SparseGMM is a Bayesian generative model for learning the regulatory relationships among genes. In the context of gene regulatory networks, we classify genes into one of two types: target genes and regulator genes. Regulator genes are genes undergoing genomic events that are relevant to cancer progression or tumor growth. Target genes are genes whose expression is controlled by regulator genes, and which contribute to the biological processes responsible for cancer progression. Each group of target genes is regulated by a small set of regulator genes. To model this system, our Bayesian approach combines Gaussian mixtures with 1-norm regularization. We develop an expectation-maximization (EM)-based algorithm to obtain a maximum aposteriori (MAP) estimate the Gaussian mixture of parameters.