Information-Theoretic Foundations of Differential Privacy

Mir, Darakhshan

doi:10.1007/978-3-642-37119-6_25

Cited by 21 publications

(19 citation statements)

References 12 publications

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“…Proof. This is an instance of Theorem 3 in Mir [24] (first appeared in Tishby et al [31]) by taking the distortion function to be the empirical risk. Note that this is a simple convex optimization over the functions and the proof involves substituting the solution into the optimality condition with a specific Lagrange multiplier chosen to appropriately adjust the normalization constant.…”

Section: Definition 8 (Conditional Entropy) Conditional Entropymentioning

confidence: 91%

“…The variational solution of p(h|Z) that minimizesĨ(h; Z) + γE Z E h|Z L(Z, h) is proportional to exp(−L(Z, h))π(h). This provides an alternative way of seeing the class of algorithms A that we consider.Ĩ(h; Z) can be thought of as a informationtheoretic quantification of privacy loss, as described in [38,24]. As a result, we can think of the class of A that samples from MaxEnt distributions as the most private algorithm among all algorithms that achieves a given utility constraint.…”

Section: Definition 8 (Conditional Entropy) Conditional Entropymentioning

confidence: 99%

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On-Average KL-Privacy and Its Equivalence to Generalization for Max-Entropy Mechanisms

Wang

Lei

Fienberg

2016

Privacy in Statistical Databases

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We define On-Average KL-Privacy and present its properties and connections to differential privacy, generalization and informationtheoretic quantities including max-information and mutual information. The new definition significantly weakens differential privacy, while preserving its minimalistic design features such as composition over small group and multiple queries as well as closeness to post-processing. Moreover, we show that On-Average KL-Privacy is equivalent to generalization for a large class of commonly-used tools in statistics and machine learning that samples from Gibbs distributions-a class of distributions that arises naturally from the maximum entropy principle. In addition, a byproduct of our analysis yields a lower bound for generalization error in terms of mutual information which reveals an interesting interplay with known upper bounds that use the same quantity.

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Section: Definition 8 (Conditional Entropy) Conditional Entropymentioning

confidence: 91%

Section: Definition 8 (Conditional Entropy) Conditional Entropymentioning

confidence: 99%

On-Average KL-Privacy and Its Equivalence to Generalization for Max-Entropy Mechanisms

Wang

Lei

Fienberg

2016

Privacy in Statistical Databases

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“…Firstly, the privacy-preserving mechanism can be modeled as a noisy channel model [13], [17], [23], [24], including the radio channel model [25] connected with IoT devices. Then, the privacy leakage can be measured by entropy [19], [26], [27]. In particular, Alvim et al proposed measure information uncertainty based on the idea of quantitative information flow (QIF).…”

Section: Related Workmentioning

confidence: 99%

“…Intuitively, the more randomness of the privacy mechanism will be obtained the better privacy performance. The works [16], [18], [19] utilize MI measuring the privacy leakage about privacy-preserving mechanisms because the notion of MI has a clear meaning, that is, measuring the amount of uncertainty reduction about original information. However, the works [7], [20] adopt MI as utility metrics, and further preserve the useful information as much as possible.…”

Section: Introductionmentioning

confidence: 99%

A Privacy-Preserving Game Model for Local Differential Privacy by Using Information-Theoretic Approach

Peng

Niu

2020

IEEE Access

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Local differential privacy (LDP) is an effective privacy-preserving model to address the problems which do not have a trusted entity. The main idea of the LDP is to add randomness in real data to guarantee individual's private sensitive information. Here, the technology of randomized response is an effective method to realize the LDP mechanism. In fact, the randomized response is a probabilistic mapping from the real data to perturbed data, which can be modeled as an information-theoretic lossy compression mechanism. What's more, the privacy budget ε has become a de facto standard to quantify the worstcase privacy leakage. However, such a metrics can not capture the question that which one is the optimal privacy mechanism in a set of equivalent ε-privacy mechanisms. Besides, the privacy and utility are closely correlated with the privacy mechanism, and existing methods do not consider the strategic adversary's behavior. In this paper, we tackle the problem of tradeoffs privacy and utility under the rational framework within an information-theoretic approach as the metrics. To address the problem, we first formulate this trade-off as a minimax information leakage problem. Then, we propose a privacy preserving attack and defense (PPAD) game framework, that is, a two-person zero-sum (TPZS) game. Further, we develop an alternating optimization algorithm to compute the saddle point of the proposed PPAD game. As a case study, we apply our method to compare several alternative ln 2-privacy mechanisms, the experimental result demonstrates that can provide an effective method to compare equivalent ε-privacy mechanisms. Furthermore, the numeric simulation result confirms that the proposed method also be useful for the protector to assess privacy disclosure risks.

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“…Although several information-theoretic interpretations of differential privacy have been presented [16][17][18], the available literature does not offer an operational meaning for the concept as well as a systematic approach for setting the differential privacy parameter (except a broad sweep). Further, in practice, it may not be possible to use an additive noise with infinite support as the noise might need to satisfy certain constraints, e.g., it must belong to a bounded set for smart metering [19].…”

Section: Introductionmentioning

confidence: 99%

Ensuring privacy with constrained additive noise by minimizing Fisher information

Farokhi

2019

Automatica

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The problem of preserving the privacy of individual entries of a database when responding to linear or nonlinear queries with constrained additive noise is considered. For privacy protection, the response to the query is systematically corrupted with an additive random noise whose support is a subset or equal to a pre-defined constraint set. A measure of privacy using the inverse of the trace of the Fisher information matrix is developed. The Cramér-Rao bound relates the variance of any estimator of the database entries to the introduced privacy measure. The probability density that minimizes the trace of the Fisher information (as a proxy for maximizing the measure of privacy) is computed. An extension to dynamic problems is also presented. Finally, the results are compared to the differential privacy methodology.

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Information-Theoretic Foundations of Differential Privacy

Cited by 21 publications

References 12 publications

On-Average KL-Privacy and Its Equivalence to Generalization for Max-Entropy Mechanisms

On-Average KL-Privacy and Its Equivalence to Generalization for Max-Entropy Mechanisms

A Privacy-Preserving Game Model for Local Differential Privacy by Using Information-Theoretic Approach

Ensuring privacy with constrained additive noise by minimizing Fisher information

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