6,657 research outputs found

    Privacy Games: Optimal User-Centric Data Obfuscation

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    In this paper, we design user-centric obfuscation mechanisms that impose the minimum utility loss for guaranteeing user's privacy. We optimize utility subject to a joint guarantee of differential privacy (indistinguishability) and distortion privacy (inference error). This double shield of protection limits the information leakage through obfuscation mechanism as well as the posterior inference. We show that the privacy achieved through joint differential-distortion mechanisms against optimal attacks is as large as the maximum privacy that can be achieved by either of these mechanisms separately. Their utility cost is also not larger than what either of the differential or distortion mechanisms imposes. We model the optimization problem as a leader-follower game between the designer of obfuscation mechanism and the potential adversary, and design adaptive mechanisms that anticipate and protect against optimal inference algorithms. Thus, the obfuscation mechanism is optimal against any inference algorithm

    Extremal Mechanisms for Local Differential Privacy

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    Local differential privacy has recently surfaced as a strong measure of privacy in contexts where personal information remains private even from data analysts. Working in a setting where both the data providers and data analysts want to maximize the utility of statistical analyses performed on the released data, we study the fundamental trade-off between local differential privacy and utility. This trade-off is formulated as a constrained optimization problem: maximize utility subject to local differential privacy constraints. We introduce a combinatorial family of extremal privatization mechanisms, which we call staircase mechanisms, and show that it contains the optimal privatization mechanisms for a broad class of information theoretic utilities such as mutual information and ff-divergences. We further prove that for any utility function and any privacy level, solving the privacy-utility maximization problem is equivalent to solving a finite-dimensional linear program, the outcome of which is the optimal staircase mechanism. However, solving this linear program can be computationally expensive since it has a number of variables that is exponential in the size of the alphabet the data lives in. To account for this, we show that two simple privatization mechanisms, the binary and randomized response mechanisms, are universally optimal in the low and high privacy regimes, and well approximate the intermediate regime.Comment: 52 pages, 10 figures in JMLR 201

    Selling Privacy at Auction

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    We initiate the study of markets for private data, though the lens of differential privacy. Although the purchase and sale of private data has already begun on a large scale, a theory of privacy as a commodity is missing. In this paper, we propose to build such a theory. Specifically, we consider a setting in which a data analyst wishes to buy information from a population from which he can estimate some statistic. The analyst wishes to obtain an accurate estimate cheaply. On the other hand, the owners of the private data experience some cost for their loss of privacy, and must be compensated for this loss. Agents are selfish, and wish to maximize their profit, so our goal is to design truthful mechanisms. Our main result is that such auctions can naturally be viewed and optimally solved as variants of multi-unit procurement auctions. Based on this result, we derive auctions for two natural settings which are optimal up to small constant factors: 1. In the setting in which the data analyst has a fixed accuracy goal, we show that an application of the classic Vickrey auction achieves the analyst's accuracy goal while minimizing his total payment. 2. In the setting in which the data analyst has a fixed budget, we give a mechanism which maximizes the accuracy of the resulting estimate while guaranteeing that the resulting sum payments do not exceed the analysts budget. In both cases, our comparison class is the set of envy-free mechanisms, which correspond to the natural class of fixed-price mechanisms in our setting. In both of these results, we ignore the privacy cost due to possible correlations between an individuals private data and his valuation for privacy itself. We then show that generically, no individually rational mechanism can compensate individuals for the privacy loss incurred due to their reported valuations for privacy.Comment: Extended Abstract appeared in the proceedings of EC 201

    Truthful Mechanisms for Agents that Value Privacy

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    Recent work has constructed economic mechanisms that are both truthful and differentially private. In these mechanisms, privacy is treated separately from the truthfulness; it is not incorporated in players' utility functions (and doing so has been shown to lead to non-truthfulness in some cases). In this work, we propose a new, general way of modelling privacy in players' utility functions. Specifically, we only assume that if an outcome oo has the property that any report of player ii would have led to oo with approximately the same probability, then oo has small privacy cost to player ii. We give three mechanisms that are truthful with respect to our modelling of privacy: for an election between two candidates, for a discrete version of the facility location problem, and for a general social choice problem with discrete utilities (via a VCG-like mechanism). As the number nn of players increases, the social welfare achieved by our mechanisms approaches optimal (as a fraction of nn)

    Budget Feasible Mechanisms for Experimental Design

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    In the classical experimental design setting, an experimenter E has access to a population of nn potential experiment subjects i{1,...,n}i\in \{1,...,n\}, each associated with a vector of features xiRdx_i\in R^d. Conducting an experiment with subject ii reveals an unknown value yiRy_i\in R to E. E typically assumes some hypothetical relationship between xix_i's and yiy_i's, e.g., yiβxiy_i \approx \beta x_i, and estimates β\beta from experiments, e.g., through linear regression. As a proxy for various practical constraints, E may select only a subset of subjects on which to conduct the experiment. We initiate the study of budgeted mechanisms for experimental design. In this setting, E has a budget BB. Each subject ii declares an associated cost ci>0c_i >0 to be part of the experiment, and must be paid at least her cost. In particular, the Experimental Design Problem (EDP) is to find a set SS of subjects for the experiment that maximizes V(S) = \log\det(I_d+\sum_{i\in S}x_i\T{x_i}) under the constraint iSciB\sum_{i\in S}c_i\leq B; our objective function corresponds to the information gain in parameter β\beta that is learned through linear regression methods, and is related to the so-called DD-optimality criterion. Further, the subjects are strategic and may lie about their costs. We present a deterministic, polynomial time, budget feasible mechanism scheme, that is approximately truthful and yields a constant factor approximation to EDP. In particular, for any small δ>0\delta > 0 and ϵ>0\epsilon > 0, we can construct a (12.98, ϵ\epsilon)-approximate mechanism that is δ\delta-truthful and runs in polynomial time in both nn and loglogBϵδ\log\log\frac{B}{\epsilon\delta}. We also establish that no truthful, budget-feasible algorithms is possible within a factor 2 approximation, and show how to generalize our approach to a wide class of learning problems, beyond linear regression
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