A differentially private estimator for the stochastic Kronecker graph model

Abstract

We consider the problem of making graph databases such as social networks available to researchers for knowledge discovery while providing privacy to the participating entities. We use a parametric graph model, the stochastic Kronecker graph model, to model the observed graph and construct an estimator of the "true parameter" in a way that both satisfies the rigorous requirements of differential privacy and demonstrates experimental utility on several important graph statistics. The estimator, which may then be published, defines a probability distribution on graphs. Sampling such a distribution yields a synthetic graph that mimics important properties of the original sensitive graph and consequently, could be useful for knowledge discovery.

An Advanced Private Social Activity Invitation Framework with Friendship Protection

“…The output graph will be regenerated from these noisy intermediary structures. Popular algorithms in this category include 1K-series, 2K-series [24,25], Kronecker graph model [13], graph spectral analysis [26], DER [27], HRG-MCMC [28], and ERGM [29]. Most existing privacypreserving algorithms for graph publication assume the graph is undirected and published by a trusted and altruistic server.…”

“…Based on the above estimated habits about existing users, the server will disseminate the invitations to appropriate candidates via the Adv-k-core algorithm such that all of the invitees meet the group activity requirements and have a high chance to attend the activities. Since any privacy-preserving algorithm that satisfies differential privacy will protect the individual's information regardless of the adversary's background information [13], the server can release the statistical information about the current users safely to the public. Our framework does not need to keep track of actual mutual friendships, but which users enjoy doing activities with whom.…”

“…Differential privacy requires no computational/informational assumptions about attackers, data type-agnosticity, composability, and so on [13].…”

Private Release of Graph Statistics using Ladder Functions

“…Here we adopt the stochastic Kronecker model [20], a sophisticated method which can simulate large real-world graphs with only a few parameters. The algorithm in [13,26] provides a way to estimate parameters of the simplest Kronecker model from a small set of subgraph counts: f e (the number of edges), f , f 2 and f 3 . Therefore, one can easily build a Kronecker model then generate synthetic Kronecker graphs with differential privacy guarantees, if provided four private counts in advance.…”

“…For example, it is straightforward to release the number of nodes and edges with this guarantee, by appealing to standard techniques. It is valuable to find statistical properties of the graph, since there are many random graph models which take these as parameters (e.g., Kronecker graph models [26] and Exponential Random Graph Models [17]), and allow us to sample graphs from this family, which should have similar properties to the input graph. The properties of the graph are also important in their own right, determining, for instance, measures of how much clustering there is in the graph, and other characteristics of group behavior.…”