Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Group-Sparse Model Selection: Hardness and Relaxations   Group-based sparsity models are proven instrumental in linear regression
problems for recovering signals from much fewer measurements than standard
compressive sensing. The main promise of these models is the recovery of
"interpretable" signals through the identification of their constituent groups.
In this paper, we establish a combinatorial framework for group-model selection
problems and highlight the underlying tractability issues. In particular, we
show that the group-model selection problem is equivalent to the well-known
NP-hard weighted maximum coverage problem (WMC). Leveraging a graph-based
understanding of group models, we describe group structures which enable
correct model selection in polynomial time via dynamic programming.
Furthermore, group structures that lead to totally unimodular constraints have
tractable discrete as well as convex relaxations. We also present a
generalization of the group-model that allows for within group sparsity, which
can be used to model hierarchical sparsity. Finally, we study the Pareto
frontier of group-sparse approximations for two tractable models, among which
the tree sparsity model, and illustrate selection and computation trade-offs
between our framework and the existing convex relaxations.

3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin