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Abstract: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.

Submission history

From: Gemma Moran [view email]
[v1] Mon, 26 Jan 2026 04:16:47 UTC (307 KB)
[v2] Tue, 11 Aug 2026 17:36:11 UTC (346 KB)