Adaptive nonlinear learning framework with dynamic representations for scalar-on-function regression

Area of Science:

• Statistics and Machine Learning
• Functional Data Analysis
• Biomedical Engineering

Background:

• Continuous functional data are vital in science and industry.
• Scalar-on-function regression faces challenges in modelling infinite-dimensional predictors.
• A universal framework for this task is currently lacking.

Purpose of the Study:

• To propose an adaptive nonlinear learning framework for scalar-on-function regression.
• To preserve the intrinsic structure of functional predictors during modeling.
• To develop a flexible representation for complex functional data.

Main Methods:

• An adaptive nonlinear learning framework utilizing dynamic representations.
• Adaptation across multiple basis function families.
• Sequential optimization of basis component number and location.

Main Results:

• Flexible functional representations capturing complex, localized structures.
• Preservation of key characteristics of original functional predictors.
• Consistent and substantial improvements in prediction accuracy across seven benchmark datasets.
• Significant reduction in root-mean-squared error (rRMSE) on Gasoline and DTI datasets.

Conclusions:

• The proposed framework offers practical and scalable solutions for scalar-on-function regression.
• It demonstrates superior performance compared to existing methods.
• The approach effectively handles complex functional data in various scientific domains.