Multinomial belief networks

A Bayesian approach to machine learning is attractive when we need to quantify uncertainty, deal with missing observations, when samples are scarce, or when the data is sparse. All of these commonly apply when analysing healthcare data. To address these analytical requirements, we propose a deep generative model for multinomial count data where both the weights and hidden units of the network are Dirichlet distributed. A Gibbs sampling procedure is formulated that takes advantage of a series of augmentation relations, analogous to the Zhou--Cong--Chen model. We apply the model on small handwritten digits, and a large experimental dataset of DNA mutations in cancer, and we show how the model is able to extract biologically meaningful meta-signatures in a fully data-driven way.