Empirical Bayes Linked Matrix Decomposition for Integration of Multi-Omic Multi-Cohort Data

Music City Center 

We propose an empirical variational Bayesian approach to factorization of linked matrices that has several advantages over existing techniques. It has the flexibility to accommodate shared signal over any number of row or column sets (i.e., bidimensional integration), an intuitive model-based objective function that yields appropriate shrinkage for the inferred signals, and a relatively efficient estimation algorithm with no tuning parameters. A general result establishes conditions for the uniqueness of the underlying decomposition for a broad family of methods that includes the proposed approach. For scenarios with missing data, we describe an associated iterative imputation approach that is novel for the single-matrix context and a powerful approach for "blockwise" imputation (in which an entire row or column is missing) in various linked matrix contexts. he approach is applied to gene expression and miRNA data from breast cancer tissue and normal breast tissue, for which it gives an informative decomposition of variation and outperforms alternative strategies for missing data imputation.

Data integration

Missing data imputation

Matrix completion

Low-rank factorizåtion

Variational Bayes

Dimension reduction