Inference of biological network structures is often performed on high-dimensional data, yet is hindered by the limited sample size of high throughput “omics” data typically available. To overcome this challenge, often referred to as the “smalln, largepproblem,” we exploit known organizing principles of biological networks that are sparse, modular, and likely share a large portion of their underlying architecture. We present SHINE—Structure Learning forHierarchicalNetworks—a framework for defining data-driven structural constraints and incorporating a shared learning paradigm for efficiently learning multiple Markov networks from high-dimensional data at largep/nratios not previously feasible. We evaluated SHINE on Pan-Cancer data comprising 23 tumor types, and found that learned tumor-specific networks exhibit expected graph properties of real biological networks, recapture previously validated interactions, and recapitulate findings in literature. Application of SHINE to the analysis of subtype-specific breast cancer networks identified key genes and biological processes for tumor maintenance and survival as well as potential therapeutic targets for modulating known breast cancer disease genes.