  Multi-omics data analysis has the potential to discover hidden molecular
interactions, revealing potential regulatory and/or signal transduction
pathways for cellular processes of interest when studying life and disease
systems. One of critical challenges when dealing with real-world multi-omics
data is that they may manifest heterogeneous structures and data quality as
often existing data may be collected from different subjects under different
conditions for each type of omics data. We propose a novel deep Bayesian
generative model to efficiently infer a multi-partite graph encoding molecular
interactions across such heterogeneous views, using a fused Gromov-Wasserstein
(FGW) regularization between latent representations of corresponding views for
integrative analysis. With such an optimal transport regularization in the deep
Bayesian generative model, it not only allows incorporating view-specific side
information, either with graph-structured or unstructured data in different
views, but also increases the model flexibility with the distribution-based
regularization. This allows efficient alignment of heterogeneous latent
variable distributions to derive reliable interaction predictions compared to
the existing point-based graph embedding methods. Our experiments on several
real-world datasets demonstrate enhanced performance of MoReL in inferring
meaningful interactions compared to existing baselines.
