# Encoding Domain Knowledge in Multi-view Latent Variable Models: A Bayesian Approach with Structured Sparsity

arXiv: https://arxiv.org/abs/2204.06242 · HTML: https://mlsanity.com/paper/2204.06242/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 53 references that are in the map.
- First posted on arXiv 13 Apr 2022.

## Builds on (most cited first, 12 of 12)

- [Pyro: Deep Universal Probabilistic Programming](https://mlsanity.com/paper/1810.09538/) (2018)
- [Black Box Variational Inference](https://mlsanity.com/paper/1401.0118/) (2013)
- [Don't Blame the ELBO! A Linear VAE Perspective on Posterior Collapse](https://mlsanity.com/paper/1911.02469/) (2019)
- [Bayesian Compression for Deep Learning](https://mlsanity.com/paper/1705.08665/) (2017)
- [Generalized Product of Experts for Automatic and Principled Fusion of Gaussian Process Predictions](https://mlsanity.com/paper/1410.7827/) (2014)
- [Model Selection in Bayesian Neural Networks via Horseshoe Priors](https://mlsanity.com/paper/1705.10388/) (2017)
- [Sparsity information and regularization in the horseshoe and other shrinkage priors](https://mlsanity.com/paper/1707.01694/) (2017)
- [A Variational Information Bottleneck Approach to Multi-Omics Data Integration](https://mlsanity.com/paper/2102.03014/) (2021)
- [Structured Variational Learning of Bayesian Neural Networks with Horseshoe Priors](https://mlsanity.com/paper/1806.05975/) (2018)
- [Adaptive Estimation in Structured Factor Models with Applications to Overlapping Clustering](https://mlsanity.com/paper/1704.06977/) (2017)
- [Group Factor Analysis](https://mlsanity.com/paper/1411.5799/) (2014)
- [Tag-Aware Ordinal Sparse Factor Analysis for Learning and Content Analytics](https://mlsanity.com/paper/1412.5967/) (2014)

## Built on by (most cited first, 3 of 3)

- [Inference on covariance structure in high-dimensional multi-view data](https://mlsanity.com/paper/2509.02772/) (2025)
- [Factor Analysis with Correlated Topic Model for Multi-Modal Data](https://mlsanity.com/paper/2504.18914/) (2025)
- [The Trade-off Between Covariate Dependence and Latent Structure in Representation Learning](https://mlsanity.com/paper/2608.16245/) (2026)

## Abstract (arXiv)

Many real-world systems are described not only by data from a single source but via multiple data views. In genomic medicine, for instance, patients can be characterized by data from different molecular layers. Latent variable models with structured sparsity are a commonly used tool for disentangling variation within and across data views. However, their interpretability is cumbersome since it requires a direct inspection and interpretation of each factor from domain experts. Here, we propose MuVI, a novel multi-view latent variable model based on a modified horseshoe prior for modeling structured sparsity. This facilitates the incorporation of limited and noisy domain knowledge, thereby allowing for an analysis of multi-view data in an inherently explainable manner. We demonstrate that our model (i) outperforms state-of-the-art approaches for modeling structured sparsity in terms of the reconstruction error and the precision/recall, (ii) robustly integrates noisy domain expertise in the form of feature sets, (iii) promotes the identifiability of factors and (iv) infers interpretable and biologically meaningful axes of variation in a real-world multi-view dataset of cancer patients.