Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Efficient Lipschitz Extensions for High-Dimensional Graph Statistics and
  Node Private Degree Distributions   Lipschitz extensions were recently proposed as a tool for designing node
differentially private algorithms. However, efficiently computable Lipschitz
extensions were known only for 1-dimensional functions (that is, functions that
output a single real value). In this paper, we study efficiently computable
Lipschitz extensions for multi-dimensional (that is, vector-valued) functions
on graphs. We show that, unlike for 1-dimensional functions, Lipschitz
extensions of higher-dimensional functions on graphs do not always exist, even
with a non-unit stretch. We design Lipschitz extensions with small stretch for
the sorted degree list and for the degree distribution of a graph. Crucially,
our extensions are efficiently computable.
  We also develop new tools for employing Lipschitz extensions in the design of
differentially private algorithms. Specifically, we generalize the exponential
mechanism, a widely used tool in data privacy. The exponential mechanism is
given a collection of score functions that map datasets to real values. It
attempts to return the name of the function with nearly minimum value on the
data set. Our generalized exponential mechanism provides better accuracy when
the sensitivity of an optimal score function is much smaller than the maximum
sensitivity of score functions.
  We use our Lipschitz extension and the generalized exponential mechanism to
design a node-differentially private algorithm for releasing an approximation
to the degree distribution of a graph. Our algorithm is much more accurate than
algorithms from previous work.

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The categories of this paper are: comp-gas
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ph
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The categories of this paper are: funct-an
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The categories of this paper are: atom-ph
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The categories of this paper are: q-fin
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-lat
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The categories of this paper are: q-alg
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The categories of this paper are: alg-geom
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The categories of this paper are: eess
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-bio