The talk will deal with the key challenge of creating prediction sets in the functional data framework. Starting from the investigation of the literature concerning this topic, we propose an innovative approach building on top of Conformal Prediction able to overcome the main drawbacks characterizing the existing approaches. We will show how the new proposed nonparametric method is able to construct finite-sample either valid or exact prediction bands under minimal distributional assumptions. Different specifications of the method will be compared in terms of efficiency in some simulated and real case scenarios.
References: Diquigiovanni, J., Fontana, M., Vantini, S. (2021): The importance of being a band: Finite-sample exact distribution-free prediction sets for functional data. arXiv:2102.06746
Diquigiovanni, J., Fontana, M., Vantini, S., (2022): “Conformal Prediction Bands for Multivariate Functional Data”, Journal of Multivariate Analysis, 189, 104879.