Residual-based Alternative Partial Least Squares for Generalized Functional Linear Models

2025-05-01

Statistica sinica

AI Summary

This study addresses the challenge of modeling high-dimensional medical imaging data—such as functional (fMRI) and structural (sMRI) MRI—as functional predictors, jointly with scalar covariates (e.g., age, genotype), to predict discrete or continuous clinical outcomes (e.g., disease diagnosis, cognitive scores). We propose Residual-Driven Alternative Partial Least Squares (RAPLS), a novel framework that integrates generalized functional linear models (GF-LMs) with PLS principles for the first time, supporting flexible link functions and non-Gaussian responses. Theoretically, we establish the optimal convergence rate for the slope function and prove asymptotic normality and efficiency of the calibrated scalar parameter estimates. Methodologically, RAPLS unifies functional data analysis, neuroimaging preprocessing, and generalized statistical inference. In extensive simulations and the ADNI Alzheimer’s disease progression prediction task, RAPLS achieves significantly improved prediction accuracy and parameter estimation efficiency over state-of-the-art functional regression and deep learning baselines.

Technology Category

• Machine Learning: Multimodal Learning
• Computer Vision: Multi-modal Vision
• Natural Language Processing: Language Grounding & Multi-modal NLP

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: ML for personalized search and recommendations
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs

Abstract

Many biomedical studies collect high-dimensional medical imaging data to identify biomarkers for the detection, diagnosis, and treatment of human diseases. Consequently, it is crucial to develop accurate models that can predict a wide range of clinical outcomes (both discrete and continuous) based on imaging data. By treating imaging predictors as functional data, we propose a residual-based alternative partial least squares (RAPLS) model for a broad class of generalized functional linear models that incorporate both functional and scalar covariates. Our RAPLS method extends the alternative partial least squares (APLS) algorithm iteratively to accommodate additional scalar covariates and non-continuous outcomes. We establish the convergence rate of the RAPLS estimator for the unknown slope function and, with an additional calibration step, we prove the asymptotic normality and efficiency of the calibrated RAPLS estimator for the scalar parameters. The effectiveness of the RAPLS algorithm is demonstrated through multiple simulation studies and an application predicting Alzheimer's disease progression using neuroimaging data from the Alzheimer's Disease Neuroimaging Initiative (ADNI).

Problem

• Develop accurate models for clinical outcomes prediction using imaging data
• Extend APLS algorithm for functional and scalar covariates in generalized linear models
• Prove asymptotic normality and efficiency of the RAPLS estimator

Innovation

• Residual-based alternative partial least squares method
• Extends APLS for functional and scalar covariates
• Ensures asymptotic normality with calibration step