Empirical Bayes Matrix Factorization Workshop

Materials for a 1-hour mini-workshop on Empirical Bayes Normal Means (EBNM), Empirical Bayes Matrix Factorization (EBMF), and multi-block extensions.

Delivered Tue 24 March at Melbourne Integrative Genomics, University of Melbourne.

Let me know if you have any suggestions for improving the materials, or that you'd want to use the materials for some other purposes (e.g. a different dataset): Jiadong Mao's email.

Workshop materials

Material	Format	Description
Workshop slides	xaringan slides	45 min presentation + 15 min hands-on
EBNMF handout	HTML document	Technical reference covering EBNM, prior families, flashier, and GBCD
DIVAS handout	HTML document	Multi-block decomposition via DIVAS

Topics covered

1. Empirical Bayes shrinkage -- connecting limma, edgeR, and ashr to the EBNM framework
2. The EBNM problem -- prior families, the ebnm R package, and adaptive shrinkage
3. EBMF and flashier -- matrix factorization with EB priors; automatic K selection
4. GBCD -- Generalized Binary Covariance Decomposition for shared/context-specific programs
5. DIVAS -- Data Integration Via Analysis of Subspaces for multi-block data

Case study

The workshop uses a COVID-19 multiomics cohort (Su et al., Cell 2020) as a running example: 120 patients, Olink proteomics at two time points, severity scores 1--7.

Source files

• EBNMF.md -- handout source (Markdown)
• DIVAS.md -- DIVAS handout source
• slides_workshop.Rmd -- slides source (xaringan/R Markdown)
• workshopCode.R -- hands-on R code for participants
• EBNMF_guide.md -- flashier + GBCD API reference
• DIVAS_guide.md -- DIVAS API reference

Key R packages

• ebnm -- Empirical Bayes Normal Means
• flashier -- Empirical Bayes Matrix Factorization
• fastTopics -- Topic models / Poisson NMF
• DIVAS -- Multi-block decomposition

References

• Willwerscheid, Carbonetto & Stephens (2025). ebnm: an R package for solving the empirical Bayes normal means problem using a variety of prior families. JSS.
• Liu, Carbonetto et al. (2025). Dissecting tumor transcriptional heterogeneity from multi-tumor single-cell RNA-seq data. Nature Genetics.
• Carbonetto, Sarkar, Wang & Stephens (2021). Non-negative matrix factorization algorithms greatly improve topic model fits. arXiv.
• Carbonetto, Luo, Sarkar et al. (2023). GoM DE: interpreting structure in sequence count data with differential expression analysis allowing for grades of membership. Genome Biology.
• Sun, Marron, Le Cao & Mao (2026). DIVAS: Data Integration Via Analysis of Subspaces. bioRxiv.