# Bayesian Combinatorial Multi-Study Factor Analysis

arXiv: https://arxiv.org/abs/2007.12616 · HTML: https://mlsanity.com/paper/2007.12616/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jul 2020.

## Built on by (most cited first, 4 of 4)

- [Stacked SVD or SVD stacked? A Random Matrix Theory perspective on data integration](https://mlsanity.com/paper/2507.22170/) (2025)
- [Nonlinear multi-study sparse factor analysis](https://mlsanity.com/paper/2601.18128/) (2026)
- [Unveiling Invariant and Transferable Latent Factors Across Heterogeneous Environments via ATLAS](https://mlsanity.com/paper/2607.18209/) (2026)
- [Effects of Structural Allocation of Geometric Task Diversity in Linear Meta-Learning Models](https://mlsanity.com/paper/2509.18349/) (2025)

## Abstract (arXiv)

Analyzing multiple studies allows leveraging data from a range of sources and populations, but until recently, there have been limited methodologies to approach the joint unsupervised analysis of multiple high-dimensional studies. A recent method, Bayesian Multi-Study Factor Analysis (BMSFA), identifies latent factors common to all studies, as well as latent factors specific to individual studies. However, BMSFA does not allow for partially shared factors, i.e. latent factors shared by more than one but less than all studies. We extend BMSFA by introducing a new method, Tetris, for Bayesian combinatorial multi-study factor analysis, which identifies latent factors that can be shared by any combination of studies. We model the subsets of studies that share latent factors with an Indian Buffet Process. We test our method with an extensive range of simulations, and showcase its utility not only in dimension reduction but also in covariance estimation. Finally, we apply Tetris to high-dimensional gene expression datasets to identify patterns in breast cancer gene expression, both within and across known classes defined by germline mutations.