  Integration of data from multiple omics techniques is becoming increasingly
important in biomedical research. Due to non-uniformity and technical
limitations in omics platforms, such integrative analyses on multiple omics,
which we refer to as views, involve learning from incomplete observations with
various view-missing patterns. This is challenging because i) complex
interactions within and across observed views need to be properly addressed for
optimal predictive power and ii) observations with various view-missing
patterns need to be flexibly integrated. To address such challenges, we propose
a deep variational information bottleneck (IB) approach for incomplete
multi-view observations. Our method applies the IB framework on marginal and
joint representations of the observed views to focus on intra-view and
inter-view interactions that are relevant for the target. Most importantly, by
modeling the joint representations as a product of marginal representations, we
can efficiently learn from observed views with various view-missing patterns.
Experiments on real-world datasets show that our method consistently achieves
gain from data integration and outperforms state-of-the-art benchmarks.
