The primary goal of this thesis is to discover multivariate interactions in high-throughput biological data. The criteria for a valid multivariate interaction is quite strict. It is required that the “whole” of the interaction demonstrate a greater association than the “sum of the parts”. This phenomenon is called synergy. This concept is rigorously defined in information theoretic terms and the subtleties of its implications explored. Various methods for estimating synergy in biological settings are presented.

Next, a gene expression data set consisting of prostate cancer samples and normal prostate tissue are used to create a “synergy network” of gene pairs with respect to the phenotype. The strongest connections in the network are validated in an independent data set. The network as well as its hub gene members could help shed light on the etiology and progression of the disease.

In a different setting, gene regulatory interactions are inferred from a compendium of E. coli gene expressiou samples. The existence of a synergistic partner interacting with a transcription factor and its putative target adds additional evidence that the transcription factor does indeed regulate the target. The method was the best-performing in the DREAM2 Genome Scale Network Challenge.

Expanding on the E. coli results, two large H. sapiens gene expression data sets consisting of ovarian cancer samples are studied. A validated interaction network is generated, and Gene Ontology enrichment is performed to find putative biological processes associated with ovarian cancer progression.

Finally, a synergy metric is defined for genotype data, called synergy disequilibrium. It is closely related to the concept of linkage disequilibrium, but directly involves a phenotype as a third variable. The method is used to characterize some well-known disease associations. The method shows real promise in discovering epistatically disease-associated pairs of loci once data sets become sufficiently large and statistically powerful.