Semi-parametric Bayes regression with network-valued covariates.

Area of Science:

• Network analysis
• Statistical modeling
• Computational neuroscience

Background:

• High-dimensional network data is rapidly increasing across disciplines.
• Existing regression models struggle with network data complexity, linearity assumptions, and dimensionality.
• Current methods fail to capture non-linear relationships or higher-order interactions.

Purpose of the Study:

• To develop a novel Bayesian non-parametric regression framework for high-dimensional networks.
• To overcome limitations of existing linear and non-linear network regression models.
• To enable node selection and improve prediction accuracy in network analysis.

Main Methods:

• A two-stage Bayesian non-parametric regression framework is proposed.
• Networks are first represented in a lower-dimensional, node-specific manner.
• Gaussian process regression with spike-and-slab priors is used for modeling and node selection.

Main Results:

• The proposed model demonstrates superior performance in prediction, coverage, and node selection compared to existing methods.
• Significant gains were observed in predicting posttraumatic stress disorder (PTSD) resilience using brain networks.
• The model successfully identified important brain regions associated with PTSD.

Conclusions:

• The novel framework effectively handles high-dimensional network data, overcoming limitations of previous approaches.
• The node-level analysis and Gaussian process regression enable scalable and flexible modeling.
• This approach offers improved predictive power and robust feature selection for neuroimaging and other network-based studies.