|13 febrero, 2020|
Título: Generalized Multisource Regression: A framework for locating hyperplanes to fitting sets of points.
Ponente: Justo Puerto (Universidad de Sevilla).
Organizador: Ana Meca
Fecha: Jueves 13 de febrero a las 11:00 horas.
Lugar: Aulas 0.1 y 0.2S del CIO en el Edificio Torretamarit, Universidad Miguel Hernández (Campus de Elche)
Resumen: In this talk we revisit common problems of Data Science. Specifically, we focus on the problem of locating a given number of hyperplanes minimizing a globalizing function of the closest distances from a set of points. Following an initial attempt in, we propose a general framework for the problem in which general norm-based distances are used to measure the residuals and an ordered median aggregation function of them has to be minimized. A compact Mixed Integer Linear (or Non Linear) programming formulation is presented for the problem and also an extended set partitioning formulation with an exponential number of variables is developed. The set partitioning formulation is analyzed and a column generation procedure is proposed for solving the problem by adequately performing preprocessing, pricing and branching (see for similar approaches to a different problem in Location Analysis). The issue of scalability is also addressed showing theoretical upper bounds on the errors assumed by replacing the original datasets by aggregated versions. Finally, the results of an extensive computational experience are reported.