  This paper tackles the problem of decomposing binary data using matrix
factorization. We consider the family of mean-parametrized Bernoulli models, a
class of generative models that are well suited for modeling binary data and
enables interpretability of the factors. We factorize the Bernoulli parameter
and consider an additional Beta prior on one of the factors to further improve
the model's expressive power. While similar models have been proposed in the
literature, they only exploit the Beta prior as a proxy to ensure a valid
Bernoulli parameter in a Bayesian setting; in practice it reduces to a uniform
or uninformative prior. Besides, estimation in these models has focused on
costly Bayesian inference. In this paper, we propose a simple yet very
efficient majorization-minimization algorithm for maximum a posteriori
estimation. Our approach leverages the Beta prior whose parameters can be tuned
to improve performance in matrix completion tasks. Experiments conducted on
three public binary datasets show that our approach offers an excellent
trade-off between prediction performance, computational complexity, and
interpretability.
