Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: High-dimensional nonconvex lasso-type $M$-estimators   This paper proposes a theory for $\ell_1$-norm penalized high-dimensional
$M$-estimators, with nonconvex risk and unrestricted domain. Under high-level
conditions, the estimators are shown to attain the rate of convergence
$s_0\sqrt{\log(nd)/n}$, where $s_0$ is the number of nonzero coefficients of
the parameter of interest. Sufficient conditions for our main assumptions are
then developed and finally used in several examples including robust linear
regression, binary classification and nonlinear least squares.

17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph