# Nonlinear multi-study sparse factor analysis

arXiv: https://arxiv.org/abs/2601.18128 · HTML: https://mlsanity.com/paper/2601.18128/

## Key facts

- Cited by 1 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 26 Jan 2026.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Deep Learning is Not So Mysterious or Different](https://mlsanity.com/paper/2503.02113/) (2025)
- [Identifiable Deep Generative Models via Sparse Decoding](https://mlsanity.com/paper/2110.10804/) (2021)
- [Indeterminacy in Generative Models: Characterization and Strong Identifiability](https://mlsanity.com/paper/2206.00801/) (2022)
- [Unpaired Multi-Domain Causal Representation Learning](https://mlsanity.com/paper/2302.00993/) (2023)
- [Adaptive Estimation in Structured Factor Models with Applications to Overlapping Clustering](https://mlsanity.com/paper/1704.06977/) (2017)
- [Towards Interpretable Deep Generative Models via Causal Representation Learning](https://mlsanity.com/paper/2504.11609/) (2025)
- [Bayesian Combinatorial Multi-Study Factor Analysis](https://mlsanity.com/paper/2007.12616/) (2020)
- [Inferring Covariance Structure from Multiple Data Sources via Subspace Factor Analysis](https://mlsanity.com/paper/2305.04113/) (2023)
- [Spectral decomposition-assisted multi-study factor analysis](https://mlsanity.com/paper/2502.14600/) (2025)
- [Identifiable and interpretable nonparametric factor analysis](https://mlsanity.com/paper/2311.08254/) (2023)
- [Detecting approximate replicate components of a high-dimensional random vector with latent structure](https://mlsanity.com/paper/2010.02288/) (2020)
- [Fast Variational Inference for Bayesian Factor Analysis in Single and Multi-Study Settings](https://mlsanity.com/paper/2305.13188/) (2023)

## Built on by (most cited first, 1 of 1)

- [Unveiling Invariant and Transferable Latent Factors Across Heterogeneous Environments via ATLAS](https://mlsanity.com/paper/2607.18209/) (2026)

## Abstract (arXiv)

High-dimensional data often exhibit variation that can be captured by lower-dimensional factors. For high-dimensional data from multiple studies, one goal is to understand which underlying factors are common to all studies, and which factors are study-specific. As a particular example, we consider platelet gene expression data from patients in different disease groups. In this data, factors correspond to clusters of genes which are co-expressed; we may expect some clusters (or biological pathways) to be active for all diseases, while some clusters are only active for a specific disease. To learn these factors, we consider a nonlinear multi-study sparse factor model, which allows for both shared and study-specific factors. To fit this model, we propose a multi-study sparse variational autoencoder. The underlying model is sparse in that each observed feature (i.e. each dimension of the data) depends on a small subset of the latent factors. In the genomics example, this means each gene is active in only a few biological processes. We prove that the latent factor distributions are identifiable (up to element-wise transformations), and that the canonical shared and study-specific support structure is identifiable. Empirically, we demonstrate our method recovers meaningful factors in the platelet gene expression data.