Empirical Bayes Linked Matrix Decomposition.

Area of Science:

• Biostatistics
• Bioinformatics
• Computational Biology

Background:

• Diverse data applications, especially in molecular biomedical research, involve multiple linked matrices.
• Integrative matrix factorization is crucial for identifying shared and specific low-dimensional signals across these matrices.

Purpose of the Study:

• To propose an empirical variational Bayesian approach for integrative matrix factorization.
• To offer flexibility in accommodating shared signals across multiple row or column sets (bidimensional integration).
• To provide an efficient estimation algorithm with no tuning parameters and a model-based objective function.

Main Methods:

• An empirical variational Bayesian framework for matrix factorization.
• A general theoretical result establishing conditions for decomposition uniqueness.
• An iterative imputation approach for missing data, including novel blockwise imputation.

Main Results:

• The proposed method accurately recovers low-rank signals and decomposes shared and specific components.
• Simulations demonstrate strong performance in various scenarios, including missing data imputation.
• The approach successfully applied to gene expression and miRNA data from breast cancer, outperforming alternatives.

Conclusions:

• The novel Bayesian method offers a flexible and efficient tool for integrative matrix factorization in complex biological data.
• The method provides accurate signal decomposition and robust missing data imputation.
• This approach enhances the understanding of variation in molecular omics data, as shown in breast cancer analysis.