Conformal prediction bands for multivariate functional data

Jacopo Diquigiovanni, Matteo Fontana and Simone Vantini

Journal of Multivariate Analysis, 2022, vol. 189, issue C

Abstract: Motivated by the pressing request of methods able to create prediction sets in a general regression framework for a multivariate functional response, we propose a set of conformal predictors that produce finite-sample either valid or exact multivariate simultaneous prediction bands under the mild assumption of exchangeable regression pairs. The fact that the prediction bands can be built around any regression estimator and that can be easily found in closed form yields a very widely usable method, which is fairly straightforward to implement. In addition, we first introduce and then describe a specific conformal predictor that guarantees an asymptotic result in terms of efficiency and inducing prediction bands able to modulate their width based on the local behavior and magnitude of the functional data. The method is investigated and analyzed through a simulation study and a real-world application in the field of urban mobility.

Keywords: Conformal Prediction; Distribution-free prediction set; Exact prediction set; Finite-sample prediction set; Functional data; Prediction band (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.jmva.2021.104879

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