Some equivalence relationships of regularized regressions

Regularization is a powerful framework for solving ill-posed problem and preventing model overfitting in modern regression analysis. It is especially useful for high-dimensional or functional (infinite dimensional) regression models. In this paper, we construct two useful equivalence relationships for regularized regression: 1. An equivalence between regularized functional regression and regularized multi- variate regression. This equivalence provides a computationally efficient way to fit the concurrent functional regression model. 2. An equivalence of penalized multi- variate regression under a group of scaling transformation. This equivalence can be used to solve weighted principal component regression efficiently.

Keywords

regularization, elastic-net regression, functional concurrent model, principal com- ponent regression, high-dimensional data

Citation

Mathematics for Applications. 2018 vol. 7, č. 1, s. 3-10. ISSN 1805-3629
http://ma.fme.vutbr.cz/archiv/7_1/ma_7_1_1_zhang_et_al_final.pdf

Document type

Peer-reviewed

Document version

Published version

Language of document

en

Document licence