Statistical analysis of network data, while popular in a broad range of fields, can also be highly problematic from a privacy standpoint. In this thesis, we study privacy-preserving inference on network data using the rigorous notion of differential privacy. We propose new methods for differentially private inference using a common class of models known as Exponential Random Graph Models (ERGMs). The goal of our work is to accurately estimate the parameters of an ERGM applied to a network dataset, while offering meaningful privacy guarantees to participants. We propose methods that provably guarantee differential privacy at two different granularities: edge-level privacy, which protects the privacy of any single relationship in the network and node-level privacy, which protects all of the relationships of a participant. Specifically, using the framework of "restricted sensitivity," we take advantage of the sparsity of real-world networks to perturb data much less than prior work while guaranteeing differential privacy. We empirically evaluate the accuracy of inference in a series of experiments on both synthetic networks and a real network dataset. Experimental results suggest that our proposed methods enable accurate inference under meaningful privacy guarantees in settings where current methods do not, moving us closer to the goal of useful differentially private statistical modeling of network data.
We consider the problem of designing and analyzing differentially private algorithms that can be implemented on discrete models of computation in strict polynomial time, motivated by known attacks on floating point implementations of real-arithmetic differentially private algorithms (Mironov, CCS 2012) and the potential for timing attacks on expected polynomialtime algorithms. We use a case study the basic problem of approximating the histogram of a categorical dataset over a possibly large data universe X . The classic Laplace Mechanism (Dwork, McSherry, Nissim, Smith, TCC 2006 and J. Privacy & Confidentiality 2017) does not satisfy our requirements, as it is based on real arithmetic, and natural discrete analogues, such as the Geometric Mechanism (Ghosh, Roughgarden, Sundarajan, STOC 2009 and SICOMP 2012), take time at least linear in |X |, which can be exponential in the bit length of the input.
In this paper, we provide strict polynomial-time discrete algorithms for approximate histograms whose simultaneous accuracy (the maximum error over all bins) matches that of the Laplace Mechanism up to constant factors, while retaining the same (pure) differential privacy guarantee. One of our algorithms produces a sparse histogram as output. Its “per-bin accuracy” (the error on individual bins) is worse than that of the Laplace Mechanism by a factor of log |X |, but we prove a lower bound showing that this is necessary for any algorithm that produces a sparse histogram. A second algorithm avoids this lower bound, and matches the per-bin accuracy of the Laplace Mechanism, by producing a compact and efficiently computable representation of a dense histogram; it is based on an (n + 1)-wise independent implementation of an appropriately clamped version of the Discrete Geometric Mechanism.
This position paper observes how different technical and normative conceptions of privacy have evolved in parallel and describes the practical challenges that these divergent approaches pose. Notably, past technologies relied on intuitive, heuristic understandings of privacy that have since been shown not to satisfy expectations for privacy protection. With computations ubiquitously integrated in almost every aspect of our lives, it is increasingly important to ensure that privacy technologies provide protection that is in line with relevant social norms and normative expectations. Similarly, it is also important to examine social norms and normative expectations with respect to the evolving scientific study of privacy. To this end, we argue for a rigorous analysis of the mapping from normative to technical concepts of privacy and vice versa. We review the landscape of normative and technical definitions of privacy and discuss specific examples of gaps between definitions that are relevant in the context of privacy in statistical computation. We then identify opportunities for overcoming their differences in the design of new approaches to protecting privacy in accordance with both technical and normative standards.