Department of Statistics Unitmark
Dietrich College of Humanities and Social Sciences

A Conformal Prediction Approach to Explore Functional Data

Publication Date

February, 2013

Publication Type

Tech Report

Author(s)

Jing Lei, Alessandro Rinaldo, Larry Wasserman

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.