Bayesian Multi-Group Gaussian Process Models for Heterogeneous Group-Structured Data.

Area of Science:

• Statistics
• Machine Learning
• Functional Data Analysis

Background:

• Gaussian processes are widely used for modeling complex dependencies in various scientific fields.
• Scientific data often exhibit heterogeneity and contain discrete sample groups, requiring methods that can leverage inter-group similarities while respecting intra-group differences.

Purpose of the Study:

• To introduce Multi-Group Gaussian Processes (MGGPs) for modeling heterogeneous scientific data with multiple known discrete groups.
• To develop valid covariance functions for MGGPs defined over domains combining continuous and categorical variables.
• To enable accurate recovery of relationships between groups and efficient information sharing across samples.

Main Methods:

• Definition of MGGPs over the domain R^p x C, where C is a finite set of group labels.
• Development of general classes of valid (positive definite) covariance functions for MGGPs.
• Demonstration of inference through simulation experiments and application to gene expression data.

Main Results:

• MGGPs accurately recover relationships between groups.
• The framework efficiently shares statistical strength across all samples during inference.
• Distinct group-specific behaviors are captured in conditional posterior distributions.

Conclusions:

• MGGPs offer enhanced inferential capabilities for jointly modeling continuous and categorical variables in heterogeneous scientific data.
• The proposed regression framework effectively illustrates the behavior and advantages of MGGPs.
• MGGPs provide a powerful tool for analyzing complex, multi-group scientific datasets.