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Many real-world systems are described not only by data from a single sourcebut via multiple data views. In genomic medicine, for instance, patients can becharacterized by data from different molecular layers. Latent variable modelswith structured sparsity are a commonly used tool for disentangling variationwithin and across data views. However, their interpretability is cumbersomesince it requires a direct inspection and interpretation of each factor fromdomain experts. Here, we propose MuVI, a novel multi-view latent variable modelbased on a modified horseshoe prior for modeling structured sparsity. Thisfacilitates the incorporation of limited and noisy domain knowledge, therebyallowing for an analysis of multi-view data in an inherently explainablemanner. We demonstrate that our model (i) outperforms state-of-the-artapproaches for modeling structured sparsity in terms of the reconstructionerror and the precision/recall, (ii) robustly integrates noisy domain expertisein the form of feature sets, (iii) promotes the identifiability of factors and(iv) infers interpretable and biologically meaningful axes of variation in areal-world multi-view dataset of cancer patients.

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