Seminario 23/10 – Vanessa Guerrero (Universidad Carlos III) – On mathematical optimization approaches for constrained smoothing and feature selection in additive models.

Información

Abstract

In an era when the decision-making process is often based on the analysis of complex and evolving data, it is crucial to have systems which allow us to incorporate human knowledge and provide valuable support to the decision maker. During this talk, statistical modelling and mathematical optimization paradigms merge to address the problems of, first, estimating smooth curves and hypersurfaces which verify structural properties (e.g. about sign, monotonicity or curvature), and second, perform feature selection in additive models. In both cases, we assume that the smooth functions to be estimated are defined through a reduced-rank basis (B−splines) and fitted via a penalized splines approach (P−splines). Conic Optimization and Mixed Integer Quadratic Programming are used to address these problems. The proposed methodologies are tested in both simulated and real datasets and they are shown to be competitive against other approaches in the literature.