Differentially Private Medians and Interior Points for Non-Pathological Data

We construct differentially private estimators with low sample complexity that estimate the median of an arbitrary distribution over $\mathbb{R}$ satisfying very mild moment conditions. Our result stands in contrast to the surprising negative result of Bun et al. (FOCS 2015) that showed there is no differentially private estimator with any finite sample complexity that returns any non-trivial approximation to the median of an arbitrary distribution

Broadening the scope of Differential Privacy Using Metrics ⋆

Abstract. Differential Privacy is one of the most prominent frameworks used to deal with disclosure prevention in statistical databases. It provides a formal privacy guarantee, ensuring that sensitive information relative to individuals cannot be easily inferred by disclosing answers to aggregate queries. If two databases are adjacent, i.e. differ only for an individual, then the query should not allow to tell them apart by more than a certain factor. This induces a bound also on the distinguishability of two generic databases, which is determined by their distance on the Hamming graph of the adjacency relation. In this paper we explore the implications of differential privacy when the indistinguishability requirement depends on an arbitrary notion of distance. We show that we can naturally express, in this way, (protection against) privacy threats that cannot be represented with the standard notion, leading to new applications of the differential privacy framework. We give intuitive characterizations of these threats in terms of Bayesian adversaries, which generalize two interpretations of (standard) differential privacy from the literature. We revisit the well-known results stating that universally optimal mechanisms exist only for counting queries: We show that, in our extended setting, universally optimal mechanisms exist for other queries too, notably sum, average, and percentile queries. We explore various applications of the generalized definition, for statistical databases as well as for other areas, such that geolocation and smart metering.

Distributed Private Online Learning for Social Big Data Computing over Data Center Networks

With the rapid growth of Internet technologies, cloud computing and social networks have become ubiquitous. An increasing number of people participate in social networks and massive online social data are obtained. In order to exploit knowledge from copious amounts of data obtained and predict social behavior of users, we urge to realize data mining in social networks. Almost all online websites use cloud services to effectively process the large scale of social data, which are gathered from distributed data centers. These data are so large-scale, high-dimension and widely distributed that we propose a distributed sparse online algorithm to handle them. Additionally, privacy-protection is an important point in social networks. We should not compromise the privacy of individuals in networks, while these social data are being learned for data mining. Thus we also consider the privacy problem in this article. Our simulations shows that the appropriate sparsity of data would enhance the performance of our algorithm and the privacy-preserving method does not significantly hurt the performance of the proposed algorithm.Comment: ICC201

Noise-Aware Inference for Differential Privacy

Domains involving sensitive human data, such as health care, human mobility, and online activity, are becoming increasingly dependent upon machine learning algorithms. This leads to scenarios in which data owners wish to protect the privacy of individuals comprising the sensitive data, while at the same time data modelers wish to analyze and draw conclusions from the data. Thus there is a growing demand to develop effective private inference methods that can marry the needs of both parties. For this we turn to differential privacy, which provides a framework for executing algorithms in a private fashion by injecting specifically-designed randomization at various points in the process. The majority of existing work proceeds by ignoring the injected randomization, potentially leading to pathologies in algorithmic performance. There is, however, a small body of existing work that performs inference over the injected randomization in an attempt to design more principled algorithms. This thesis summarizes the subfield of noise-aware differentially private inference and contributes novel algorithms for important problems. Differential privacy literature provides a multitude of privacy mechanisms. We opt for sufficient statistics perturbation (SSP), in which sufficient statistics, a quantity that captures all information about the model parameters, are corrupted with random noise and released to the public. This mechanism offers desirable efficiency properties in comparison to alternatives. In this thesis we develop methods in a principled manner that directly accounts for the injected noise in three settings: maximum likelihood estimation of undirected graphical models, Bayesian inference of exponential family models, and Bayesian inference of conditional regression models