Mining of spatial data is an enabling technology for mobile services, Internet-connected cars and the Internet of Things. But the very distinctiveness of spatial data that drives utility can cost user privacy. Past work has focused upon points and trajectories for differentially private release. In this work, we continue the tradition of privacy-preserving spatial analytics, focusing not on point or path data, but on planar spatial regions. Such data represent the area of a user’s most frequent visitation—such as “around home and nearby shops”. Specifically we consider the differentially private release of data structures that support range queries for counting users’ spatial regions. Counting planar regions leads to unique challenges not faced in existing work. A user’s spatial region that straddles multiple data structure cells can lead to duplicate counting at query time. We provably avoid this pitfall by leveraging the Euler characteristic for the first time with differential privacy. To address the increased sensitivity of range queries to spatial region data, we calibrate privacy-preserving noise using bounded user region size and a constrained inference that uses robust least absolute deviations. Our novel constrained inference reduces noise and promotes covertness by (privately) imposing consistency. We provide a full end-to-end theoretical analysis of both differential privacy and high-probability utility for our approach using concentration bounds. A comprehensive experimental study on several real-world datasets establishes practical validity.
Differential privacy @cite_27 @cite_24 has now become a preferred approach to data sanitisation as it provides a strong semantic guarantee with minimal assumptions placed on the adversary's knowledge or capabilities. Differential privacy has been studied for location privacy @cite_47 . One existing approach is to obfuscate the user's location by perturbing their real geographic coordinates. The concept of geo-indistinguishability has been defined @cite_12 @cite_43 as a notion of differential privacy in location-based services. Due to its popularity, differential privacy has been applied to many algorithms and across many domains, such as specialized versions of spatial data indexing structures designed with differential privacy for the purpose of private record matching @cite_40 ; in spatial crowdsourcing to help volunteer workers' locations remain private @cite_4 ; in machine learning, releasing differentially-private learned models of SVM classifiers @cite_31 ; in geo-social networks for location recommendation @cite_42 ; and for modelling human mobility from real-world cellular network data @cite_9 .
@cite_31 @cite_4 @cite_9 @cite_42 @cite_24 @cite_43 @cite_27 @cite_40 @cite_47 @cite_12
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The ubiquitous need for analyzing privacy-sensitive information—including health records, personal communications, product ratings and social network data—is driving significant interest in privacy-preserving data analysis across several research communities. This paper explores the release of Support Vector Machine (SVM) classifiers while preserving the privacy of training data. The SVM is a popular machine learning method that maps data to a high-dimensional feature space before learning a linear decision boundary. We present efficient mechanisms for finite-dimensional feature mappings and for (potentially infinite-dimensional) mappings with translation-invariant kernels. In the latter case, our mechanism borrows a technique from large-scale learning to learn in a finite-dimensional feature space whose inner-product uniformly approximates the desired feature space inner-product (the desired kernel) with high probability. Differential privacy is established using algorithmic stability, a property used in learning theory to bound generalization error. Utility—when the private classifier is pointwise close to the non-private classifier with high probability—is proven using smoothness of regularized empirical risk minimization with respect to small perturbations to the feature mapping. Finally we conclude with lower bounds on the differential privacy of any mechanism approximating the SVM. With the wide adoption of handheld devices (e.g., smartphones, tablets), a large number of location-based services (also called LBSs) have flourished providing mobile users with real-time and contextual information on the move. Accounting for the amount of location information they are given by users, these services are able to track users wherever they go and to learn sensitive information about them (e.g., their points of interest including home, work, religious or political places regularly visited). A number of solutions have been proposed in the past few years to protect users location information while still allowing them to enjoy geo-located services. Among the most robust solutions are those that apply the popular notion of differential privacy to location privacy (e.g., Geo-Indistinguishability), promising strong theoretical privacy guarantees with a bounded accuracy loss. While these theoretical guarantees are attracting, it might be difficult for end users or practitioners to assess their effectiveness in the wild. In this paper, we carry on a practical study using real mobility traces coming from two different datasets, to assess the ability of Geo-Indistinguishability to protect users' points of interest (POIs). We show that a curious LBS collecting obfuscated location information sent by mobile users is still able to infer most of the users POIs with a reasonable both geographic and semantic precision. This precision depends on the degree of obfuscation applied by Geo-Indistinguishability. Nevertheless, the latter also has an impact on the overhead incurred on mobile devices resulting in a privacy versus overhead trade-off. Finally, we show in our study that POIs constitute a quasi-identifier for mobile users and that obfuscating them using Geo-Indistinguishability is not sufficient as an attacker is able to re-identify at least 63 of them despite a high degree of obfuscation. In this work we analyze the sample complexity of classification by differentially private algorithms. Differential privacy is a strong and well-studied notion of privacy introduced by [Lecture Notes in Comput. Sci. 3876, Springer, New York, 2006, pp. 265--284] that ensures that the output of an algorithm leaks little information about the data point provided by any of the participating individuals. Sample complexity of private probably approximately correct (PAC) and agnostic learning was studied in a number of prior works starting with [SIAM J. Comput., 40 (2011), pp. 793--826]. However, a number of basic questions remain open [A. Beimel, S. P. Kasiviswanathan, and K. Nissim, Lecture Notes in Comput. Sci. 5978, Springer, New York, 2006, pp. 437--454; K. Chaudhuri and D. Hsu, Proceedings of Conference in Learning Theory, 2011, pp. 155--186; A. Beimel, K. Nissim, and U. Stemmer, Proceedings of the 4th Conference on Innovations in Theoretical Computer Science, 2013, pp. 9... Differential privacy has emerged as one of the most promising privacy models for private data release. It can be used to release different types of data, and, in particular, histograms, which provide useful summaries of a dataset. Several differentially private histogram releasing schemes have been proposed recently. However, most of them directly add noise to the histogram counts, resulting in undesirable accuracy. In this paper, we propose two sanitization techniques that exploit the inherent redundancy of real-life datasets in order to boost the accuracy of histograms. They lossily compress the data and sanitize the compressed data. Our first scheme is an optimization of the Fourier Perturbation Algorithm (FPA) presented in RN10 . It improves the accuracy of the initial FPA by a factor of 10. The other scheme relies on clustering and exploits the redundancy between bins. Our extensive experimental evaluation over various real-life and synthetic datasets demonstrates that our techniques preserve very accurate distributions and considerably improve the accuracy of range queries over attributed histograms.