The Function-on-Scalar LASSO with Applications to Longitudinal GWAS

TL;DR

This paper introduces a new LASSO-based method for variable selection and estimation in function-on-scalar regression with high-dimensional predictors, applicable to dense and sparse functional data, with applications to GWAS.

Contribution

The paper extends LASSO to functional data in dense and sparse settings, providing theoretical guarantees for ultra-high dimensional predictors, and demonstrates its use in GWAS for cardiovascular health.

Findings

Identified genetic mutations affecting blood pressure.

Validated the methodology through simulations.

Applied to GWAS data with meaningful results.

Abstract

We present a new methodology for simultaneous variable selection and parameter estimation in function-on-scalar regression with an ultra-high dimensional predictor vector. We extend the LASSO to functional data in both the $\textit{dense}$ functional setting and the $\textit{sparse}$ functional setting. We provide theoretical guarantees which allow for an exponential number of predictor variables. Simulations are carried out which illustrate the methodology and compare the sparse/functional methods. Using the Framingham Heart Study, we demonstrate how our tools can be used in genome-wide association studies, finding a number of genetic mutations which affect blood pressure and are therefore important for cardiovascular health.