Extraction of all the biological information inherent in large-scale genetic interaction datasets remains a significant challenge for systems biology. The core problem is essentially that of classification of the relationships among phenotypes of mutant strains into biologically informative rules of gene interaction. Geneticists have determined such classifications based on insights from biological examples, but it is not clear that there is a systematic, unsupervised way to extract this information. In this paper we describe such a method that depends on maximizing a previously described context-dependent information measure to obtain maximally informative biological networks. We have successfully validated this method on two examples from yeast by demonstrating that more biological information is obtained when analysis is guided by this information measure. The context-dependent information measure is a function only of phenotype data and a set of interaction rules, involving no prior biological knowledge. Analysis of the resulting networks reveals that the most biologically informative networks are those with the greatest context-dependent information scores. We propose that these high-complexity networks reveal genetic architecture at a modular level, in contrast to classical genetic interaction rules that order genes in pathways. We suggest that our analysis represents a powerful, data-driven, and general approach to genetic interaction analysis, with particular potential in the study of mammalian systems in which interactions are complex and gene annotation data are sparse.