Transfer Learning for High‐Dimensional Huber Approximate Quantile Regression via Elastic Net

Abstract

This paper proposes a novel transfer learning framework for high‐dimensional quantile regression, addressing the non‐differentiability of quantile loss via a Huber approximation and leveraging elastic net regularization to handle sparse inference. By replacing the piecewise linear quantile check function with a smooth Huber loss, our method achieves computational efficiency while preserving robustness to heavy‐tailed errors and outliers. We develop Oracle Trans‐HAQ, a two‐step transfer algorithm that integrates source knowledge through elastic net penalties, and THAQ, a data‐driven detection framework using cross‐validation to mitigate negative transfer risks in scenarios with unknown informative sources. Numerical simulations demonstrate superior performance in high‐dimensional settings, with significantly lower estimation errors compared to convolution‐smoothed quantile regression and pure quantile loss methods. Applied to GTEx genomic data, our method improves prediction accuracy for JAM2 gene expression quantiles across brain tissues, highlighting its utility in precision medicine for modeling heterogeneous biological effects.