bayesNMF: Fast Bayesian Poisson NMF with Automatically Learned Rank Applied to Mutational Signatures

Bayesian Poisson Non-Negative Matrix Factorization (NMF) is widely used to model count data, including in cancer mutational signature analysis. However, standard Gibbs samplers rely on computationally expensive Poisson augmentation, and current software implementations learn the latent rank either through slow and potentially subjective heuristic rank selection or with automatic approaches that do not report posterior uncertainty. In this paper, we introduce bayesNMF, an MH-within-Gibbs sampler to address both of these limitations. First, we define high-overlap proposals for Metropolis-Hastings sampling to remove the need for Poisson augmentation. Second, we define a BIC-based sparsity prior to learn rank automatically within the Bayesian formulation while allowing for posterior uncertainty quantification. We provide an open-source R software package with all of the models and plotting capabilities demonstrated in this paper on GitHub at jennalandy/bayesNMF. Although our applications focus on cancer mutational signatures, our software and results can be extended to any use of Bayesian Poisson NMF.