  We present a new non-negative matrix factorization model for $(0,1)$
bounded-support data based on the doubly non-central beta (DNCB) distribution,
a generalization of the beta distribution. The expressiveness of the DNCB
distribution is particularly useful for modeling DNA methylation datasets,
which are typically highly dispersed and multi-modal; however, the model
structure is sufficiently general that it can be adapted to many other domains
where latent representations of $(0,1)$ bounded-support data are of interest.
Although the DNCB distribution lacks a closed-form conjugate prior, several
augmentations let us derive an efficient posterior inference algorithm composed
entirely of analytic updates. Our model improves out-of-sample predictive
performance on both real and synthetic DNA methylation datasets over
state-of-the-art methods in bioinformatics. In addition, our model yields
meaningful latent representations that accord with existing biological
knowledge.
