B0709
Title: The importance of being a band: finite-sample exact conformal prediction bands for functional data
Authors: Jacopo Diquigiovanni - Universita di Padova (Italy)
Matteo Fontana - Royal Holloway, University of London (Italy)
Simone Vantini - Politecnico di Milano (Italy) [presenting]
Abstract: The focus is on the key challenge of creating prediction bands for a new observation in the functional data framework given a training set of observed functional data and possibly in the presence of scalar, categorical, or functional covariates. Starting from the investigation of the literature concerning this topic, an innovative approach is proposed, building on top of conformal prediction and functional data analysis to overcome the main drawbacks associated with the existing approaches. Under minimal distributional assumptions (i.e., exchangeability of the random functions), it is shown how the new proposed nonparametric method (i) is able to provide prediction regions which could visualized in the form of bands, (ii) is guaranteed with exact coverage probability also for finite sample sizes, and finally (iii) is computational efficient. Different specifications of the method is compared in terms of efficiency in some simulated and real case scenarios, also in the case of multi-dimensional domain and/or codomain.
