Explainable Machine Learning for Functional Data
Pub. online: 16 December 2025
Type: Statistical Data Science
Open Access
Open Access
Received
27 March 2025
27 March 2025
Accepted
8 December 2025
8 December 2025
Published
16 December 2025
16 December 2025
Abstract
Black-box machine learning models are recognized as useful tools for prediction applications, but the algorithmic complexity of some models causes interpretation challenges. Explainability methods have been proposed to provide insight into these models, but there is little research focused on supervised modeling with functional data inputs. We argue that, especially in applications of high consequence, it is important to explicitly model the functional dependence in a black-box analysis to not obscure or misrepresent patterns in explanations. As such, we propose the Variable importance Explainable Elastic Shape Analysis (VEESA) pipeline for training supervised machine learning models with functional inputs. The pipeline is an analysis process that includes the data preprocessing, modeling, and post-hoc explanations. The preprocessing is done using elastic functional principal components analysis, which accounts for vertical and horizontal variability in functional data and, ultimately, allows for explanations in the original data space that identify the important functional variability without bias due to correlated variables. Here, we demonstrate the pipeline on two high-consequence applications: explosives classification for national security and inkjet printer identification in forensic science. The applications exhibit the VEESA pipeline’s ability to provide an understanding of the characteristics of the functional data useful for prediction. Code for implementing the pipeline is available in the veesa R package (and supplemental python code).
Supplementary material
Supplementary MaterialThe supplementary materials include additional analyses on the shifted peaks, H-CT, and inkjet printer data, implementation details, R and Python code, and the shifted peaks and inkjet datasets. Due to proprietary reasons, the H-CT dataset is not able to be shared.
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