El Departamento de Matemática y Estadística de la Universidad Torcuato Di Tella invita al seminario “Set-to-set regression for convex bodies”, a cargo de Gabriel Martos Venturini, profesor investigador asociado del Departamento.

Abstract
In many applications the objects of interest are naturally represented as geometric sets rather than as vectors in a Euclidean space. This motivates the development of statistical models in which both predictors and responses take the form of sets. This paper introduces a regression framework for pairs of convex sets, allowing for additional covariates through a single-index structure. The approach builds on the support function representation of convex bodies. Within this representation, the regression problem is formulated in the support function space where convexity is enforced by modeling the radius of curvature through a generalized function-to-function regression model. The proposed methodology yields a flexible set-to-set regression framework that preserves the geometric structure of convex sets while accommodating complex relationships between input and output shapes. Inferential tools for the conditional mean set are also discussed, including the construction of confidence regions and hypothesis testing procedures based on bootstrap methods. Numerical experiments and an application to longitudinal brain tumor morphology illustrate the practical performance of the proposed methodology.

Gabriel Martos Venturini es licenciado en Ciencias Económicas por la Universidad Nacional de Córdoba y doctor en Ingeniería Matemática por la Universidad Carlos III de Madrid (España). Ha realizado estancias de investigación en el Politécnico de Milán, la Universidad Católica de Chile y la Universidad de Edimburgo. Sus líneas de investigación se centran en el estudio de métodos de inferencia estadística para datos funcionales y de alta dimensión, estadística computacional y métodos de aprendizaje automáticos con aplicaciones en ciencia y tecnología. Ha publicado en revistas especializadas de primer nivel, como el Pattern Recognition, Biometrical Journal, Journal of Statistics in Medicine y el International Journal of Forecasting, entre otras.