On Perfect Privacy

Rassouli, Borzoo; Gündüz, Deniz

doi:10.1109/isit.2018.8437481

Cited by 30 publications

(60 citation statements)

References 5 publications

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“…As before, replacing randomized function

with conditional distribution

, we can equivalently express ( 3 ) as where

and r denote the level of desired privacy and informativeness, respectively. The case

is particularly interesting in practice and specifies perfect privacy, see e.g., [ 13 , 78 ]. As before, we write

and

for

and

when

is clear from the context.…”

Section: Information Bottleneck and Privacy Funnel: Definitions Anmentioning

confidence: 99%

Bottleneck Problems: An Information and Estimation-Theoretic View

Asoodeh

Calmon

2020

Entropy

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Information bottleneck (IB) and privacy funnel (PF) are two closely related optimization problems which have found applications in machine learning, design of privacy algorithms, capacity problems (e.g., Mrs. Gerber’s Lemma), and strong data processing inequalities, among others. In this work, we first investigate the functional properties of IB and PF through a unified theoretical framework. We then connect them to three information-theoretic coding problems, namely hypothesis testing against independence, noisy source coding, and dependence dilution. Leveraging these connections, we prove a new cardinality bound on the auxiliary variable in IB, making its computation more tractable for discrete random variables. In the second part, we introduce a general family of optimization problems, termed “bottleneck problems”, by replacing mutual information in IB and PF with other notions of mutual information, namely f-information and Arimoto’s mutual information. We then argue that, unlike IB and PF, these problems lead to easily interpretable guarantees in a variety of inference tasks with statistical constraints on accuracy and privacy. While the underlying optimization problems are non-convex, we develop a technique to evaluate bottleneck problems in closed form by equivalently expressing them in terms of lower convex or upper concave envelope of certain functions. By applying this technique to a binary case, we derive closed form expressions for several bottleneck problems.

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“…As before, replacing randomized function

with conditional distribution

, we can equivalently express ( 3 ) as where

and r denote the level of desired privacy and informativeness, respectively. The case

is particularly interesting in practice and specifies perfect privacy, see e.g., [ 13 , 78 ]. As before, we write

and

for

and

when

is clear from the context.…”

Section: Information Bottleneck and Privacy Funnel: Definitions Anmentioning

confidence: 99%

Bottleneck Problems: An Information and Estimation-Theoretic View

Asoodeh

Calmon

2020

Entropy

View full text Add to dashboard Cite

show abstract

Section: System Model and Preliminariesmentioning

confidence: 99%

“…Let r = α v T T (α = 0, = e 1 ) be an extreme point of S X,Y , where v is a vector of probability masses that sum to 1 − α. Since r ∈ S X,Y , we must have p X = P X|Y r, which, from p X|Y (•|y 0 ) = p X (•), results in p X = P X|Y r 0 , where r 0 = 0 1 1−α v T T is a probability vector. Therefore, r 0 ∈ S X,Y .…”

Section: Appendix Dmentioning

confidence: 99%

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On Perfect Privacy

Rassouli

Gündüz

2021

IEEE J. Sel. Areas Inf. Theory

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The problem of private data disclosure is studied from an information theoretic perspective. Considering a pair of dependent random variables (X, Y ), where X and Y denote the private and useful data, respectively, the following problem is addressed: What is the maximum information that can be revealed about Y , measured by mutual information I(Y ; U ), in which U denotes the revealed data, while disclosing no information about X, captured by the condition of statistical independence, i.e., X ⊥ ⊥ U , and henceforth called perfect privacy)? We analyze the supremization of utility, i.e., I(Y ; U ) under the condition of perfect privacy for two scenarios: output perturbation and full data observation models, which correspond to the cases where a Markov kernel, called privacy-preserving mapping, applies to Y and the pair (X, Y ), respectively. When both X and Y have a finite alphabet, the linear algebraic analysis involved in the solution provides some interesting results, such as upper/lower bounds on the size of the released alphabet and the maximum utility. Afterwards, it is shown that for the jointly Gaussian (X, Y ), perfect privacy is not possible in the output perturbation model in contrast to the full data observation model. Finally, an asymptotic analysis is provided to obtain the rate of released information when a sufficiently small leakage is allowed. In particular, in the context of output perturbation model, it is shown that this rate is always finite when perfect privacy is not feasible, and two lower bounds are provided for it; When perfect privacy is feasible, it is shown that under mild conditions, this rate becomes unbounded.

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“…Privacy is an important concern for the adoption of many IoT services, and there is a growing demand from consumers to keep their personal information private. Privacy has been widely studied in the literature [1][2][3][4][5][6][7][8][9][10], and a vast number of privacy measures have been introduced, including differential privacy [1], mutual information (MI) [2][3][4][5][6][7][8], total variation distance [11], maximal leakage [12,13], and guessing leakage [14], to count a few.…”

Section: Introductionmentioning

confidence: 99%

Active Privacy-Utility Trade-Off Against A Hypothesis Testing Adversary

Erdemir

Dragotti

Gündüz

2021

ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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We consider a user releasing her data containing some personal information in return of a service. We model user's personal information as two correlated random variables, one of them, called the secret variable, is to be kept private, while the other, called the useful variable, is to be disclosed for utility. We consider active sequential data release, where at each time step the user chooses from among a finite set of release mechanisms, each revealing some information about the user's personal information, i.e., the true hypotheses, albeit with different statistics. The user manages data release in an online fashion such that maximum amount of information is revealed about the latent useful variable, while the confidence for the sensitive variable is kept below a predefined level. For the utility, we consider both the probability of correct detection of the useful variable and the mutual information (MI) between the useful variable and released data. We formulate both problems as a Markov decision process (MDP), and numerically solve them by advantage actor-critic (A2C) deep reinforcement learning (RL).

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On Perfect Privacy

Cited by 30 publications

References 5 publications

Bottleneck Problems: An Information and Estimation-Theoretic View

Bottleneck Problems: An Information and Estimation-Theoretic View

On Perfect Privacy

Active Privacy-Utility Trade-Off Against A Hypothesis Testing Adversary

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