90 research outputs found
Non-Stochastic Hypothesis Testing with Application to Privacy Against Hypothesis-Testing Adversary
In this paper, we consider privacy against hypothesis testing adversaries
within a non-stochastic framework. We develop a theory of non-stochastic
hypothesis testing by borrowing the notion of uncertain variables from
non-stochastic information theory. We define tests as binary-valued mappings on
uncertain variables and prove a fundamental bound on the best performance of
tests in non-stochastic hypothesis testing. We use this bound to develop a
measure of privacy. We then construct reporting policies with prescribed
privacy and utility guarantees. The utility of a reporting policy is measured
by the distance between the reported and original values. We illustrate the
effects of using such privacy-preserving reporting polices on a
publicly-available practical dataset of preferences and demographics of young
individuals, aged between 15-30, with Slovakian nationality
Development and Analysis of Deterministic Privacy-Preserving Policies Using Non-Stochastic Information Theory
A deterministic privacy metric using non-stochastic information theory is
developed. Particularly, minimax information is used to construct a measure of
information leakage, which is inversely proportional to the measure of privacy.
Anyone can submit a query to a trusted agent with access to a non-stochastic
uncertain private dataset. Optimal deterministic privacy-preserving policies
for responding to the submitted query are computed by maximizing the measure of
privacy subject to a constraint on the worst-case quality of the response
(i.e., the worst-case difference between the response by the agent and the
output of the query computed on the private dataset). The optimal
privacy-preserving policy is proved to be a piecewise constant function in the
form of a quantization operator applied on the output of the submitted query.
The measure of privacy is also used to analyze the performance of -anonymity
methodology (a popular deterministic mechanism for privacy-preserving release
of datasets using suppression and generalization techniques), proving that it
is in fact not privacy-preserving.Comment: improved introduction and numerical exampl
Ensuring Privacy with Constrained Additive Noise by Minimizing Fisher Information
The problem of preserving the privacy of individual entries of a database
when responding to linear or nonlinear queries with constrained additive noise
is considered. For privacy protection, the response to the query is
systematically corrupted with an additive random noise whose support is a
subset or equal to a pre-defined constraint set. A measure of privacy using the
inverse of the trace of the Fisher information matrix is developed. The
Cramer-Rao bound relates the variance of any estimator of the database entries
to the introduced privacy measure. The probability density that minimizes the
trace of the Fisher information (as a proxy for maximizing the measure of
privacy) is computed. An extension to dynamic problems is also presented.
Finally, the results are compared to the differential privacy methodology
A Study of Truck Platooning Incentives Using a Congestion Game
We introduce an atomic congestion game with two types of agents, cars and
trucks, to model the traffic flow on a road over various time intervals of the
day. Cars maximize their utility by finding a trade-off between the time they
choose to use the road, the average velocity of the flow at that time, and the
dynamic congestion tax that they pay for using the road. In addition to these
terms, the trucks have an incentive for using the road at the same time as
their peers because they have platooning capabilities, which allow them to save
fuel. The dynamics and equilibria of this game-theoretic model for the
interaction between car traffic and truck platooning incentives are
investigated. We use traffic data from Stockholm to validate parts of the
modeling assumptions and extract reasonable parameters for the simulations. We
use joint strategy fictitious play and average strategy fictitious play to
learn a pure strategy Nash equilibrium of this game. We perform a comprehensive
simulation study to understand the influence of various factors, such as the
drivers' value of time and the percentage of the trucks that are equipped with
platooning devices, on the properties of the Nash equilibrium.Comment: Updated Introduction; Improved Literature Revie
Privacy-Preserving Public Release of Datasets for Support Vector Machine Classification
We consider the problem of publicly releasing a dataset for support vector
machine classification while not infringing on the privacy of data subjects
(i.e., individuals whose private information is stored in the dataset). The
dataset is systematically obfuscated using an additive noise for privacy
protection. Motivated by the Cramer-Rao bound, inverse of the trace of the
Fisher information matrix is used as a measure of the privacy. Conditions are
established for ensuring that the classifier extracted from the original
dataset and the obfuscated one are close to each other (capturing the utility).
The optimal noise distribution is determined by maximizing a weighted sum of
the measures of privacy and utility. The optimal privacy-preserving noise is
proved to achieve local differential privacy. The results are generalized to a
broader class of optimization-based supervised machine learning algorithms.
Applicability of the methodology is demonstrated on multiple datasets
Distributionally-Robust Optimization with Noisy Data for Discrete Uncertainties Using Total Variation Distance
Stochastic programs where the uncertainty distribution must be inferred from
noisy data samples are considered. The stochastic programs are approximated
with distributionally-robust optimizations that minimize the worst-case
expected cost over ambiguity sets, i.e., sets of distributions that are
sufficiently compatible with the observed data. In this paper, the ambiguity
sets capture the set of probability distributions whose convolution with the
noise distribution remains within a ball centered at the empirical noisy
distribution of data samples parameterized by the total variation distance.
Using the prescribed ambiguity set, the solutions of the
distributionally-robust optimizations converge to the solutions of the original
stochastic programs when the numbers of the data samples grow to infinity.
Therefore, the proposed distributionally-robust optimization problems are
asymptotically consistent. This is proved under the assumption that the
distribution of the noise is uniformly diagonally dominant. More importantly,
the distributionally-robust optimization problems can be cast as tractable
convex optimization problems and are therefore amenable to large-scale
stochastic problems
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