Doubly Non-Central Beta Matrix Factorization for DNA Methylation Data

Aaron Schein, Anjali Nagulpally, Hanna Wallach, Patrick Flaherty

Abstract:

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 stateof-
the-art methods in bioinformatics. In addition,
our model yields meaningful latent representations
that accord with existing biological knowledge