Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Model Selection for High Dimensional Quadratic Regression via
  Regularization   Quadratic regression (QR) models naturally extend linear models by
considering interaction effects between the covariates. To conduct model
selection in QR, it is important to maintain the hierarchical model structure
between main effects and interaction effects. Existing regularization methods
generally achieve this goal by solving complex optimization problems, which
usually demands high computational cost and hence are not feasible for high
dimensional data. This paper focuses on scalable regularization methods for
model selection in high dimensional QR. We first consider two-stage
regularization methods and establish theoretical properties of the two-stage
LASSO. Then, a new regularization method, called Regularization Algorithm under
Marginality Principle (RAMP), is proposed to compute a hierarchy-preserving
regularization solution path efficiently. Both methods are further extended to
solve generalized QR models. Numerical results are also shown to demonstrate
performance of the methods.

9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th