Filtration-Based Learning of Multiscale Shared Structures for Multiple Functional Predictors

TL;DR

This paper introduces a filtration-based hierarchical framework for learning shared structures among multiple functional predictors, improving prediction accuracy and interpretability in complex multiscale data.

Contribution

It proposes a novel filtration-based approach that organizes predictors hierarchically to identify shared and specific components across multiple resolutions.

Findings

Successfully recovers coarse-to-fine shared structures in simulations

Enhances prediction accuracy over existing methods

Reveals interpretable joint coordination patterns in kinematic data

Abstract

It is crucial to learn the shared structures among functional predictors, as these structures characterize how predictor components exert common effects and, more generally, how predictors are homogeneously associated with the response. However, learning from multiple functional predictors is challenging because response-predictor dependencies may vary across representation dimensions and emerge at multiple resolutions, ranging from globally shared effects to predictor-specific effects. To address this issue, we propose a filtration-based shared structure learning framework for multiple functional predictors. The proposed framework organizes predictors through a hierarchical forest structure, in which shared and predictor-specific components are progressively identified from coarse to fine filtration layers. Building on this structure, we develop a filtration-based pursuit pipeline for shared structure discovery, together with a filtrated functional partial least squares method for shared component extraction and coefficient estimation under the learned shared structures. Simulation studies show that the proposed framework is able to recover the dominant coarse-to-fine organization of the underlying shared structures and yield improved prediction performance relative to competing methods. Applied to lower-limb angular kinematics, the proposed framework improves evaluation accuracy and reveals interpretable joint coordination patterns associated with aging. More broadly, it provides a new multiscale representation-learning perspective for complex data consisting of multiple multidimensional objects.