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Title: Finite-sample exact prediction bands for functional data based on conformal prediction Authors:  Matteo Fontana - European Commission, Joint Research Centre (Italy) [presenting]
Simone Vantini - Politecnico di Milano (Italy)
Jacopo Diquigiovanni - Universita di Padova (Italy)
Abstract: The focus is 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 that could be visualized in the form of bands, (ii) guaranteed with exact coverage probability for any sample size, (iii) not relying on parametric assumptions about the specific distribution of the functional data set, and finally (iv) being computationally 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 nonparametric predictive approach from Machine Learning). We will present the general theoretical framework and some simulations enlightening the flexibility of the approach and the effect on the amplitude of prediction bands of different algorithmic choices.