Modern high-throughput experimental assays provide exquisitely detailed measurements of the molecular state of biological samples by simultaneously probing 105-106 markers per sample in a variety of modalities (DNA sequence and copy number variation, gene expression, microRNA expression, methylation states, protein abundances, and so forth). However, the nature of biological complexity presents two major challenges in the analysis of this data. First, we expect that complex traits and diseases are driven by the action of molecular systems, rather than individual genes; as a result, analysis techniques that rely upon single-marker associations are likely to miss multi-gene effects in which no individual gene achieves significance. Second, the observed molecular diversity even in phenotypically similar samples suggests that there is more than one path to an outcome---for instance, "hits" to a critical, disease-associated pathway may be acquired through mutation in one sample, altered methylation in another, disregulated expression in a third, and so forth. These two challenges motivate a need for analysis techniques with the power to reveal system-level biological differences between phenotypes.