In this paper, the regulatory interactions between genes are modeled by alinear genetic network that is estimated from gene expression data. The inference of such a genetic network is hampered by the dimensionality problem. This problem is inherent in all gene expression data since the number of genes by far exceeds the number of measured time points. Consequently, there are infinitely many solutions that t the data set perfectly. In this paper, this problem is tackled by combining genes with similar expression profiles in a single prototypical gene. Instead of modeling the genes individually, the relations between prototypical genes are modeled. In this way, genes that cannot be distinguished based on their expression profiles are grouped together and their common control action is modeled instead. This process reduces the number of signals and imposes a structure on the model that is supported by the fact that biological genetic networks are thought to be redundant and sparsely connected. In essence, the ambiguity in model solutions is represented explicitly by providing a generalized model that expresses the basic regulatory interactions between groups of similarly expressed genes. The modeling approach is illustrated on artificial as well as real data.