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Register a new userA Programming Framework for Differential Privacy with Accuracy Concentration Bounds
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Added by
Elisabet Lobo-Vesga
Publication date
2019
fields
Informatics Engineering
and research's language is
English
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Differential privacy offers a formal framework for reasoning about privacy and accuracy of computations on private data. It also offers a rich set of building blocks for constructing data analyses. When carefully calibrated, these analyses simultaneously guarantee privacy of the individuals contributing their data, and accuracy of their results for inferring useful properties about the population. The compositional nature of differential privacy has motivated the design and implementation of several programming languages aimed at helping a data analyst in programming differentially private analyses. However, most of the programming languages for differential privacy proposed so far provide support for reasoning about privacy but not for reasoning about the accuracy of data analyses. To overcome this limitation, in this work we present DPella, a programming framework providing data analysts with support for reasoning about privacy, accuracy and their trade-offs. The distinguishing feature of DPella is a novel component which statically tracks the accuracy of different data analyses. In order to make tighter accuracy estimations, this component leverages taint analysis for automatically inferring statistical independence of the different noise quantities added for guaranteeing privacy. We show the flexibility of our approach by not only implementing classical counting queries (e.g., CDFs) but also by analyzing hierarchical counting queries (like those done by Census Bureaus), where accuracy have different constraints per level and data analysts should figure out the best manner to calibrate privacy to meet the accuracy requirements.
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Extended differential privacy, a generalization of standard differential privacy (DP) using a general metric, has been widely studied to provide rigorous privacy guarantees while keeping high utility. However, existing works on extended DP are limited to few metrics, such as the Euclidean metric. Consequently, they have only a small number of applications, such as location-based services and document processing. In this paper, we propose a couple of mechanisms providing extended DP with a different metric: angular distance (or cosine distance). Our mechanisms are based on locality sensitive hashing (LSH), which can be applied to the angular distance and work well for personal data in a high-dimensional space. We theoretically analyze the privacy properties of our mechanisms, and prove extended DP for input data by taking into account that LSH preserves the original metric only approximately. We apply our mechanisms to friend matching based on high-dimensional personal data with angular distance in the local model, and evaluate our mechanisms using two real datasets. We show that LDP requires a very large privacy budget and that RAPPOR does not work in this application. Then we show that our mechanisms enable friend matching with high utility and rigorous privacy guarantees based on extended DP.
Differential privacy is a mathematical framework for developing statistical computations with provable guarantees of privacy and accuracy. In contrast to the privacy component of differential privacy, which has a clear mathematical and intuitive meaning, the accuracy component of differential privacy does not have a generally accepted definition; accuracy claims of differential privacy algorithms vary from algorithm to algorithm and are not instantiations of a general definition. We identify program discontinuity as a common theme in existing emph{ad hoc} definitions and introduce an alternative notion of accuracy parametrized by, what we call, {distance} -- the {distance} of an input $x$ w.r.t., a deterministic computation $f$ and a distance $d$, is the minimal distance $d(x,y)$ over all $y$ such that $f(y) eq f(x)$. We show that our notion of accuracy subsumes the definition used in theoretical computer science, and captures known accuracy claims for differential privacy algorithms. In fact, our general notion of accuracy helps us prove better claims in some cases. Next, we study the decidability of accuracy. We first show that accuracy is in general undecidable. Then, we define a non-trivial class of probabilistic computations for which accuracy is decidable (unconditionally, or assuming Schanuels conjecture). We implement our decision procedure and experimentally evaluate the effectiveness of our approach for generating proofs or counterexamples of accuracy for common algorithms from the literature.
Differential privacy is a definition of privacy for algorithms that analyze and publish information about statistical databases. It is often claimed that differential privacy provides guarantees against adversaries with arbitrary side information. In this paper, we provide a precise formulation of these guarantees in terms of the inferences drawn by a Bayesian adversary. We show that this formulation is satisfied by both vanilla differential privacy as well as a relaxation known as (epsilon,delta)-differential privacy. Our formulation follows the ideas originally due to Dwork and McSherry [Dwork 2006]. This paper is, to our knowledge, the first place such a formulation appears explicitly. The analysis of the relaxed definition is new to this paper, and provides some concrete guidance for setting parameters when using (epsilon,delta)-differential privacy.
Local Differential Privacy (LDP) is popularly used in practice for privacy-preserving data collection. Although existing LDP protocols offer high utility for large user populations (100,000 or more users), they perform poorly in scenarios with small user populations (such as those in the cybersecurity domain) and lack perturbation mechanisms that are effective for both ordinal and non-ordinal item sequences while protecting sequence length and content simultaneously. In this paper, we address the small user population problem by introducing the concept of Condensed Local Differential Privacy (CLDP) as a specialization of LDP, and develop a suite of CLDP protocols that offer desirable statistical utility while preserving privacy. Our protocols support different types of client data, ranging from ordinal data types in finite metric spaces (numeric malware infection statistics), to non-ordinal items (O
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