# Bayesian Simultaneous Factorization and Prediction Using Multi-Omic Data

arXiv: https://arxiv.org/abs/2211.16403 · HTML: https://mlsanity.com/paper/2211.16403/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 48 references that are in the map.
- First posted on arXiv 29 Nov 2022.

## Builds on (most cited first, 14 of 14)

- [Angle-Based Joint and Individual Variation Explained](https://mlsanity.com/paper/1704.02060/) (2017)
- [Structural Learning and Integrative Decomposition of Multi-View Data](https://mlsanity.com/paper/1707.06573/) (2017)
- [Cooperative learning for multiview analysis](https://mlsanity.com/paper/2112.12337/) (2021)
- [sJIVE: Supervised Joint and Individual Variation Explained](https://mlsanity.com/paper/2102.13278/) (2021)
- [Bayesian cumulative shrinkage for infinite factorizations](https://mlsanity.com/paper/1902.04349/) (2019)
- [Integrative Factor Regression and Its Inference for Multimodal Data Analysis](https://mlsanity.com/paper/1911.04056/) (2019)
- [Estimating the error variance in a high-dimensional linear model](https://mlsanity.com/paper/1712.02412/) (2017)
- [Sparse Linear Discriminant Analysis for Multi-view Structured Data](https://mlsanity.com/paper/1911.05643/) (2019)
- [Joint association and classification analysis of multi-view data](https://mlsanity.com/paper/1811.08511/) (2018)
- [Bidimensional linked matrix factorization for pan-omics pan-cancer analysis](https://mlsanity.com/paper/2002.02601/) (2020)
- [Integrative Factorization of Bidimensionally Linked Matrices](https://mlsanity.com/paper/1906.03722/) (2019)
- [Bayesian Integrative Analysis and Prediction with Application to Atherosclerosis Cardiovascular Disease](https://mlsanity.com/paper/2005.11586/) (2020)
- [Matrix Completion with Model-free Weighting](https://mlsanity.com/paper/2106.05850/) (2021)
- [Integrative clustering of high-dimensional data with joint and individual clusters, with an application to the Metabric study](https://mlsanity.com/paper/1410.8679/) (2014)

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

- [Bayesian Joint Additive Factor Models for Multiview Learning](https://mlsanity.com/paper/2406.00778/) (2024)
- [Interpretable Generative and Discriminative Learning for Multimodal and Incomplete Clinical Data](https://mlsanity.com/paper/2510.09513/) (2025)
- [Empirical Bayes Linked Matrix Decomposition](https://mlsanity.com/paper/2408.00237/) (2024)
- [Probabilistic Joint and Individual Variation Explained (ProJIVE) for Data Integration](https://mlsanity.com/paper/2603.12351/) (2026)

## Abstract (arXiv)

Understanding of the pathophysiology of obstructive lung disease (OLD) is limited by available methods to examine the relationship between multi-omic molecular phenomena and clinical outcomes. Integrative factorization methods for multi-omic data can reveal latent patterns of variation describing important biological signal. However, most methods do not provide a framework for inference on the estimated factorization, simultaneously predict important disease phenotypes or clinical outcomes, nor accommodate multiple imputation. To address these gaps, we propose Bayesian Simultaneous Factorization (BSF). We use conjugate normal priors and show that the posterior mode of this model can be estimated by solving a structured nuclear norm-penalized objective that also achieves rank selection and motivates the choice of hyperparameters. We then extend BSF to simultaneously predict a continuous or binary response, termed Bayesian Simultaneous Factorization and Prediction (BSFP). BSF and BSFP accommodate concurrent imputation and full posterior inference for missing data, including "blockwise" missingness, and BSFP offers prediction of unobserved outcomes. We show via simulation that BSFP is competitive in recovering latent variation structure, as well as the importance of propagating uncertainty from the estimated factorization to prediction. We also study the imputation performance of BSF via simulation under missing-at-random and missing-not-at-random assumptions. Lastly, we use BSFP to predict lung function based on the bronchoalveolar lavage metabolome and proteome from a study of HIV-associated OLD. Our analysis reveals a distinct cluster of patients with OLD driven by shared metabolomic and proteomic expression patterns, as well as multi-omic patterns related to lung function decline. Software is freely available at https://github.com/sarahsamorodnitsky/BSFP .