Distribution free prediction intervals for multiple functional regression

This paper applies conformal prediction techniques to the problem of constructing prediction intervals in a multiple functional regression setting. After a short introduction to the Signature expansion and its favorable properties, a method utilizing this feature set is developed with great modeling flexibility. With minimal assumptions, the resulting algorithm produces a closed form solution for a prediction set with guaranteed coverage. The good performance of the proposed method is illustrated using simulations and data examples.

Keywords

multiple functional regression, prediction intervals, conformal prediction, signature expansion

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Received 25 February 2020

Accepted 14 October 2020

Published 11 January 2022