🤖 AI Summary
Disentangling shared and study-specific latent factors from high-dimensional data across multiple studies remains a key challenge in cross-disease gene expression analysis. This work proposes a nonlinear multi-study sparse variational autoencoder that, for the first time, integrates a sparse nonlinear factor model into a multi-study framework. By implicitly penalizing the number of latent factors and modeling sparse dependencies between features and latent factors, the method automatically separates shared from study-specific components. Theoretical analysis establishes identifiability of the latent factors, and experiments on platelet gene expression data successfully recover biologically meaningful co-expression modules, demonstrating both the effectiveness and interpretability of the approach.
📝 Abstract
High-dimensional data often exhibit variation that can be captured by lower dimensional factors. For high-dimensional data from multiple studies or environments, one goal is to understand which underlying factors are common to all studies, and which factors are study or environment-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 factor model, which allows for both shared and 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. Further, the model implicitly induces a penalty on the number of latent factors, which helps separate the shared factors from the group-specific factors. We prove that the latent factors are identified, and demonstrate our method recovers meaningful factors in the platelet gene expression data.