Variable Selection in Functional Linear Quantile Regression for Identifying Associations between Daily Patterns of Physical Activity and Cognitive Function

2026-03-23

AI Summary

This study addresses the heterogeneous associations between diurnal patterns of physical activity derived from high-dimensional wearable data and cognitive function across different quantiles. To this end, the authors propose a novel variable selection method tailored for functional linear quantile regression. The approach uniquely integrates group Minimax Concave Penalty (MCP) with Functional Principal Component Analysis (FPCA) to impose sparsity on functional coefficients. Optimization is achieved through a smooth approximation of the quantile loss combined with an efficient group descent algorithm, making the method suitable for both densely and sparsely observed functional data. Simulation studies demonstrate superior performance over existing methods in variable selection, parameter estimation, and prediction accuracy. Applied to NHANES accelerometer data, the method successfully identifies time-varying physical activity patterns significantly associated with cognitive function in older adults.

Technology Category

• Machine Learning: Active Learning
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• User Modeling, Personalization and Recommendation: Practical large-scale studies of user experience
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Quantile regression is useful for characterizing the conditional distribution of a response variable and understanding heterogeneity in the covariate effects at different quantiles. The rise of high-dimensional physiological data in biomedical research through wearable and sensor devices underscores the need for effective variable selection methods for interpretable and accurate quantile regression, which can offer robust insights into heterogeneous and dynamic covariate effects. We develop a flexible variable selection approach for functional linear quantile regression with multiple functional and scalar predictors. We use a smooth approximation of the quantile loss function and integrate functional principal component analysis (FPCA) with a group minimax concave penalty (MCP) to impose sparsity on the functional coefficients. A computationally efficient group descent algorithm is employed for optimization. Through numerical simulations, we demonstrate a satisfactory selection, estimation, and prediction accuracy of the proposed method across different quantiles for both dense and sparsely observed functional data. The proposed method is applied to accelerometer data from the 2011-2014 National Health and Nutrition Examination Survey (NHANES) to identify key time-varying distributional patterns of physical activity and demographic predictors associated with cognitive function across different quantiles. Our analysis provides new insights into the complex relationship between the daily distributional patterns of physical activity and cognitive function among older adults, capturing heterogeneous associations across different quantiles.

Problem

• variable selection
• functional linear quantile regression
• physical activity patterns
• cognitive function
• high-dimensional data

Innovation

• functional linear quantile regression
• variable selection
• group MCP penalty
• functional principal component analysis
• heterogeneous effects