Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The composite absolute penalties family for grouped and hierarchical
  variable selection   Extracting useful information from high-dimensional data is an important
focus of today's statistical research and practice. Penalized loss function
minimization has been shown to be effective for this task both theoretically
and empirically. With the virtues of both regularization and sparsity, the
$L_1$-penalized squared error minimization method Lasso has been popular in
regression models and beyond. In this paper, we combine different norms
including $L_1$ to form an intelligent penalty in order to add side information
to the fitting of a regression or classification model to obtain reasonable
estimates. Specifically, we introduce the Composite Absolute Penalties (CAP)
family, which allows given grouping and hierarchical relationships between the
predictors to be expressed. CAP penalties are built by defining groups and
combining the properties of norm penalties at the across-group and within-group
levels. Grouped selection occurs for nonoverlapping groups. Hierarchical
variable selection is reached by defining groups with particular overlapping
patterns. We propose using the BLASSO and cross-validation to compute CAP
estimates in general. For a subfamily of CAP estimates involving only the $L_1$
and $L_{\infty}$ norms, we introduce the iCAP algorithm to trace the entire
regularization path for the grouped selection problem. Within this subfamily,
unbiased estimates of the degrees of freedom (df) are derived so that the
regularization parameter is selected without cross-validation. CAP is shown to
improve on the predictive performance of the LASSO in a series of simulated
experiments, including cases with $p\gg n$ and possibly mis-specified
groupings. When the complexity of a model is properly calculated, iCAP is seen
to be parsimonious in the experiments.

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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-lat
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The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: ao-sci
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The categories of this paper are: nlin