Seminar
Gareth James Ph.D
Functional Linear Regression That's Interpretable
Regression models to relate a scalar Y to a functional predictor X(t) are becoming increasingly common. Work in this area has concentrated on estimating a coefficient function, beta(t), with Y related to X(t) through the integral of beta(t)X(t). Regions where beta(t) is not equal to 0 correspond to places where there is a relationship between X(t) and Y. Alternatively, points where beta(t) = 0 indicate no relationship. Hence, for interpretation purposes, it is desirable for a regression procedure to be capable of producing estimates of beta(t) that are exactly zero over certain regions and have simple structure, such as a piecewise constant or linear form, over the other regions. Unfortunately, most fitting procedures result in an estimate for beta(t) that is rarely exactly zero and has unnatural wiggles making the curve hard to interpret. In this talk I will introduce a new approach called Functional Linear Regression That's Interpretable. FLiRTI uses variable selection ideas, applied to various derivatives of beta(t), to produce
estimates that are both interpretable, flexible and accurate. In addition one can prove non-asymptotic theoretical bounds on the estimation error which provide strong theoretical motivation for our approach. I will demonstrate FLiRTI on simulated and real world data
sets. Time permitting, I will also discuss some extensions of FLiRTI.
