Title: Permutation-based prediction bands for functional data: A conformal prediction approach
Authors: Matteo Fontana - Politecnico di Milano (Italy)
Alexander Gammerman - Royal Holloway University of London (United Kingdom)
Simone Vantini - Politecnico di Milano (Italy) [presenting]
Vladimir Vovk - Royal Holloway, University of London (United Kingdom)
Abstract: The focus will be on the prediction of a new unobserved functional datum given a set of observed functional data, possibly in presence of covariates, either scalar, categorical, or functional. In particular, we will present an approach (i) able to provide prediction regions which could visualized in the form of bands, (ii) guaranteed with exact coverage probability, (iii) not relying on parametric assumptions about the specific distribution of the functional data set, and finally (iv) being computational efficient. The method is built on a combination of ideas coming from the recent literature pertaining to functional data analysis (i.e., the statistical analysis of datasets made of functions) and conformal prediction (i.e., a predictive version of permutation tests). We will present some simulations enlightening the flexibility of the approach and the effect on the amplitude of prediction bands of different algorithmic choices. Finally, we will apply the method to some benchmark case studies and to a more thorough application pertaining to the prediction of time varying mobility flows within the city of Milan.