Title: A one-stage estimation of principal component regression for generalized linear models
Authors: Shuichi Kawano - The University of Electro-Communications (Japan) [presenting]
Hironori Fujisawa - The 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 two-stage procedure: principal component analysis (PCA) is performed, and then a regression model with the selected principal components is constructed. Since PCA is based only on the explanatory variables, the principal components do not include the information on the response variable. To address the problem, we propose a one-stage estimation of PCR in the framework of generalized linear models. The loss function is based on a combination of the PCA loss and the negative log-likelihood function for an exponential family. An estimate of the parameters is obtained as the minimizer of the loss function with an L1-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. We examine the effectiveness of SPCR-glm through numerical studies.