High-Dimensional Function-on-Scale Regression via the Alternating Direction Method of Multipliers

Abstract

In [10] and [16], we proposed tools for simultaneous variable selection and parameter estimation in a functional linear model with a functional outcome and a large number of scalar predictor. We call these techniques Function-on-Scalar Lasso (FSL) and Adaptive Function-on-Scalar Lasso(AFSL). A scalar group lasso was used to fit the FSL and AFSL estimates. While this approach works well, we improve it by producing custom ADMM methods which are specifically designed for functional data. We propose this new framework as a computational tool for finding FSL estimates. Through our numerical studies, we demonstrate the computational improvement of our methodology.