Efficient least angle regression for identification of linear-in-the-parameters models

Zhao, Wanqing ORCID: https://orcid.org/0000-0001-6160-9547, Beach, Thomas H. ORCID: https://orcid.org/0000-0001-5610-8027 and Rezgui, Yacine ORCID: https://orcid.org/0000-0002-5711-8400 2017. Efficient least angle regression for identification of linear-in-the-parameters models. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 473 (2198) , 20160775. 10.1098/rspa.2016.0775

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Abstract

Least angle regression, as a promising model selection method, differentiates itself from conventional stepwise and stagewise methods, in that it is neither too greedy nor too slow. It is closely related to L1 norm optimization, which has the advantage of low prediction variance through sacrificing part of model bias property in order to enhance model generalization capability. In this paper, we propose an efficient least angle regression algorithm for model selection for a large class of linear-in-the-parameters models with the purpose of accelerating the model selection process. The entire algorithm works completely in a recursive manner, where the correlations between model terms and residuals, the evolving directions and other pertinent variables are derived explicitly and updated successively at every subset selection step. The model coefficients are only computed when the algorithm finishes. The direct involvement of matrix inversions is thereby relieved. A detailed computational complexity analysis indicates that the proposed algorithm possesses significant computational efficiency, compared with the original approach where the well-known efficient Cholesky decomposition is involved in solving least angle regression. Three artificial and real-world examples are employed to demonstrate the effectiveness, efficiency and numerical stability of the proposed algorithm.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Engineering
Subjects:	Q Science > QA Mathematics > QA75 Electronic computers. Computer science T Technology > TA Engineering (General). Civil engineering (General)
Publisher:	Royal Society, The
ISSN:	1364-5021
Related URLs:	Publisher
Date of First Compliant Deposit:	2 February 2017
Date of Acceptance:	3 January 2017
Last Modified:	20 Nov 2024 16:30
URI:	https://orca.cardiff.ac.uk/id/eprint/97983

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