Deciding accuracy of differential privacy schemes

Abstract

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 ad hoc definitions and introduce an alternative notion of accuracy parametrized by, what we call, — the 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 )≠ 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 Schanuel’s 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.

Symbolic Execution for Randomized Programs

“…There are also many domain-specific automated analyses for specific probabilistic properties, such as termination and resource analysis [Chatterjee et al 2016;Moosbrugger et al 2021;Wang et al 2021], accuracy Smith et al 2019], reliability [Carbin et al 2012], differential privacy [Albarghouthi and Hsu 2018b;Barthe et al 2021] and other relational properties [Albarghouthi and Hsu 2018a;Farina et al 2021], and long-run properties of probabilistic loops [Bartocci et al 2019[Bartocci et al , 2020. Our approach aims to create a general-purpose analysis.…”

Contextualize differential privacy in image database: a lightweight image differential privacy approach based on principle component analysis inverse

“…Among varieties of techniques to protect privacy, e.g., anonymization [10], encryption [11], data access control [12], data outsourcing [13], digital forgetting [14], and data summarization [15], differential privacy (DP) offers a promising approach to make the contribution of individual data items hardly distinguishable toward given data analyzing tasks [16]. Such a feature leads to a provable privacy guarantee with a quantitative privacy measurement called privacy budget [17], making DP the de-facto standard for privacy preservation in data analysis both in academia and industry [18,19]. However, though DP has observed its prosperity in a wide range of applications [20][21][22][23][24], its integration into image data is understood in a limited way.…”