A New Sparse Bayesian Quantile Neural Network-based Approach and Its Application to Discover Physiological Sweet Spots in the Canadian Longitudinal Study on Aging

Identifying physiological sweet spots (optimal ranges for homeostasis) is essential for precision medicine. However, traditional statistical methods often rely on globally linear or locally jagged models that struggle to capture the smooth, non-linear nature of biological regulation in high-dimensional data. We present the Quantile Feature Selection Network (Q-FSNet), a neural network-based framework that integrates quantile regression, feature selection, and uncertainty estimation to identify biomarkers with sweet spots. Unlike traditional methods, Q-FSNet learns continuous response curves without requiring pre-specified number of change points. We further introduce Quantile Dirichlet Network (Q-DirichNet), a fully Bayesian extension that utilizes Dirichlet priors to automate feature shrinkage. Using data from the Canadian Longitudinal Study on Aging, we identified 25 metabolites with distinct homeostatic ranges for which biological age acceleration is minimized. The metabolites with sweet spots for biological aging include some derived from diet or produced by the gut microbiome; this highlights their potential for knowledge translation and public health impact. Our results, corroborated by existing literature, demonstrate that these sparse neural network-based methods offer a scalable and interpretable tool for discovering metabolic signatures of healthy aging vs. dysregulation in large-scale omics research.