A classic problem in computational biology is the identification of altered subnetworks: subnetworks of an interaction network that contain genes/proteins that are differentially expressed, highly mutated, or otherwise aberrant compared to other genes/proteins. Numerous methods have been developed to solve this problem under various assumptions, but the statistical properties of these methods are often unknown. For example, some widely-used methods are reported to output very large subnetworks that are difficult to interpret biologically. In this work, we formulate the identification of altered subnetworks as the problem of estimating the parameters of a class of probability distributions which we call the Altered Subset Distribution (ASD). We derive a connection between a popular method, jActiveModules, and the maximum likelihood estimator (MLE) of the ASD. We show that the MLE is statistically biased, explaining the large subnetworks output by jActiveModules. We introduce NetMix, an algorithm that uses Gaussian mixture models to obtain less biased estimates of the parameters of the ASD. We demonstrate that NetMix outperforms existing methods in identifying altered subnetworks on both simulated and real data, including the identification of differentially expressed genes from both microarray and RNA-seq experiments and the identification of cancer driver genes in somatic mutation data.