1,148 research outputs found
An Adaptive Mechanism for Accurate Query Answering under Differential Privacy
We propose a novel mechanism for answering sets of count- ing queries under
differential privacy. Given a workload of counting queries, the mechanism
automatically selects a different set of "strategy" queries to answer
privately, using those answers to derive answers to the workload. The main
algorithm proposed in this paper approximates the optimal strategy for any
workload of linear counting queries. With no cost to the privacy guarantee, the
mechanism improves significantly on prior approaches and achieves near-optimal
error for many workloads, when applied under (\epsilon, \delta)-differential
privacy. The result is an adaptive mechanism which can help users achieve good
utility without requiring that they reason carefully about the best formulation
of their task.Comment: VLDB2012. arXiv admin note: substantial text overlap with
arXiv:1103.136
Linear and Range Counting under Metric-based Local Differential Privacy
Local differential privacy (LDP) enables private data sharing and analytics
without the need for a trusted data collector. Error-optimal primitives (for,
e.g., estimating means and item frequencies) under LDP have been well studied.
For analytical tasks such as range queries, however, the best known error bound
is dependent on the domain size of private data, which is potentially
prohibitive. This deficiency is inherent as LDP protects the same level of
indistinguishability between any pair of private data values for each data
downer.
In this paper, we utilize an extension of -LDP called Metric-LDP or
-LDP, where a metric defines heterogeneous privacy guarantees for
different pairs of private data values and thus provides a more flexible knob
than does to relax LDP and tune utility-privacy trade-offs. We show
that, under such privacy relaxations, for analytical workloads such as linear
counting, multi-dimensional range counting queries, and quantile queries, we
can achieve significant gains in utility. In particular, for range queries
under -LDP where the metric is the -distance function scaled by
, we design mechanisms with errors independent on the domain sizes;
instead, their errors depend on the metric , which specifies in what
granularity the private data is protected. We believe that the primitives we
design for -LDP will be useful in developing mechanisms for other analytical
tasks, and encourage the adoption of LDP in practice
Optimizing Batch Linear Queries under Exact and Approximate Differential Privacy
Differential privacy is a promising privacy-preserving paradigm for
statistical query processing over sensitive data. It works by injecting random
noise into each query result, such that it is provably hard for the adversary
to infer the presence or absence of any individual record from the published
noisy results. The main objective in differentially private query processing is
to maximize the accuracy of the query results, while satisfying the privacy
guarantees. Previous work, notably \cite{LHR+10}, has suggested that with an
appropriate strategy, processing a batch of correlated queries as a whole
achieves considerably higher accuracy than answering them individually.
However, to our knowledge there is currently no practical solution to find such
a strategy for an arbitrary query batch; existing methods either return
strategies of poor quality (often worse than naive methods) or require
prohibitively expensive computations for even moderately large domains.
Motivated by this, we propose low-rank mechanism (LRM), the first practical
differentially private technique for answering batch linear queries with high
accuracy. LRM works for both exact (i.e., -) and approximate (i.e.,
(, )-) differential privacy definitions. We derive the
utility guarantees of LRM, and provide guidance on how to set the privacy
parameters given the user's utility expectation. Extensive experiments using
real data demonstrate that our proposed method consistently outperforms
state-of-the-art query processing solutions under differential privacy, by
large margins.Comment: ACM Transactions on Database Systems (ACM TODS). arXiv admin note:
text overlap with arXiv:1212.230
Convex Optimization for Linear Query Processing under Approximate Differential Privacy
Differential privacy enables organizations to collect accurate aggregates
over sensitive data with strong, rigorous guarantees on individuals' privacy.
Previous work has found that under differential privacy, computing multiple
correlated aggregates as a batch, using an appropriate \emph{strategy}, may
yield higher accuracy than computing each of them independently. However,
finding the best strategy that maximizes result accuracy is non-trivial, as it
involves solving a complex constrained optimization program that appears to be
non-linear and non-convex. Hence, in the past much effort has been devoted in
solving this non-convex optimization program. Existing approaches include
various sophisticated heuristics and expensive numerical solutions. None of
them, however, guarantees to find the optimal solution of this optimization
problem.
This paper points out that under (, )-differential privacy,
the optimal solution of the above constrained optimization problem in search of
a suitable strategy can be found, rather surprisingly, by solving a simple and
elegant convex optimization program. Then, we propose an efficient algorithm
based on Newton's method, which we prove to always converge to the optimal
solution with linear global convergence rate and quadratic local convergence
rate. Empirical evaluations demonstrate the accuracy and efficiency of the
proposed solution.Comment: to appear in ACM SIGKDD 201
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