Keywords: Feature selection, Group Elastic Net, Function-on-Scalar regression, Functional Principal Components, Augmented Lagrangian, GWAS
TL;DR: We propose a new highly efficient dual augmented Lagrangian method to solve Group Elastic Net and Function-on-Scalar feature selection
Abstract: Feature Selection and Functional Data Analysis are two dynamic areas of research, with important applications in the analysis of large and complex data sets. Straddling these two areas, we propose a new highly efficient algorithm to perform Group Elastic Net with application to function-on-scalar feature selection, where a functional response is modeled against a very large number of potential scalar predictors. First, we introduce a new algorithm to solve Group Elastic Net in ultra-high dimensional settings, which exploits the sparsity structure of the Augmented Lagrangian to greatly reduce the computational burden. Next, taking advantage of the properties of Functional Principal Components, we extend our algorithm to the function-on-scalar regression framework. We use simulations to demonstrate the CPU time gains afforded by our approach compared to its best existing competitors, and present an application to data from a Genome-Wide Association Study on childhood obesity.
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