A Conformal Prediction Approach to Explore Functional Data

TL;DR

This paper introduces a conformal prediction framework for functional data that provides reliable prediction bands and clustering tools with finite sample guarantees, using computationally efficient methods and novel conformity scores.

Contribution

It develops a new conformal prediction approach tailored for functional data, enabling efficient prediction and clustering with guaranteed coverage without distributional assumptions.

Findings

Provides finite sample valid prediction bands for functional data

Introduces novel conformity scores for computational efficiency

Demonstrates methods on real data examples

Abstract

This paper applies conformal prediction techniques to compute simultaneous prediction bands and clustering trees for functional data. These tools can be used to detect outliers and clusters. Both our prediction bands and clustering trees provide prediction sets for the underlying stochastic process with a guaranteed finite sample behavior, under no distributional assumptions. The prediction sets are also informative in that they correspond to the high density region of the underlying process. While ordinary conformal prediction has high computational cost for functional data, we use the inductive conformal predictor, together with several novel choices of conformity scores, to simplify the computation. Our methods are illustrated on some real data examples.