Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sparse PCA from Sparse Linear Regression   Sparse Principal Component Analysis (SPCA) and Sparse Linear Regression (SLR)
have a wide range of applications and have attracted a tremendous amount of
attention in the last two decades as canonical examples of statistical problems
in high dimension. A variety of algorithms have been proposed for both SPCA and
SLR, but an explicit connection between the two had not been made. We show how
to efficiently transform a black-box solver for SLR into an algorithm for SPCA:
assuming the SLR solver satisfies prediction error guarantees achieved by
existing efficient algorithms such as those based on the Lasso, the SPCA
algorithm derived from it achieves near state of the art guarantees for testing
and for support recovery for the single spiked covariance model as obtained by
the current best polynomialtime algorithms. Our reduction not only highlights
the inherent similarity between the two problems, but also, from a practical
standpoint, allows one to obtain a collection of algorithms for SPCA directly
from known algorithms for SLR. We provide experimental results on simulated
data comparing our proposed framework to other algorithms for SPCA.

22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int