We propose a model-driven approach for analyzing genomic expression data that permits genetic regulatory networks to be represented in a biologically interpretable computational form. Our models permit latent variables capturing unobserved factors, describe arbitrarily complex (more than pair-wise) relationships at varying levels of refinement, and can be scored rigorously against observational data. The models that we use are based on Bayesian networks and their extensions. As a demonstration of this approach, we utilize 52 genomes worth of Affymetrix GeneChip expression data to correctly differentiate between alternative hypotheses of the galactose regulatory network in S. cerevisiae. When we extend the graph semantics to permit annotated edges, we are able to score models describing relationships at a finer degree of specification.