Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Differentially Private High Dimensional Sparse Covariance Matrix
  Estimation   In this paper, we study the problem of estimating the covariance matrix under
differential privacy, where the underlying covariance matrix is assumed to be
sparse and of high dimensions. We propose a new method, called DP-Thresholding,
to achieve a non-trivial $\ell_2$-norm based error bound, which is
significantly better than the existing ones from adding noise directly to the
empirical covariance matrix. We also extend the $\ell_2$-norm based error bound
to a general $\ell_w$-norm based one for any $1\leq w\leq \infty$, and show
that they share the same upper bound asymptotically. Our approach can be easily
extended to local differential privacy. Experiments on the synthetic datasets
show consistent results with our theoretical claims.

25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg