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:

institute.tuwien.ac.at/cstat/home/, opens an external URL in a new window