Selective Factor Extraction in High Dimensions
This method addresses the challenge of capturing low-dimensional structures in high-dimensional multivariate data for fields like macroeconomics and computer vision, representing an incremental improvement through joint variable selection and projection.
The paper tackles the problem of simultaneous feature selection and extraction in high-dimensional data by proposing selective reduced rank regression, which achieves optimal explanatory factors with sharp oracle inequalities and adapts to unknown sparsity.
This paper studies simultaneous feature selection and extraction in supervised and unsupervised learning. We propose and investigate selective reduced rank regression for constructing optimal explanatory factors from a parsimonious subset of input features. The proposed estimators enjoy sharp oracle inequalities, and with a predictive information criterion for model selection, they adapt to unknown sparsity by controlling both rank and row support of the coefficient matrix. A class of algorithms is developed that can accommodate various convex and nonconvex sparsity-inducing penalties, and can be used for rank-constrained variable screening in high-dimensional multivariate data. The paper also showcases applications in macroeconomics and computer vision to demonstrate how low-dimensional data structures can be effectively captured by joint variable selection and projection.