Sparse principal component regression with adaptive loading

Abstract

Principal component regression (PCR) is a two-stage procedure that selects some principal components and then constructs a regression model regarding them as new explanatory variables. Note that the principal components are obtained from only explanatory variables and not considered with the response variable. To address this problem, we propose the sparse principal component regression (SPCR) that is a one-stage procedure for PCR. SPCR enables us to adaptively obtain sparse principal component loadings that are related to the response variable and select the number of principal components simultaneously. SPCR can be obtained by the convex optimization problem for each of parameters with the coordinate descent algorithm. Monte Carlo simulations and real data analyses are performed to illustrate the effectiveness of SPCR.

24 pages

References in corpus (2)

• Sparse logistic principal components analysis for binary data
• Sparse estimation via nonconcave penalized likelihood in a factor analysis model

Cited by in corpus (7)

• Optimization Problems for Machine Learning: A Survey
• Sparse principal component regression for generalized linear models
• Interpretable Sparse Proximate Factors for Large Dimensions
• Sparse principal component regression via singular value decomposition approach
• A Fast deflation Method for Sparse Principal Component Analysis via Subspace Projections
• Supervised PCA: A Multiobjective Approach
• Estimation and visualization of treatment effects for multiple outcomes