Some equivalence relationships of regularized regressions

Abstract

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.