Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Sample Complexity of Privately Learning Unbounded
  High-Dimensional Gaussians   We provide sample complexity upper bounds for agnostically learning
multivariate Gaussians under the constraint of approximate differential
privacy. These are the first finite sample upper bounds for general Gaussians
which do not impose restrictions on the parameters of the distribution. Our
bounds are near-optimal in the case when the covariance is known to be the
identity, and conjectured to be near-optimal in the general case. From a
technical standpoint, we provide analytic tools for arguing the existence of
global "locally small" covers from local covers of the space. These are
exploited using modifications of recent techniques for differentially private
hypothesis selection. Our techniques may prove useful for privately learning
other distribution classes which do not possess a finite cover.

30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
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The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg