Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: PrivTree: A Differentially Private Algorithm for Hierarchical
  Decompositions   Given a set D of tuples defined on a domain Omega, we study differentially
private algorithms for constructing a histogram over Omega to approximate the
tuple distribution in D. Existing solutions for the problem mostly adopt a
hierarchical decomposition approach, which recursively splits Omega into
sub-domains and computes a noisy tuple count for each sub-domain, until all
noisy counts are below a certain threshold. This approach, however, requires
that we (i) impose a limit h on the recursion depth in the splitting of Omega
and (ii) set the noise in each count to be proportional to h. This leads to
inferior data utility due to the following dilemma: if we use a small h, then
the resulting histogram would be too coarse-grained to provide an accurate
approximation of data distribution; meanwhile, a large h would yield a
fine-grained histogram, but its quality would be severely degraded by the
increased amount of noise in the tuple counts.
  To remedy the deficiency of existing solutions, we present PrivTree, a
histogram construction algorithm that also applies hierarchical decomposition
but features a crucial (and somewhat surprising) improvement: when deciding
whether or not to split a sub-domain, the amount of noise required in the
corresponding tuple count is independent of the recursive depth. This enables
PrivTree to adaptively generate high-quality histograms without even asking for
a pre-defined threshold on the depth of sub-domain splitting. As concrete
examples, we demonstrate an application of PrivTree in modelling spatial data,
and show that it can also be extended to handle sequence data (where the
decision in sub-domain splitting is not based on tuple counts but a more
sophisticated measure). Our experiments on a variety of real datasets show that
PrivTree significantly outperforms the states of the art in terms of data
utility.

20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con