Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Robust Mean Estimation in High Dimensions: An Outlier Fraction Agnostic
  and Efficient Algorithm   We study the robust mean estimation problem in high dimensions, where less
than half of the datapoints can be arbitrarily corrupted. Motivated by
compressive sensing, we formulate the robust mean estimation problem as the
minimization of the $\ell_0$-`norm' of an \emph{outlier indicator vector},
under a second moment constraint on the datapoints. We further relax the
$\ell_0$-`norm' to the $\ell_p$-norm ($0<p\leq 1$) in the objective and prove
that the global minima for each of these objectives are order-optimal for the
robust mean estimation problem. Then we propose a computationally tractable
iterative $\ell_p$-minimization and hard thresholding algorithm that outputs an
order-optimal robust estimate of the population mean. Both synthetic and real
data experiments demonstrate that the proposed algorithm outperforms
state-of-the-art robust mean estimation methods.

30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an