Hypothesis Testing Under Mutual Information Privacy Constraints in the High Privacy Regime

Liao, Jiachun; Sankar, Lalitha; Tan, Vincent Y. F.; Calmon, Flávio P.

doi:10.1109/tifs.2017.2779108

Cited by 55 publications

(41 citation statements)

References 33 publications

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“…Therefore, for α = ∞, the minimal expected α-loss is the minimal expected probability of error. In addition, the optimal estimation strategy in (23) becomes the true posterior distribution of X for α = 1 and the MAP estimator for α = ∞, respectively. Example 1.…”

Section: A α-Loss Functionmentioning

confidence: 99%

“…Such an approach has also been studied in rate-distortion theory as a potential distortion measure (see, for example, [42] for the use of per symbol distortion constraints). In addition, compared to average-case distortion constraints [23], [38]- [41], a hard distortion measure is quite stringent but allows the data curator to make specific, deterministic guarantees on the fidelity of the released dataset relative to the original. Such a deterministic guarantee can lead to more accurate statistical estimators, e.g., the empirical distribution estimation for publicly released datasets such as the census.…”

Section: Introduction and Overviewmentioning

confidence: 99%

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Tunable Measures for Information Leakage and Applications to Privacy-Utility Tradeoffs

Liao

Kosut

Sankar

et al. 2019

IEEE Trans. Inform. Theory

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We introduce a tunable measure for information leakage called maximal α-leakage. This measure quantifies the maximal gain of an adversary in inferring any (potentially random) function of a dataset from a release of the data. The inferential capability of the adversary is, in turn, quantified by a class of adversarial loss functions that we introduce as αloss, α ∈ [1, ∞) ∪ {∞}. The choice of α determines the specific adversarial action and ranges from refining a belief (about any function of the data) for α = 1 to guessing the most likely value for α = ∞ while refining the α th moment of the belief for α in between. Maximal α-leakage then quantifies the adversarial gain under α-loss over all possible functions of the data. In particular, for the extremal values of α = 1 and α = ∞, maximal αleakage simplifies to mutual information and maximal leakage, respectively. For α ∈ (1, ∞) this measure is shown to be the Arimoto channel capacity of order α. We show that maximal αleakage satisfies data processing inequalities and a sub-additivity property thereby allowing for a weak composition result. Building upon these properties, we use maximal α-leakage as the privacy measure and study the problem of data publishing with privacy guarantees, wherein the utility of the released data is ensured via a hard distortion constraint. Unlike average distortion, hard distortion provides a deterministic guarantee of fidelity. We show that under a hard distortion constraint, for α > 1 the optimal mechanism is independent of α, and therefore, the resulting optimal tradeoff is the same for all values of α > 1. Finally, the tunability of maximal α-leakage as a privacy measure is also illustrated for binary data with average Hamming distortion as the utility measure.

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Section: A α-Loss Functionmentioning

confidence: 99%

Section: Introduction and Overviewmentioning

confidence: 99%

Tunable Measures for Information Leakage and Applications to Privacy-Utility Tradeoffs

Liao

Kosut

Sankar

et al. 2019

IEEE Trans. Inform. Theory

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“…If there exists a distribution Q Y achieving the infimum in (11), an optimal mechanism P * Y |X is given by Fig. 1: An optimal mechanism for α > 1 with (n, m) = (8,2). Note that the hard distortion forces conditional probabilities of outputs outside the feasible ball of a given input to be zero.…”

Section: Privacy-utility Tradeoff With a Hard Distortion Constraintmentioning

confidence: 99%

Privacy Under Hard Distortion Constraints

Liao

Kosut

Sankar

et al. 2018

2018 IEEE Information Theory Workshop (ITW)

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We study the problem of data disclosure with privacy guarantees, wherein the utility of the disclosed data is ensured via a hard distortion constraint. Unlike average distortion, hard distortion provides a deterministic guarantee of fidelity. For the privacy measure, we use a tunable information leakage measure, namely maximal α-leakage (α ∈ [1, ∞]), and formulate the privacy-utility tradeoff problem. The resulting solution highlights that under a hard distortion constraint, the nature of the solution remains unchanged for both local and nonlocal privacy requirements. More precisely, we show that both the optimal mechanism and the optimal tradeoff are invariant for any α > 1; i.e., the tunable leakage measure only behaves as either of the two extrema, i.e., mutual information for α = 1 and maximal leakage for α = ∞.

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“…Privacy-utility trade-offs have been studied in different contexts [1]- [9]. The privacy leakage can be modeled as a statistical inference and measured by the mutual information [1]- [3], [6], [7], divergence [4], differential privacy [9], or variance [8]. Depending on the application, the utility measure can be the expectation of cost [5], [6], [8], divergence [4], [7], or data rate [1], [3].…”

Section: Introductionmentioning

confidence: 99%

“…The privacy leakage can be modeled as a statistical inference and measured by the mutual information [1]- [3], [6], [7], divergence [4], differential privacy [9], or variance [8]. Depending on the application, the utility measure can be the expectation of cost [5], [6], [8], divergence [4], [7], or data rate [1], [3]. With the privacy and utility measures, the trade-off problem can be formulated as a worst case analysis [2], [4], [6]- [8] or zero-sum game [5].…”

Section: Introductionmentioning

confidence: 99%

Privacy-Utility Management of Hypothesis Tests

Oechtering

2018

2018 IEEE Information Theory Workshop (ITW)

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The trade-off of hypothesis tests on the correlated privacy hypothesis and utility hypothesis is studied. The error exponent of the Bayesian composite hypothesis test on the privacy or utility hypothesis can be characterized by the corresponding minimal Chernoff information rate. An optimal management protects the privacy by minimizing the error exponent of the privacy hypothesis test and meanwhile guarantees the utility hypothesis testing performance by satisfying a lower bound on the corresponding minimal Chernoff information rate. The asymptotic minimum error exponent of the privacy hypothesis test is shown to be characterized by the infimum of corresponding minimal Chernoff information rates subject to the utility guarantees.

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Hypothesis Testing Under Mutual Information Privacy Constraints in the High Privacy Regime

Cited by 55 publications

References 33 publications

Tunable Measures for Information Leakage and Applications to Privacy-Utility Tradeoffs

Tunable Measures for Information Leakage and Applications to Privacy-Utility Tradeoffs

Privacy Under Hard Distortion Constraints

Privacy-Utility Management of Hypothesis Tests

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