Elastic Distance Metrics and Conformal Methods for Functional Classification and Regression

Thomas M. Menino Convention & Exhibition Center 

Functional covariates pose a challenge in classification and regression tasks. Functional data, by its definition is cursed by dimensionality and may have complicated structures, both of which hinder the use of functional covariates in supervised learning situations. In this work, we present a unique combination of elastic functional distance metrics and conformal prediction methods. Elastic distance metrics enable the measurement of functions in ways that capture both the underlying shape and phase variability, rather than focusing solely on magnitude variability. Conformal prediction methods provide uncertainty quantification (UQ) with theoretical coverage guarantees. We provide a comprehensive simulation study to examine the compatibility of various classification and regression algorithms with UQ metrics in the conformal prediction framework and an application of these methods to real world data to demonstrate utility and ease. The results demonstrate that the unique combination enhances predictive accuracy while delivering reliable uncertainty estimates for responses in the presence of functional covariates.

Functional Data Analysis

Conformal Prediction

Uncertainty Quantification 

Section on Statistical Learning and Data Science