Inferring Covariance Structure from Multiple Data Sources via Subspace Factor Analysis.

Area of Science:

• Statistics
• Bioinformatics
• Genomics

Background:

• Factor analysis is key for dimensionality reduction in high-dimensional data.
• Analyzing data across different conditions requires distinguishing shared from specific structures.
• Existing hierarchical factor analysis models struggle with identifiability.

Purpose of the Study:

• To propose a novel class of Subspace Factor Analysis (SUFA) models.
• To address identifiability challenges in hierarchical factor analysis.
• To enable learning of shared and group-specific covariance structures.

Main Methods:

• Developed SUFA models characterizing variation at the subspace level.
• Proved identifiability of shared and group-specific covariance components.
• Employed a Bayesian approach with efficient posterior computation algorithms.

Main Results:

• Demonstrated identifiability of shared versus group-specific covariance.
• Analyzed posterior contraction properties of SUFA models.
• Developed a parallelizable sampler with sample-size independent complexity.

Conclusions:

• SUFA models offer a statistically sound and computationally efficient solution for multi-condition data analysis.
• The proposed Bayesian framework facilitates robust inference and scalable computation.
• Applied SUFA to integrate multiple gene expression datasets in immunology, showcasing practical utility.