A0824
Title: PDE-regularized models for spatiotemporal and quantile regression
Authors: Eleonora Arnone - University of Turin (Italy) [presenting]
Laura Sangalli - Politecnico di Milano (Italy)
Abstract: The focus is on the development of flexible statistical models for spatiotemporal data, designed to accommodate complex structural features such as anisotropy, non-stationarity, and domain irregularity. It begins by introducing a class of semiparametric regression models that incorporate partial differential equations (PDEs) as a means of regularization. These models employ differential operators in the penalty term to encode structural assumptions or prior scientific insight, such as geometric constraints or directional trends within the estimation procedure. The use of PDE-based roughness penalties allows for accurate modelling over irregular spatial domains and naturally captures anisotropic behaviors. The framework is then extended to the spatiotemporal quantile regression setting, where the modelling target shifts from the conditional mean to specific distributional quantiles of the response. This is particularly relevant in contexts where the variability and tail behavior of the process are of interest. A spatiotemporal quantile regression model is formulated in which the quantile field is estimated by minimizing a pinball loss function, regularized by space-time differential penalties. The resulting model allows for a nonparametric representation of the quantile function and accommodates complex spatial and temporal dependence.
