On Functional Linear Regression with Smooth/Sparse Penalties

• Activity Number: 321 - Machine Learning and Variable Selection
• Type: Contributed
• Date/Time: Wednesday, August 11, 2021 : 3:30 PM to 5:20 PM
• Sponsor: Section on Statistical Computing
• Author(s): Rebecca Marie North* and Jon Stallrich
• Companies: North Carolina State University and North Carolina State
• Keywords: functional data; variable selection; group lasso

Abstract

For high-dimensional scalar-on-function linear regression, the functional coefficients are assumed to be sparse and smooth to aid with interpretability. A common method for imposing smoothness on the estimates is to penalize the second derivative of the functional coefficients and sparsity is achieved by penalizing the coefficients’ magnitudes. Much of the current literature performs this penalized estimation through a group lasso representation that combines the smoothness and sparsity penalties into a single joint penalty with two tuning parameters. However, tuning parameter exploration can be challenging because the sparsity tuning parameter also influences the smoothness parameter. This talk compares the established joint penalty with two alternate penalties that separately impose smoothness and sparsity. Estimates under the alternate penalties can be calculated with modifications of an existing group lasso fitting algorithm. The competing penalties are compared via simulation studies and an analysis of a data set that relates forearm muscle activity with hand movements.