541 research outputs found
Renyi Differential Privacy
We propose a natural relaxation of differential privacy based on the Renyi
divergence. Closely related notions have appeared in several recent papers that
analyzed composition of differentially private mechanisms. We argue that the
useful analytical tool can be used as a privacy definition, compactly and
accurately representing guarantees on the tails of the privacy loss.
We demonstrate that the new definition shares many important properties with
the standard definition of differential privacy, while additionally allowing
tighter analysis of composite heterogeneous mechanisms
Concentrated Differential Privacy: Simplifications, Extensions, and Lower Bounds
"Concentrated differential privacy" was recently introduced by Dwork and
Rothblum as a relaxation of differential privacy, which permits sharper
analyses of many privacy-preserving computations. We present an alternative
formulation of the concept of concentrated differential privacy in terms of the
Renyi divergence between the distributions obtained by running an algorithm on
neighboring inputs. With this reformulation in hand, we prove sharper
quantitative results, establish lower bounds, and raise a few new questions. We
also unify this approach with approximate differential privacy by giving an
appropriate definition of "approximate concentrated differential privacy.
Hypothesis Testing Interpretations and Renyi Differential Privacy
Differential privacy is a de facto standard in data privacy, with
applications in the public and private sectors. A way to explain differential
privacy, which is particularly appealing to statistician and social scientists
is by means of its statistical hypothesis testing interpretation. Informally,
one cannot effectively test whether a specific individual has contributed her
data by observing the output of a private mechanism---any test cannot have both
high significance and high power.
In this paper, we identify some conditions under which a privacy definition
given in terms of a statistical divergence satisfies a similar interpretation.
These conditions are useful to analyze the distinguishability power of
divergences and we use them to study the hypothesis testing interpretation of
some relaxations of differential privacy based on Renyi divergence. This
analysis also results in an improved conversion rule between these definitions
and differential privacy
Revealing Network Structure, Confidentially: Improved Rates for Node-Private Graphon Estimation
Motivated by growing concerns over ensuring privacy on social networks, we
develop new algorithms and impossibility results for fitting complex
statistical models to network data subject to rigorous privacy guarantees. We
consider the so-called node-differentially private algorithms, which compute
information about a graph or network while provably revealing almost no
information about the presence or absence of a particular node in the graph.
We provide new algorithms for node-differentially private estimation for a
popular and expressive family of network models: stochastic block models and
their generalization, graphons. Our algorithms improve on prior work, reducing
their error quadratically and matching, in many regimes, the optimal nonprivate
algorithm. We also show that for the simplest random graph models ( and
), node-private algorithms can be qualitatively more accurate than for
more complex models---converging at a rate of
instead of . This result uses a new extension lemma
for differentially private algorithms that we hope will be broadly useful
Truncated Laplace and Gaussian mechanisms of RDP
The Laplace mechanism and the Gaussian mechanism are primary mechanisms in
differential privacy, widely applicable to many scenarios involving numerical
data. However, due to the infinite-range random variables they generate, the
Laplace and Gaussian mechanisms may return values that are semantically
impossible, such as negative numbers. To address this issue, we have designed
the truncated Laplace mechanism and Gaussian mechanism. For a given truncation
interval [a, b], the truncated Gaussian mechanism ensures the same Renyi
Differential Privacy (RDP) as the untruncated mechanism, regardless of the
values chosen for the truncation interval [a, b]. Similarly, the truncated
Laplace mechanism, for specified interval [a, b], maintains the same RDP as the
untruncated mechanism. We provide the RDP expressions for each of them. We
believe that our study can further enhance the utility of differential privacy
in specific applications
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