A generalized likelihood-based Bayesian approach for scalable joint regression and covariance selection in high...

Area of Science:

• Statistics
• Computational Biology
• Machine Learning

Background:

• High-dimensional multivariate regression models require joint sparsity selection for understanding complex relationships.
• Existing Bayesian methods often lack scalability or comprehensive uncertainty quantification.

Purpose of the Study:

• To develop a scalable Bayesian algorithm for joint sparsity selection in regression coefficients and error precision matrices.
• To enable accurate uncertainty quantification and accommodate general sparsity patterns.

Main Methods:

• Developed the Joint Regression Network Selector (JRNS) algorithm using a bi-convex regression generalized likelihood and spike-and-slab priors.
• Implemented an efficient computational approach for joint regression and covariance selection.

Main Results:

• The JRNS algorithm demonstrates scalability and is significantly faster than existing Bayesian methods.
• Achieved accurate uncertainty quantification and accommodated general sparsity patterns.
• Validated through synthetic data and cancer datasets, showing statistical and computational efficacy.

Conclusions:

• The proposed JRNS algorithm offers a scalable and effective Bayesian approach for joint sparsity selection in high-dimensional settings.
• Provides robust uncertainty quantification crucial for network analysis in biological and statistical applications.