7,988 research outputs found
Private Graphon Estimation for Sparse Graphs
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 , 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 is an instance of the
network obtained from a generative nonparametric model defined in terms of a
graphon , our model guarantees consistency, in the sense that as the number
of vertices tends to infinity, the output of our algorithm converges to in
an appropriate version of the norm. In particular, this means we can
estimate the sizes of all multi-way cuts in .
Our results hold as long as is bounded, the average degree of 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.Comment: 36 page
Differentially Private Exponential Random Graphs
We propose methods to release and analyze synthetic graphs in order to
protect privacy of individual relationships captured by the social network.
Proposed techniques aim at fitting and estimating a wide class of exponential
random graph models (ERGMs) in a differentially private manner, and thus offer
rigorous privacy guarantees. More specifically, we use the randomized response
mechanism to release networks under -edge differential privacy. To
maintain utility for statistical inference, treating the original graph as
missing, we propose a way to use likelihood based inference and Markov chain
Monte Carlo (MCMC) techniques to fit ERGMs to the produced synthetic networks.
We demonstrate the usefulness of the proposed techniques on a real data
example.Comment: minor edit
Sharing Social Network Data: Differentially Private Estimation of Exponential-Family Random Graph Models
Motivated by a real-life problem of sharing social network data that contain
sensitive personal information, we propose a novel approach to release and
analyze synthetic graphs in order to protect privacy of individual
relationships captured by the social network while maintaining the validity of
statistical results. A case study using a version of the Enron e-mail corpus
dataset demonstrates the application and usefulness of the proposed techniques
in solving the challenging problem of maintaining privacy \emph{and} supporting
open access to network data to ensure reproducibility of existing studies and
discovering new scientific insights that can be obtained by analyzing such
data. We use a simple yet effective randomized response mechanism to generate
synthetic networks under -edge differential privacy, and then use
likelihood based inference for missing data and Markov chain Monte Carlo
techniques to fit exponential-family random graph models to the generated
synthetic networks.Comment: Updated, 39 page
MVG Mechanism: Differential Privacy under Matrix-Valued Query
Differential privacy mechanism design has traditionally been tailored for a
scalar-valued query function. Although many mechanisms such as the Laplace and
Gaussian mechanisms can be extended to a matrix-valued query function by adding
i.i.d. noise to each element of the matrix, this method is often suboptimal as
it forfeits an opportunity to exploit the structural characteristics typically
associated with matrix analysis. To address this challenge, we propose a novel
differential privacy mechanism called the Matrix-Variate Gaussian (MVG)
mechanism, which adds a matrix-valued noise drawn from a matrix-variate
Gaussian distribution, and we rigorously prove that the MVG mechanism preserves
-differential privacy. Furthermore, we introduce the concept
of directional noise made possible by the design of the MVG mechanism.
Directional noise allows the impact of the noise on the utility of the
matrix-valued query function to be moderated. Finally, we experimentally
demonstrate the performance of our mechanism using three matrix-valued queries
on three privacy-sensitive datasets. We find that the MVG mechanism notably
outperforms four previous state-of-the-art approaches, and provides comparable
utility to the non-private baseline.Comment: Appeared in CCS'1
Revealing Network Structure, Confidentially: Improved Rates for Node-Private Graphon Estimation
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 ( and
), node-private algorithms can be qualitatively more accurate than for
more complex models---converging at a rate of
instead of . This result uses a new extension lemma
for differentially private algorithms that we hope will be broadly useful
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