Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Structured Sparsity: Discrete and Convex approaches   Compressive sensing (CS) exploits sparsity to recover sparse or compressible
signals from dimensionality reducing, non-adaptive sensing mechanisms. Sparsity
is also used to enhance interpretability in machine learning and statistics
applications: While the ambient dimension is vast in modern data analysis
problems, the relevant information therein typically resides in a much lower
dimensional space. However, many solutions proposed nowadays do not leverage
the true underlying structure. Recent results in CS extend the simple sparsity
idea to more sophisticated {\em structured} sparsity models, which describe the
interdependency between the nonzero components of a signal, allowing to
increase the interpretability of the results and lead to better recovery
performance. In order to better understand the impact of structured sparsity,
in this chapter we analyze the connections between the discrete models and
their convex relaxations, highlighting their relative advantages. We start with
the general group sparse model and then elaborate on two important special
cases: the dispersive and the hierarchical models. For each, we present the
models in their discrete nature, discuss how to solve the ensuing discrete
problems and then describe convex relaxations. We also consider more general
structures as defined by set functions and present their convex proxies.
Further, we discuss efficient optimization solutions for structured sparsity
problems and illustrate structured sparsity in action via three applications.

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The categories of this paper are: eess
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga