| 1. |
- Kronvall, Ted, et al.
(author)
-
Group-Sparse Regression Using the Covariance Fitting Criterion
- 2017
-
In: Signal Processing. - : Elsevier BV. - 0165-1684. ; 139, s. 116-130
-
Journal article (peer-reviewed)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 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.
|
|
| 2. |
- Kronvall, Ted, et al.
(author)
-
Hyperparameter-free sparse regression of grouped variables
- 2017
-
In: Conference Record of the 50th Asilomar Conference on Signals, Systems and Computers, ACSSC 2016. - 9781538639542 ; , s. 394-398
-
Conference paper (peer-reviewed)abstract
- In this paper, we introduce a novel framework for semi-parametric estimation of an unknown number of signals, each parametrized by a group of components. Via a reformulation of the covariance fitting criteria, we formulate a convex optimization problem over a grid of candidate representations, promoting solutions with only a few active groups. Utilizing the covariance fitting allows for a hyperparameter-free estimation procedure, highly robust against coherency between candidates, while still allowing for a computationally efficient implementation. Numerical simulations illustrate how the proposed method offers a performance similar to the group-LASSO for incoherent dictionaries, and superior performance for coherent dictionaries.
|
|
| 3. |
- Kronvall, Ted, et al.
(author)
-
Online group-sparse estimation using the covariance fitting criterion
- 2017
-
In: 25th European Signal Processing Conference, EUSIPCO 2017. - 9780992862671 ; , s. 2101-2105
-
Conference paper (peer-reviewed)abstract
- In this paper, we present a time-recursive implementation of a recent hyperparameter-free group-sparse estimation technique. This is achieved by reformulating the original method, termed group-SPICE, as a square-root group-LASSO with a suitable regularization level, for which a time-recursive implementation is derived. Using a proximal gradient step for lowering the computational cost, the proposed method may effectively cope with data sequences consisting of both stationary and non-stationary signals, such as transients, and/or amplitude modulated signals. Numerical examples illustrates the efficacy of the proposed method for both coherent Gaussian dictionaries and for the multi-pitch estimation problem.
|
|
| 4. |
- Kronvall, Ted, et al.
(author)
-
Online Group-Sparse Regression Using the Covariance Fitting Criterion
- 2017
-
In: Proceedings of the 25th European Signal Processing Conference (EUSIPCO). - 2076-1465. - 9780992862688 ; CFP1740S-USB
-
Conference paper (peer-reviewed)abstract
- In this paper, we present a time-recursive implementation of a recent hyperparameter-free group-sparse estimation technique. This is achieved byr eformulating the original method, termed group-SPICE, as a square-root group-LASSO with a suitable regularization level, for which a time-recursive implementation is derived. Using a proximal gradient step for lowering the computational cost, the proposed method may effectively cope with data sequences consisting of both stationary and non-stationary signals, such as transients, and/or amplitude modulated signals. Numerical examples illustrates the efficacy of the proposed method for both coherent Gaussian dictionaries and for the multi-pitch estimation problem.
|
|
