Privacy-aware guessing efficiency

Abstract

We investigate the problem of guessing a discrete random variable Y under a privacy constraint dictated by another correlated discrete random variable X, where both guessing efficiency and privacy are assessed in terms of the probability of correct guessing. We define h(PXY , ε)as the maximum probability of correctly guessing Y given an auxiliary random variable Z, where the maximization is taken over all P Z|Y ensuring that the probability of correctly guessing X given Z does not exceed ε. We show that the map ε → h(PXY , ε) is strictly increasing, concave, and piecewise linear, which allows us to derive a closed form expression for h(PXY , ε) when X and Y are connected via a binary-input binary-output channel. For {(Xi, Yi)} n i=1 being pairs of independent and identically distributed binary random vectors, we similarly define h n (PXnY n , ε) under the assumption that Z n is also a binary vector. Then we obtain a closed form expression for h n (PXnY n , ε) for sufficiently large, but nontrivial values of ε.

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

“…It is not difficult to check that the optimal privacy mechanisms (in Fig. 7b) for different values of α give the same probability of correctly guessing, defined as y P Y (y) max x P Y |X (y|x) [27], which equals to 1 − D in this example. Probability of correctly guessing is, in fact, the average accuracy of estimating the value of original data X from Y when the maximal posterior (MAP) estimator is used.…”

“…Note that for any specific function U of X, the joint probability distribution of X and the U is known, and therefore, α-leakage can also be used to measure the the inference gain in inferring the specific function U from the released data Y . In addition, the two maximizations in the numerator and denominator of the logarithmic ratio in (27) imply the optimal adversarial actions in the sense of minimizing the expected αloss in Lemma 1. Therefore, it limits the inference gain that an adversary can obtain by minimizing the expected α-loss, no matter the adversary has prior knowledge (i.e., the probability distribution of the original data) of the original data or not.…”

Context-Aware Generative Adversarial Privacy

“…In this context, information-theoretic metrics for privacy are naturally well suited. In fact, the adversarial model determines the appropriate information metric: an estimating adversary that minimizes mean square error is captured by χ 2 -squared measures [40], a belief refining adversary is captured by MI [39], an adversary that can make a hard MAP decision for a specific set of private features is captured by the Arimoto MI of order ∞ [58,59], and an adversary that can guess any function of the private features is captured by the maximal (over all distributions of the dataset for a fixed support) Sibson information of order ∞ [55,57].…”

“…They also showed that their adversarial model can be generalized to encompass local DP (wherein the mechanism ensures limited distinction for any pair of entries-a stronger DP notion without a neighborhood constraint [27,56]) [57]. When one restricts the adversary to guessing specific private features (and not all functions of these features), the resulting adversary is a maximum a posteriori (MAP) adversary that has been studied by Asoodeh et al in [52,53,58,59]. Context-aware data perturbation techniques have also been studied in privacy preserving cloud computing [60][61][62].…”

Robustness of Maximal α-Leakage to Side Information

“…This surprising result provides further motivation for using α-leakage as a robust and tunable privacy metric. Finally, other metrics of note that may be amenable to such analysis include probability of correct guessing [7], total variation-based metrics [8], and metrics based on Rényi divergence [9].…”