This week's Graduate Student Seminar speaker is Mathew McLean, from ORIE.
Talk Title: Functional Generalized Additive Models
Abstract
I will introduce the functional generalized additive model (FGAM), a novel regression model for association studies between a scalar response and a functional predictor. The link-transformed mean response is modelled as the integral with respect to t of F{X(t), t} where F(·, ·) is an unknown regression function and X(t) is a functional covariate. The model incorporates the functional predictor directly and thus can be viewed as the natural functional extension of generalized additive models. It will be demonstrated that the FGAM is both highly flexible and easily interpretable. I will show how to estimate F(·, ·) using tensor-product B-splines with roughness penalties. If the mood strikes me, I may demonstrate the usefulness of the approach through an application to brain tractography, where X(t) is a signal from diffusion tensor imaging at position, t, along a tract in the brain. The response is either disease-status (case or control) or the score on a cognitive test. More likely, I will give an overview of an alternative estimation approach via Bayesian mixed models which can be used for handling the case of sparsely observed functional predictors measured with error. Both Markov Chain Monte Carlo and variational Bayes approaches will be considered. Finally, I will discuss my on-going efforts to develop an approximate test for the FGAM against the ubiquitous functional linear model using the mixed model framework.