### Abstract

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 L_{2} 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.

Original language | English (US) |
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Pages (from-to) | 1369-1377 |

Number of pages | 9 |

Journal | Advances in Neural Information Processing Systems |

Volume | 2015-January |

State | Published - Jan 1 2015 |

Event | 29th Annual Conference on Neural Information Processing Systems, NIPS 2015 - Montreal, Canada Duration: Dec 7 2015 → Dec 12 2015 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Computer Networks and Communications
- Information Systems
- Signal Processing

### Cite this

*Advances in Neural Information Processing Systems*,

*2015-January*, 1369-1377.

}

*Advances in Neural Information Processing Systems*, vol. 2015-January, pp. 1369-1377.

**Private graphon estimation for sparse graphs.** / Borgs, Christian; Chayes, Jennifer T.; Smith, Adam Davison.

Research output: Contribution to journal › Conference article

TY - JOUR

T1 - Private graphon estimation for sparse graphs

AU - Borgs, Christian

AU - Chayes, Jennifer T.

AU - Smith, Adam Davison

PY - 2015/1/1

Y1 - 2015/1/1

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.

UR - http://www.scopus.com/inward/record.url?scp=84965171597&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84965171597&partnerID=8YFLogxK

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

ER -