Title: Coupled Compound Poisson Factorization,
Abstract: We present a general framework, the coupled compound Poisson factorization
(CCPF), to capture the missing-data mechanism in extremely sparse data sets by
coupling a hierarchical Poisson factorization with an arbitrary data-generating
model. We derive a stochastic variational inference algorithm for the resulting
model and, as examples of our framework, implement three different
data-generating models---a mixture model, linear regression, and factor
analysis---to robustly model non-random missing data in the context of
clustering, prediction, and matrix factorization. In all three cases, we test
our framework against models that ignore the missing-data mechanism on large
scale studies with non-random missing data, and we show that explicitly
modeling the missing-data mechanism substantially improves the quality of the
results, as measured using data log likelihood on a held-out test set.