*********************************
There is now a CONTENT FREEZE for Mercury while we switch to a new platform. It began on Friday, March 10 at 6pm and will end on Wednesday, March 15 at noon. No new content can be created during this time, but all material in the system as of the beginning of the freeze will be migrated to the new platform, including users and groups. Functionally the new site is identical to the old one. webteam@gatech.edu
*********************************
TITLE: Penalized regularization for functional linear models
SPEAKER: Dr. Tim Randolph
ABSTRACT:
In a 'functional linear model' the aim is to estimate the linear relationship between a scaler response, y, and a random L2 function, x. This formally fits into the classical regression model, y = X*b + e, but the estimation of b is inherently ill-posed. A common method used to address this problem regularizes the solution by penalizing L*b, where L is a linear operator. This constrains b (which is nominally any L2 function) by bounding the norm of L*b. Special cases include Marquardt's generalized regression, Hoerl's ridge regression (L=I) and
Tikhonov-Philips' regularization (L=D, a differential operator). This talk considers (linear) penalized estimates in general and their expression via generalized singular vectors of the pair (X,L). This provides perspective on the functional structure of an estimate and on criteria for choosing the penalty operator. Corresponding explicit expressions for bias and variance provide insight regarding the trade-off between the properties of L versus X.
