Joint Estimation and Inference for Data Integration Problems based on Multiple Multi-layered Gaussian Graphical Models

Aberrations in complex biological systems develop in the background of diverse genetic and environmental factors and are associated with multiple complex molecular events. These include changes in the genome, transcriptome, proteome and metabolome, as well as epigenetic effects. Advances in high-throughput profiling techniques have enabled a systematic and comprehensive exploration of the genetic and epigenetic basis of various diseases, including cancer (Kaushik et al., 2016; Lee et al., 2016), diabetes (Sas et al., 2018; Yuan et al., 2014), chronic kidney disease (Atzler et al., 2014), etc. Further, such multi-Omics collections have become available for patients belonging to different, but related disease subtypes, with The Cancer Genome Atlas (TCGA: Tomczak et al. (2015)) being a prototypical one. Hence, there is an increasing need for models that can integrate such complex data both vertically across multiple modalities and horizontally across different disease subtypes. Figure 1 provides a schematic representation of the horizontal and vertical structure of such heterogeneous multi-modal Omics data as outlined above.