Title: Principal component regression for generalized linear models via L1-type regularization
Authors: Shuichi Kawano - The University of Electro-Communications (Japan) [presenting]
Hironori Fujisawa - Institute of Statistical Mathematics (Japan)
Toyoyuki Takada - National Institute of Genetics (Japan)
Toshihiko Shiroishi - National Institute of Genetics (Japan)
Abstract: Principal component regression (PCR) is a widely used two-stage procedure: principal component analysis (PCA), followed by regression in which the selected principal components are regarded as new explanatory variables in the model. Note that PCA is based only on the explanatory variables, so the principal components are not selected using the information on the response variable. To address this problem, we propose a one-stage procedure for PCR in the framework of generalized linear models. The loss function is based on a combination of the regression loss and PCA loss. An estimate of the regression parameter is obtained as the minimizer of the loss function with an L1-type regularization term. We call this method sparse principal component regression for generalized linear models (SPCR-glm). SPCR-glm enables us to obtain sparse principal component loadings that are related to a response variable. Numerical results are given to illustrate the effectiveness of SPCR-glm.