6,657 research outputs found
Privacy Games: Optimal User-Centric Data Obfuscation
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
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 -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
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
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 has the property
that any report of player would have led to with approximately the same
probability, then has small privacy cost to player . 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 of players increases,
the social welfare achieved by our mechanisms approaches optimal (as a fraction
of )
Budget Feasible Mechanisms for Experimental Design
In the classical experimental design setting, an experimenter E has access to
a population of potential experiment subjects , each
associated with a vector of features . Conducting an experiment
with subject reveals an unknown value to E. E typically assumes
some hypothetical relationship between 's and 's, e.g., , and estimates 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 . Each subject declares an associated cost 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 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 ; our objective
function corresponds to the information gain in parameter that is
learned through linear regression methods, and is related to the so-called
-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 and , we can construct a (12.98, )-approximate mechanism that is
-truthful and runs in polynomial time in both and
. 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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