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Activity Number: 176
Type: Contributed
Date/Time: Monday, August 1, 2016 : 10:30 AM to 12:20 PM
Sponsor: Section on Statistical Learning and Data Science
Abstract #320346 View Presentation
Title: Scalars-on-Function Linear Regression with Large Number of Functional Predictors
Author(s): Ruiyan Luo* and Xin Qi
Companies: and Georgia State University
Keywords: functional regression ; scalar-on-function regression ; generalized eigenvalue optimization problem ; EEG data ; fMRI data

With the advance of technology, simultaneous electroencephalography (EEG) and fMRI data have been achieved. People are interested in the relationship between various features extracted from EEG data (such as the powers in different frequency bands) and fMRI signals hidden in thousands of voxel time series curves. We consider the functional linear regression model with multiple scalar response variables and thousands of predictive curves. Aiming at finding the best finite dimensional approximation to the signal part of the regression model, we propose a generalized eigenvalue optimization problem to seek sparse and smooth components whose projection on the predictive curves have the largest generalized correlations with the response variables. Then we transform the original scalar-on-function regression model to a multivariate regression model with uncorrelated scalar predictors. Upper bound for the prediction error is presented. The proposed method has been applied to the simultaneous EEG and fMRI data.

Authors who are presenting talks have a * after their name.

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