Conformal Prediction Bands for Multivariate Functional Data

TL;DR

This paper introduces conformal prediction bands for multivariate functional data that provide valid or exact finite-sample coverage, adaptable to various regression estimators, and demonstrated through simulations and real-world urban mobility data.

Contribution

It develops a flexible conformal prediction method for multivariate functional data that guarantees finite-sample validity and adapts to local data behavior.

Findings

Prediction bands are valid or exact in finite samples.

The method is easy to implement and adaptable to any regression estimator.

Application to urban mobility data demonstrates practical utility.

Abstract

Motivated by the pressing request of methods able to create prediction sets in a general regression framework for a multivariate functional response and pushed by new methodological advancements in non-parametric prediction for functional data, 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.