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Group-Sparse Regression Using the Covariance Fitting Criterion

Kronvall, Ted LU ; Adalbjörnsson, Stefan Ingi LU ; Nadig, Santhosh and Jakobsson, Andreas LU (2017) In Signal Processing 139. p.116-130
Abstract

In this work, we present a novel formulation for efficient estimation of group-sparse regression problems. By relaxing a covariance fitting criteria commonly used in array signal processing, we derive a generalization of the recent SPICE method for grouped variables. Such a formulation circumvents cumbersome model order estimation, while being inherently hyperparameter-free. We derive an implementation which iteratively decomposes into a series of convex optimization problems, each being solvable in closed-form. Furthermore, we show the connection between the proposed estimator and the class of LASSO-type estimators, where a dictionary-dependent regularization level is inherently set by the covariance fitting criteria. We also show how... (More)

In this work, we present a novel formulation for efficient estimation of group-sparse regression problems. By relaxing a covariance fitting criteria commonly used in array signal processing, we derive a generalization of the recent SPICE method for grouped variables. Such a formulation circumvents cumbersome model order estimation, while being inherently hyperparameter-free. We derive an implementation which iteratively decomposes into a series of convex optimization problems, each being solvable in closed-form. Furthermore, we show the connection between the proposed estimator and the class of LASSO-type estimators, where a dictionary-dependent regularization level is inherently set by the covariance fitting criteria. We also show how the proposed estimator may be used to form group-sparse estimates for sparse groups, as well as validating its robustness against coherency in the dictionary, i.e., the case of overlapping dictionary groups. Numerical results show preferable estimation performance, on par with a group-LASSO bestowed with oracle regularization, and well exceeding comparable greedy estimation methods.

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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Convex optimization, Covariance fitting, Group sparsity, Group-LASSO, Hyperparameter-free, SPICE
in
Signal Processing
volume
139
pages
15 pages
publisher
Elsevier
external identifiers
  • scopus:85018743100
  • wos:000402214200013
  • scopus:85017960022
ISSN
0165-1684
DOI
10.1016/j.sigpro.2017.03.025
language
English
LU publication?
yes
id
ef7c6723-9eea-4b0e-aeca-9d00be69fc64
date added to LUP
2017-05-11 14:00:04
date last changed
2018-01-07 12:03:19
@article{ef7c6723-9eea-4b0e-aeca-9d00be69fc64,
  abstract     = {<p>In this work, we present a novel formulation for efficient estimation of group-sparse regression problems. By relaxing a covariance fitting criteria commonly used in array signal processing, we derive a generalization of the recent SPICE method for grouped variables. Such a formulation circumvents cumbersome model order estimation, while being inherently hyperparameter-free. We derive an implementation which iteratively decomposes into a series of convex optimization problems, each being solvable in closed-form. Furthermore, we show the connection between the proposed estimator and the class of LASSO-type estimators, where a dictionary-dependent regularization level is inherently set by the covariance fitting criteria. We also show how the proposed estimator may be used to form group-sparse estimates for sparse groups, as well as validating its robustness against coherency in the dictionary, i.e., the case of overlapping dictionary groups. Numerical results show preferable estimation performance, on par with a group-LASSO bestowed with oracle regularization, and well exceeding comparable greedy estimation methods.</p>},
  author       = {Kronvall, Ted and Adalbjörnsson, Stefan Ingi and Nadig, Santhosh and Jakobsson, Andreas},
  issn         = {0165-1684},
  keyword      = {Convex optimization,Covariance fitting,Group sparsity,Group-LASSO,Hyperparameter-free,SPICE},
  language     = {eng},
  pages        = {116--130},
  publisher    = {Elsevier},
  series       = {Signal Processing},
  title        = {Group-Sparse Regression Using the Covariance Fitting Criterion},
  url          = {http://dx.doi.org/10.1016/j.sigpro.2017.03.025},
  volume       = {139},
  year         = {2017},
}