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- All Subjects: Differential privacy
- Genre: Academic theses
- Creators: Zhang, Junshan
Description
Data privacy is emerging as one of the most serious concerns of big data analytics, particularly with the growing use of personal data and the ever-improving capability of data analysis. This dissertation first investigates the relation between different privacy notions, and then puts the main focus on developing economic foundations for a market model of trading private data.
The first part characterizes differential privacy, identifiability and mutual-information privacy by their privacy--distortion functions, which is the optimal achievable privacy level as a function of the maximum allowable distortion. The results show that these notions are fundamentally related and exhibit certain consistency: (1) The gap between the privacy--distortion functions of identifiability and differential privacy is upper bounded by a constant determined by the prior. (2) Identifiability and mutual-information privacy share the same optimal mechanism. (3) The mutual-information optimal mechanism satisfies differential privacy with a level at most a constant away from the optimal level.
The second part studies a market model of trading private data, where a data collector purchases private data from strategic data subjects (individuals) through an incentive mechanism. The value of epsilon units of privacy is measured by the minimum payment such that an individual's equilibrium strategy is to report data in an epsilon-differentially private manner. For the setting with binary private data that represents individuals' knowledge about a common underlying state, asymptotically tight lower and upper bounds on the value of privacy are established as the number of individuals becomes large, and the payment--accuracy tradeoff for learning the state is obtained. The lower bound assures the impossibility of using lower payment to buy epsilon units of privacy, and the upper bound is given by a designed reward mechanism. When the individuals' valuations of privacy are unknown to the data collector, mechanisms with possible negative payments (aiming to penalize individuals with "unacceptably" high privacy valuations) are designed to fulfill the accuracy goal and drive the total payment to zero. For the setting with binary private data following a general joint probability distribution with some symmetry, asymptotically optimal mechanisms are designed in the high data quality regime.
The first part characterizes differential privacy, identifiability and mutual-information privacy by their privacy--distortion functions, which is the optimal achievable privacy level as a function of the maximum allowable distortion. The results show that these notions are fundamentally related and exhibit certain consistency: (1) The gap between the privacy--distortion functions of identifiability and differential privacy is upper bounded by a constant determined by the prior. (2) Identifiability and mutual-information privacy share the same optimal mechanism. (3) The mutual-information optimal mechanism satisfies differential privacy with a level at most a constant away from the optimal level.
The second part studies a market model of trading private data, where a data collector purchases private data from strategic data subjects (individuals) through an incentive mechanism. The value of epsilon units of privacy is measured by the minimum payment such that an individual's equilibrium strategy is to report data in an epsilon-differentially private manner. For the setting with binary private data that represents individuals' knowledge about a common underlying state, asymptotically tight lower and upper bounds on the value of privacy are established as the number of individuals becomes large, and the payment--accuracy tradeoff for learning the state is obtained. The lower bound assures the impossibility of using lower payment to buy epsilon units of privacy, and the upper bound is given by a designed reward mechanism. When the individuals' valuations of privacy are unknown to the data collector, mechanisms with possible negative payments (aiming to penalize individuals with "unacceptably" high privacy valuations) are designed to fulfill the accuracy goal and drive the total payment to zero. For the setting with binary private data following a general joint probability distribution with some symmetry, asymptotically optimal mechanisms are designed in the high data quality regime.
ContributorsWang, Weina (Author) / Ying, Lei (Thesis advisor) / Zhang, Junshan (Thesis advisor) / Scaglione, Anna (Committee member) / Zhang, Yanchao (Committee member) / Arizona State University (Publisher)
Created2016
Description
Modern digital applications have significantly increased the leakage of private and sensitive personal data. While worst-case measures of leakage such as Differential Privacy (DP) provide the strongest guarantees, when utility matters, average-case information-theoretic measures can be more relevant. However, most such information-theoretic measures do not have clear operational meanings. This dissertation addresses this challenge.
This work introduces a tunable leakage measure called maximal $\alpha$-leakage which quantifies the maximal gain of an adversary in inferring any function of a data set. The inferential capability of the adversary is modeled by a class of loss functions, namely, $\alpha$-loss. The choice of $\alpha$ determines specific adversarial actions ranging from refining a belief for $\alpha =1$ to guessing the best posterior for $\alpha = \infty$, and for the two specific values maximal $\alpha$-leakage simplifies to mutual information and maximal leakage, respectively. Maximal $\alpha$-leakage is proved to have a composition property and be robust to side information.
There is a fundamental disjoint between theoretical measures of information leakages and their applications in practice. This issue is addressed in the second part of this dissertation by proposing a data-driven framework for learning Censored and Fair Universal Representations (CFUR) of data. This framework is formulated as a constrained minimax optimization of the expected $\alpha$-loss where the constraint ensures a measure of the usefulness of the representation. The performance of the CFUR framework with $\alpha=1$ is evaluated on publicly accessible data sets; it is shown that multiple sensitive features can be effectively censored to achieve group fairness via demographic parity while ensuring accuracy for several \textit{a priori} unknown downstream tasks.
Finally, focusing on worst-case measures, novel information-theoretic tools are used to refine the existing relationship between two such measures, $(\epsilon,\delta)$-DP and R\'enyi-DP. Applying these tools to the moments accountant framework, one can track the privacy guarantee achieved by adding Gaussian noise to Stochastic Gradient Descent (SGD) algorithms. Relative to state-of-the-art, for the same privacy budget, this method allows about 100 more SGD rounds for training deep learning models.
This work introduces a tunable leakage measure called maximal $\alpha$-leakage which quantifies the maximal gain of an adversary in inferring any function of a data set. The inferential capability of the adversary is modeled by a class of loss functions, namely, $\alpha$-loss. The choice of $\alpha$ determines specific adversarial actions ranging from refining a belief for $\alpha =1$ to guessing the best posterior for $\alpha = \infty$, and for the two specific values maximal $\alpha$-leakage simplifies to mutual information and maximal leakage, respectively. Maximal $\alpha$-leakage is proved to have a composition property and be robust to side information.
There is a fundamental disjoint between theoretical measures of information leakages and their applications in practice. This issue is addressed in the second part of this dissertation by proposing a data-driven framework for learning Censored and Fair Universal Representations (CFUR) of data. This framework is formulated as a constrained minimax optimization of the expected $\alpha$-loss where the constraint ensures a measure of the usefulness of the representation. The performance of the CFUR framework with $\alpha=1$ is evaluated on publicly accessible data sets; it is shown that multiple sensitive features can be effectively censored to achieve group fairness via demographic parity while ensuring accuracy for several \textit{a priori} unknown downstream tasks.
Finally, focusing on worst-case measures, novel information-theoretic tools are used to refine the existing relationship between two such measures, $(\epsilon,\delta)$-DP and R\'enyi-DP. Applying these tools to the moments accountant framework, one can track the privacy guarantee achieved by adding Gaussian noise to Stochastic Gradient Descent (SGD) algorithms. Relative to state-of-the-art, for the same privacy budget, this method allows about 100 more SGD rounds for training deep learning models.
ContributorsLiao, Jiachun (Author) / Sankar, Lalitha (Thesis advisor) / Kosut, Oliver (Committee member) / Zhang, Junshan (Committee member) / Dasarathy, Gautam (Committee member) / Arizona State University (Publisher)
Created2020