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

Music City Center 

Bayesian Non-Negative Matrix Factorization (NMF) is a method of interest across fields including genomics, neuroscience, and audio and image processing. Bayesian Poisson NMF is of particular importance for count data, such as in cancer mutational signatures analysis. However, MCMC methods for Bayesian Poisson NMF require a computationally intensive Poisson augmentation. Further, identifying the latent rank is necessary, but commonly used heuristic approaches are slow and potentially subjective, and methods that learn rank automatically fail to provide posterior uncertainties. We introduce bayesNMF, a computationally efficient Gibbs sampler for Bayesian Poisson NMF. The desired Poisson-likelihood NMF is paired with a Normal-likelihood NMF for high-overlap proposal distributions in approximate Metropolis updates, avoiding augmentation. We additionally define Bayesian factor inclusion (BFI) and sparse Bayesian factor inclusion (SBFI) to identify rank automatically while providing posterior uncertainty. We provide an open-source R software package on GitHub. Our applications focus on mutational signatures, but our software and results can be extended to any use of Bayesian Poisson NMF.

Non-negative matrix factorization

Efficient Bayesian computation

Gibbs sampling

Mutational signatures 

Section on Bayesian Statistical Science