  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.
