A0318
Title: Generalized additive models for smoothing covariance matrices
Authors: Vincenzo Gioia - University of Trieste (Italy) [presenting]
Matteo Fasiolo - University of Bristol (United Kingdom)
Ruggero Bellio - University of Udine (Italy)
Abstract: Computational and methodological developments in multi-parameter Generalized Additive Models (GAMs), also known as distributional regression models, have been the primary drivers of their popularity in applied statistics. The multivariate Gaussian additive model, where both the elements of the mean vector and an unconstrained parametrisation of the covariance matrix are modelled semi-parametrically, exemplifies this class of models. The task of modelling the covariance matrix is complex, and ensuring scalability during model fitting is challenging, primarily due to the high dimensionality of the problem and the necessity of performing smoothing parameter optimisation. Furthermore, the advantage of adopting an unconstrained parametrisation of the covariance matrix complicates the interpretation of the model output, which needs to be translated into well-known quantities such as variance and correlation. In the proposed approach, the computational challenge is addressed by adopting efficient computational strategies, which are integrated into well-established GAMs' model fitting routines, while interpretability issues are mitigated by utilising accumulated local effects. The proposed modelling approach is illustrated with real-world examples, with particular emphasis on applications in the energy sector.
