Group Lasso in Functional Logistic Regression

• Activity Number: 377
• Type: Contributed
• Date/Time: Tuesday, August 6, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Jessica Godwin*+ and Nedret Billor
• Companies: Auburn University and Auburn University
• Keywords: functional data analysis ; group lasso ; functional logistic regression ; functional magnetic resonance imaging

Abstract

In this study, we consider the problem of variable selection in the functional logistic regression model with functional predictors. The lasso is an L1 regularization technique that shrinks some regression coefficients to exactly zero and selects variables. In this study, we extend the lasso to functional logistic regression. When using functional predictors, there are multiple coefficients to be estimated for each predictor. We use group lasso, considering each functional predictor as one group. We show the effectiveness of the proposed method on a simulation study and real functional Magnetic Resonance Imaging (fMRI) data. In fMRI studies, researchers are interested in predicting event categories (response) from various patterns of activation across voxels in the brain. Each voxel is sampled at different time points and can be considered as a functional predictor. As there are over a million voxels in the brain, the first step in such a problem is to identify an important subset of voxels and the BOLD amplitude, or activation, in each voxel at each of the T time points.