A common approach to protect users privacy in data collection is to perform random perturbations on user's sensitive data before collection in a way that aggregated statistics can still be inferred without endangering individual secrets. In this paper, we take a closer look at the validity of Differential Privacy guarantees, when sensitive attributes are subject to social contagion. We first show that in the absence of any knowledge about the contagion network, an adversary that tries to predict the real values from perturbed ones, cannot train a classifier that achieves an area under the ROC curve (AUC) above 1 − (1 − δ)/(1 + e ε ), if the dataset is perturbed using an (ε, δ)-differentially private mechanism. Then, we show that with the knowledge of the contagion network and model, one can do substantially better. We demonstrate that our method passes the performance limit imposed by differential privacy. Our experiments also reveal that nodes with high influence on others are at more risk of revealing their secrets than others. Our method's superior performance is demonstrated through extensive experiments on synthetic and real-world networks.
With the popularity of portable wireless devices it is important to model and predict how information or contagions spread by natural human mobility -for understanding the spreading of deadly infectious diseases and for improving delay tolerant communication schemes. Formally, we model this problem by considering M moving agents, where each agent initially carries a distinct bit of information. When two agents are at the same location or in close proximity to one another, they share all their information with each other. We would like to know the time it takes until all bits of information reach all agents, called the ood time, and how it depends on the way agents move, the size and shape of the network and the number of agents moving in the network.We provide rigorous analysis for the Manha an Random Waypoint model (which takes paths with minimum number of turns), a convenient model used previously to analyze mobile agents, and nd that with high probability the ood time is bounded by O N log M (N /M) log(N M) , where M agents move on an N × N grid. In addition to extensive simulations, we use a data set of taxi trajectories to show that our method can successfully predict ood times in both experimental se ings and the real world.
The presence of correlation is known to make privacy protection more difficult. We investigate the privacy of socially contagious attributes on a network of individuals, where each individual possessing that attribute may influence a number of others into adopting it. We show that for contagions following the Independent Cascade model there exists a giant connected component of infected nodes, containing a constant fraction of all the nodes who all receive the contagion from the same set of sources. We further show that it is extremely hard to hide the existence of this giant connected component if we want to obtain an estimate of the activated users at an acceptable level. Moreover, an adversary possessing this knowledge can predict the real status ("active" or "inactive") with decent probability for many of the individuals regardless of the privacy (perturbation) mechanism used. As a case study, we show that the Wasserstein mechanism, a state-of-the-art privacy mechanism designed specifically for correlated data, introduces a noise with magnitude of order Ω(n) in the count estimation in our setting. We provide theoretical guarantees for two classes of random networks: Erdős-Rényi graphs and Chung-Lu power-law graphs under the Independent Cascade model. Experiments demonstrate that a giant connected component of infected nodes can and does appear in real-world networks and that a simple inference attack can reveal the status of a good fraction of nodes.
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