Conformal Prediction Bandsfor Multivariate Functional Data

46/2021

Conformal Prediction Bandsfor Multivariate Functional Data

Friday 2nd July 2021

Diquigiovanni, J.; Fontana, M.; Vantini, F.

Motivated by the pressing request of methods able to create prediction sets in ageneral regression framework for a multivariate functional response and pushed bynew methodological advancements in non-parametric prediction for functional data,we propose a set of conformal predictors that produce finite-sample either validor exact multivariate simultaneous prediction bands under the mild assumption ofexchangeable regression pairs. The fact that the prediction bands can be built aroundany regression estimator and that can be easily found in closed form yields a verywidely usable method, which is fairly straightforward to implement. In addition,we first introduce and then describe a specific conformal predictor that guaranteesan asymptotic result in terms of efficiency and inducing prediction bands able tomodulate their width based on the local behavior and magnitude of the functionaldata. The method is investigated and analyzed through a simulation study and areal-world application in the field of urban mobility.