Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Subset Selection with Shrinkage: Sparse Linear Modeling when the SNR is
  low   We study a seemingly unexpected and relatively less understood overfitting
aspect of a fundamental tool in sparse linear modeling - best subset selection,
which minimizes the residual sum of squares subject to a constraint on the
number of nonzero coefficients. While the best subset selection procedure is
often perceived as the "gold standard" in sparse learning when the signal to
noise ratio (SNR) is high, its predictive performance deteriorates when the SNR
is low. In particular, it is outperformed by continuous shrinkage methods, such
as ridge regression and the Lasso. We investigate the behavior of best subset
selection in the high-noise regimes and propose an alternative approach based
on a regularized version of the least-squares criterion. Our proposed
estimators (a) mitigate, to a large extent, the poor predictive performance of
best subset selection in the high-noise regimes; and (b) perform favorably,
while generally delivering substantially sparser models, relative to the best
predictive models available via ridge regression and the Lasso. We conduct an
extensive theoretical analysis of the predictive properties of the proposed
approach and provide justification for its superior predictive performance
relative to best subset selection when the noise-level is high. Our estimators
can be expressed as solutions to mixed integer second order conic optimization
problems and, hence, are amenable to modern computational tools from
mathematical optimization.

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The categories of this paper are: physics
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The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
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The categories of this paper are: hep-lat
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The categories of this paper are: eess
12
The categories of this paper are: nucl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: cmp-lg
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The categories of this paper are: nlin
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The categories of this paper are: alg-geom
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The categories of this paper are: atom-ph