On the 'Semantics' of Differential Privacy: A Bayesian Formulation

By Shiva Prasad Kasiviswanathan, Adam D. Smith. 2008

177 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Electrical and Electronic Engineering

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Citations in the corpus

Distributed Differential Privacy via Shuffling (2018, background): “It ensures that, no matter what an attacker learns by interacting with the algorithm, it would have learned nearly the same thing whether or not the dataset contained any particular individual’s data [19].”
Tight Lower Bounds for Differentially Private Selection (2017, background): “This definition provides meaningful privacy roughly when ε ≤ 1 and δ 1 n [41].”
Privacy for Free: Posterior Sampling and Stochastic Gradient Monte Carlo (2015, background): “Related to the general topic, Kasiviswanathan & Smith (2014) explicitly modeled the “semantics” of diﬀerential privacy from a Bayesian point of view, Xiao & Xiong (2012) developed a set of tools for performing Bayesian inference under diﬀerential privacy, e.g., conditional probability and…”
Differentially private model selection with penalized and constrained likelihood (2016, background): “Privacy protection due to differential privacy can be interpreted from a Bayesian perspective, as in Abowd and Vilhuber (2008) and Kasiviswanathan and Smith (2008).”
Hypothesis Testing Interpretations and Renyi Differential Privacy (2019, background): “[18] Shiva Prasad Kasiviswanathan and Adam D.”
Is Interaction Necessary for Distributed Private Learning? (2017, background): “Differential privacy [17] is a rigorous privacy criterion for data analysis that provides meaningful guarantees regardless of what an adversary knows ahead of time about individuals’ data [25].”
Hiding in the Crowd: A Massively Distributed Algorithm for Private Averaging with Malicious Adversaries (2018, background): “This is related to the “no free lunch” theorem in data privacy (Kifer and Machanavajjhala, 2011), see also the discussions in Kasiviswanathan and Smith (2014); Li et al. (2013).”
Near-Optimal Algorithms for Differentially-Private Principal Components (2012, background): “Differential privacy has been shown to have strong semantic guarantees (Dwork et al., 2006b; Kasiviswanathan and Smith, 2008) and is resistant to many attacks (Ganta et al., 2008) that succeed against alternative definitions of privacy.”
Privacy-Preserving Distributed Multi-Task Learning with Asynchronous Updates (2017, background): “…privacy makes sure that the adversary’s prior and posterior views about an individual (i.e. before and after having access to the database) shouldn’t be “drastically different” or the access to the database shouldn’t change the adversary’s views about any individual “too much” [17, 30].”