows at least like the log of the number of vertices, and the number of blocks goes to infinity at an appropriate rate. We give explicit error bounds in terms of the parameters of the model; in several settings, our bounds improve on or match known nonprivate results.

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M3 - Conference article

AN - SCOPUS:84965171597

VL - 2015-January

SP - 1369

EP - 1377

JO - Advances in Neural Information Processing Systems

JF - Advances in Neural Information Processing Systems

SN - 1049-5258

T2 - 29th Annual Conference on Neural Information Processing Systems, NIPS 2015

Y2 - 7 December 2015 through 12 December 2015

ER -