On the Singular Value Penalized Multivariate Generalized Linear Models

This paper takes a new perspective to study the singular value penalized multivariate generalized linear models (GLMs). We start with a matrix approximation problem and introduce a matrix thresholding technique. The commonly used singular value penalties, possibly discrete and nonconvex, can be attained with various thresholding rules. The iterative matrix thresholding applies to multivariate GLMs. The singular value penalized estimator can be used for supervised dimension reduction and feature extraction in multivariate problems.