In nonparametric regression analysis, Additive Models, Generalized Additive Models and Vector Generalized Additive Models naturally avoid overﬁtting by the use of smoothing spline penalties; the prior assumption being that the ground truth is suﬃciently smooth. The latter is modeled by smoothing spline penalties and this consequently leads to spatially overall smooth estimates.
In many situations, however, such as outliers in the response, spatially highly varying curvature, jump signals or the high-dimensional setting, the assumption of the ground truth being overall smooth is partly violated and too narrow, and therefore leads to inaccurate results. It is necessary to weaken the assumptions in order to ensure appropriate results.
In this project we cope with these issues by modifying the penalized log-likelihood problem. This is done by robustifying the log-likelihood terms and the penalty terms accordingly. These modiﬁcations will lead to computational feasible nonparametric estimates which allow for quick local changes while still preserving an overall smoothing property. The newly developed methodology will therefore yield a ﬂexible and powerful framework which ensures that data being multivariate in the response and covariates can be analyzed appropriately. The developed methods will be implemented in the prominent VGAM package.
Coordinator: CSTAT, TU Wien
TU Wien team: Christopher Rieser, Peter Filzmoser
Program / Call: FWF Stand-Alone Project
Proposal: P 32819-N
Funding: Austrian Science Fund (FWF)
Start: 01 January 2020, duration: 36 months
Project web page: