Bayesian covariate-dependent graph learning with a dual group spike-and-slab prior.

Area of Science:

• Statistics
• Machine Learning
• Bioinformatics

Background:

• Covariate-dependent graph learning is crucial for analyzing heterogeneous data but faces modeling and computational challenges.
• Existing methods struggle with multi-level sparsity and interpretability in complex graphical structures.
• The parameter of interest in these models can be represented as a 3D array, requiring specialized handling.

Purpose of the Study:

• To propose a novel dual group spike-and-slab prior for enhanced covariate-dependent graph learning.
• To enable multi-level sparsity selection at covariate, node, and individual levels.
• To improve computational efficiency and interpretability in graphical modeling.

Main Methods:

• Developed a novel dual group spike-and-slab prior for multi-level sparsity.
• Introduced a nested strategy to address distinct challenges in grouping directions.
• Implemented a full Gibbs sampler for efficient posterior inference and parameter tuning.

Main Results:

• The proposed model demonstrated superior accuracy in graph recovery compared to existing methods in simulation studies.
• The dual group spike-and-slab prior effectively enables selection at covariate, node, and individual levels.
• The Gibbs sampler facilitated routine implementation and mitigated parameter tuning difficulties.

Conclusions:

• The novel dual group spike-and-slab prior offers a powerful tool for covariate-dependent graph learning.
• The method provides accurate graph recovery and facilitates understanding of complex data structures.
• Applied to microbiome data, the model enhances insights into microbial interactions and covariate effects.