Low-Rank Variational Correction Estimation for Multi-Source Heterogeneous Quantile Linear Regression Models

Area of Science:

• Genomics
• Econometrics
• Clinical Medicine
• Statistical Modeling

Background:

• High-dimensional data from multiple sources often display significant heterogeneity.
• Existing methods struggle to address both high dimensionality and between-source heterogeneity simultaneously.
• Quantile regression is a powerful tool for analyzing data distributions but faces challenges with complex data structures.

Purpose of the Study:

• To develop a scalable Bayesian framework for multi-source heterogeneous quantile regression.
• To enable simultaneous parameter estimation and feature selection in high-dimensional settings.
• To improve computational efficiency and inference accuracy for complex biological and medical data.

Main Methods:

• Proposed a Bayesian framework using spike-and-slab priors for parameter estimation and feature selection.
• Combined mean-field variational inference with Laplace approximation for computational efficiency.
• Introduced a novel low-rank variational correction strategy to enhance approximation accuracy and adaptability.
• Developed a Bayesian score test and local influence analysis for model assessment.

Main Results:

• The proposed low-rank variational correction significantly improves approximation accuracy in high-dimensional heterogeneous settings.
• The framework demonstrates computational efficiency, scalability, and practical utility through simulations and TCGA data analysis.
• The method effectively captures underlying dependence structures for more robust and efficient inference.
• Analysis of TCGA data from four cancer cohorts (ESCA, PAAD, PCPG, READ) validated the approach.

Conclusions:

• The developed Bayesian framework offers a scalable and efficient solution for high-dimensional, multi-source heterogeneous quantile regression.
• The novel low-rank variational correction is key to improving inference in complex data scenarios.
• The R package LRQVB provides a publicly available tool for applying these advanced statistical methods.
• The method shows significant promise for applications in genomics, econometrics, and clinical medicine.