# Bayesian Joint Additive Factor Models for Multiview Learning

arXiv: https://arxiv.org/abs/2406.00778 · HTML: https://mlsanity.com/paper/2406.00778/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 61 references that are in the map.
- First posted on arXiv 2 Jun 2024.

## Builds on (most cited first, 27 of 27)

- [A General Framework for Updating Belief Distributions](https://mlsanity.com/paper/1306.6430/) (2013)
- [Assigning a value to a power likelihood in a general Bayesian model](https://mlsanity.com/paper/1701.08515/) (2017)
- [Bayesian linear regression with sparse priors](https://mlsanity.com/paper/1403.0735/) (2014)
- [Robust Bayesian inference via coarsening](https://mlsanity.com/paper/1506.06101/) (2015)
- [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)
- [Bayesian Pyramids: Identifiable Multilayer Discrete Latent Structure Models for Discrete Data](https://mlsanity.com/paper/2101.10373/) (2021)
- [Multimodal Deep Learning for Finance: Integrating and Forecasting International Stock Markets](https://mlsanity.com/paper/1903.06478/) (2019)
- [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)
- [Escaping the curse of dimensionality in Bayesian model based clustering](https://mlsanity.com/paper/2006.02700/) (2020)
- [Integrative Factor Regression and Its Inference for Multimodal Data Analysis](https://mlsanity.com/paper/1911.04056/) (2019)
- [Bidimensional linked matrix factorization for pan-omics pan-cancer analysis](https://mlsanity.com/paper/2002.02601/) (2020)
- [Hierarchical nuclear norm penalization for multi-view data](https://mlsanity.com/paper/2206.12891/) (2022)
- [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)
- [Generalized infinite factorization models](https://mlsanity.com/paper/2103.10333/) (2021)
- [Sparse Bayesian Factor Analysis when the Number of Factors is Unknown](https://mlsanity.com/paper/1804.04231/) (2018)
- [Bayesian Factor Analysis for Inference on Interactions](https://mlsanity.com/paper/1904.11603/) (2019)
- [On the identifiability of Bayesian factor analytic models](https://mlsanity.com/paper/2004.05105/) (2020)
- [Bayesian Constraint Relaxation](https://mlsanity.com/paper/1801.01525/) (2018)
- [Nonparametric Copula Models for Multivariate, Mixed, and Missing Data](https://mlsanity.com/paper/2210.14988/) (2022)
- [Bayesian Simultaneous Factorization and Prediction Using Multi-Omic Data](https://mlsanity.com/paper/2211.16403/) (2022)
- [Inferring Covariance Structure from Multiple Data Sources via Subspace Factor Analysis](https://mlsanity.com/paper/2305.04113/) (2023)
- [Incorporating Covariates into Integrated Factor Analysis of Multi-View Data](https://mlsanity.com/paper/1703.05794/) (2017)
- [Discovering Inductive Bias with Gibbs Priors: A Diagnostic Tool for Approximate Bayesian Inference](https://mlsanity.com/paper/2203.03353/) (2022)

## Built on by (most cited first, 5 of 5)

- [Multi-task Learning for Heterogeneous Multi-source Block-Wise Missing Data](https://mlsanity.com/paper/2505.24413/) (2025)
- [Inference on covariance structure in high-dimensional multi-view data](https://mlsanity.com/paper/2509.02772/) (2025)
- [DAIF: A Data-Driven Intermediate Fusion Framework for Multimodal Supervised Learning via Approximate Message Passing](https://mlsanity.com/paper/2608.02769/) (2026)
- [The Trade-off Between Covariate Dependence and Latent Structure in Representation Learning](https://mlsanity.com/paper/2608.16245/) (2026)
- [FedMHAR: Federated Multimodal Human Activity Recognition using Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2609.33492/) (2026)

## Abstract (arXiv)

It is increasingly common to collect data of multiple different types on the same set of samples. Our focus is on studying relationships between such multiview features and responses. A motivating application arises in the context of precision medicine where multi-omics data are collected to correlate with clinical outcomes. It is of interest to infer dependence within and across views while combining multimodal information to improve the prediction of outcomes. The signal-to-noise ratio can vary substantially across views, motivating more nuanced statistical tools beyond standard late and early fusion. This challenge comes with the need to preserve interpretability, select features, and obtain accurate uncertainty quantification. To address these challenges, we introduce two complementary factor regression models. A baseline Joint Factor Regression (textscjfr) captures combined variation across views via a single factor set, and a more nuanced Joint Additive FActor Regression (textscjafar) that decomposes variation into shared and view-specific components. For textscjfr, we use independent cumulative shrinkage process (textsci-cusp) priors, while for textscjafar we develop a dependent version (textscd-cusp) designed to ensure identifiability of the components. We develop Gibbs samplers that exploit the model structure and accommodate flexible feature and outcome distributions. Prediction of time-to-labor onset from immunome, metabolome, and proteome data illustrates performance gains against state-of-the-art competitors. Our open-source software (textttR package) is available at https://github.com/niccoloanceschi/jafar.