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The correlations and network structure amongst individuals in datasets today---whether explicitly articulated, or deduced from biological or behavioral connections---pose new issues around privacy guarantees, because of inferences that can be made about one individual from anothers data. This motivates quantifying privacy in networked contexts in terms of inferential privacy---which measures the change in beliefs about an individuals data from the result of a computation---as originally proposed by Dalenius in the 1970s. Inferential privacy is implied by differential privacy when data are independent, but can be much worse when data are correlated; indeed, simple examples, as well as a general impossibility theorem of Dwork and Naor, preclude the possibility of achieving non-trivial inferential privacy when the adversary can have arbitrary auxiliary information. In this paper, we ask how differential privacy guarantees translate to guarantees on inferential privacy in networked contexts: specifically, under what limitations on the adversarys information about correlations, modeled as a prior distribution over datasets, can we deduce an inferential guarantee from a differential one? We prove two main results. The first result pertains to distributions that satisfy a natural positive-affiliation condition, and gives an upper bound on the inferential privacy guarantee for any differentially private mechanism. This upper bound is matched by a simple mechanism that adds Laplace noise to the sum of the data. The second result pertains to distributions that have weak correlations, defined in terms of a suitable influence matrix. The result provides an upper bound for inferential privacy in terms of the differential privacy parameter and the spectral norm of this matrix.
Differentially private algorithms protect individuals in data analysis scenarios by ensuring that there is only a weak correlation between the existence of the user in the data and the result of the analysis. Dynamic graph algorithms maintain the sol
Bayesian neural network (BNN) allows for uncertainty quantification in prediction, offering an advantage over regular neural networks that has not been explored in the differential privacy (DP) framework. We fill this important gap by leveraging rece
We introduce a new $(epsilon_p, delta_p)$-differentially private algorithm for the $k$-means clustering problem. Given a dataset in Euclidean space, the $k$-means clustering problem requires one to find $k$ points in that space such that the sum of s
Common datasets have the form of elements with keys (e.g., transactions and products) and the goal is to perform analytics on the aggregated form of key and frequency pairs. A weighted sample of keys by (a function of) frequency is a highly versatile
Correlation clustering is a widely used technique in unsupervised machine learning. Motivated by applications where individual privacy is a concern, we initiate the study of differentially private correlation clustering. We propose an algorithm that