Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lower Bounds for Differential Privacy from Gaussian Width   We study the optimal sample complexity of a given workload of linear queries
under the constraints of differential privacy. The sample complexity of a query
answering mechanism under error parameter $\alpha$ is the smallest $n$ such
that the mechanism answers the workload with error at most $\alpha$ on any
database of size $n$. Following a line of research started by Hardt and Talwar
[STOC 2010], we analyze sample complexity using the tools of asymptotic convex
geometry. We study the sensitivity polytope, a natural convex body associated
with a query workload that quantifies how query answers can change between
neighboring databases. This is the information that, roughly speaking, is
protected by a differentially private algorithm, and, for this reason, we
expect that a "bigger" sensitivity polytope implies larger sample complexity.
Our results identify the mean Gaussian width as an appropriate measure of the
size of the polytope, and show sample complexity lower bounds in terms of this
quantity. Our lower bounds completely characterize the workloads for which the
Gaussian noise mechanism is optimal up to constants as those having
asymptotically maximal Gaussian width.
  Our techniques also yield an alternative proof of Pisier's Volume Number
Theorem which also suggests an approach to improving the parameters of the
theorem.

2
The categories of this paper are: math
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat