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A l -norm penalized orthogonal forward regression

A l -norm penalized orthogonal forward regression
A l -norm penalized orthogonal forward regression
A l1-norm penalised orthogonal forward regression (l1-POFR) algorithm is proposed based on the concept of leave-one-out mean square error (LOOMSE), by defining a new l1-norm penalised cost function in the constructed orthogonal space and associating each orthogonal basis with an individually tunable regularisation parameter. Due to orthogonality, the LOOMSE can be analytically computed without actually splitting the data-set, and moreover a closed form of the optimal regularisation parameter is derived by greedily minimising the LOOMSE incrementally. We also propose a simple formula for adaptively detecting and removing regressors to an inactive set so that the computational cost of the algorithm is significantly reduced. Examples are included to demonstrate the effectiveness of this new l1-POFR approach.
0020-7721
2195-2201
Hong, Xia
e6551bb3-fbc0-4990-935e-43b706d8c679
Chen, Sheng
9310a111-f79a-48b8-98c7-383ca93cbb80
Guo, Yi
8282665c-5cfc-4cea-80f7-300892271c23
Gao, Junbin
a3dcab84-9675-402c-a19e-d41ea9973f3a
Hong, Xia
e6551bb3-fbc0-4990-935e-43b706d8c679
Chen, Sheng
9310a111-f79a-48b8-98c7-383ca93cbb80
Guo, Yi
8282665c-5cfc-4cea-80f7-300892271c23
Gao, Junbin
a3dcab84-9675-402c-a19e-d41ea9973f3a

Hong, Xia, Chen, Sheng, Guo, Yi and Gao, Junbin (2017) A l -norm penalized orthogonal forward regression. International Journal of Systems Science, 48 (10), 2195-2201. (doi:10.1080/00207721.2017.1311383).

Record type: Article

Abstract

A l1-norm penalised orthogonal forward regression (l1-POFR) algorithm is proposed based on the concept of leave-one-out mean square error (LOOMSE), by defining a new l1-norm penalised cost function in the constructed orthogonal space and associating each orthogonal basis with an individually tunable regularisation parameter. Due to orthogonality, the LOOMSE can be analytically computed without actually splitting the data-set, and moreover a closed form of the optimal regularisation parameter is derived by greedily minimising the LOOMSE incrementally. We also propose a simple formula for adaptively detecting and removing regressors to an inactive set so that the computational cost of the algorithm is significantly reduced. Examples are included to demonstrate the effectiveness of this new l1-POFR approach.

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l1-norm Penalized Orthogonal Forward Regression - Accepted Manuscript
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More information

Accepted/In Press date: 20 March 2017
e-pub ahead of print date: 5 April 2017
Published date: 1 June 2017
Organisations: Southampton Wireless Group

Identifiers

Local EPrints ID: 411262
URI: http://eprints.soton.ac.uk/id/eprint/411262
ISSN: 0020-7721
PURE UUID: 9fa6383b-c95d-4b29-ac95-9ded2cdd0bb0

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Date deposited: 16 Jun 2017 16:31
Last modified: 07 Oct 2020 05:51

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Contributors

Author: Xia Hong
Author: Sheng Chen
Author: Yi Guo
Author: Junbin Gao

University divisions

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