  Dyadic Data Prediction (DDP) is an important problem in many research areas.
This paper develops a novel fully Bayesian nonparametric framework which
integrates two popular and complementary approaches, discrete mixed membership
modeling and continuous latent factor modeling into a unified Heterogeneous
Matrix Factorization~(HeMF) model, which can predict the unobserved dyadics
accurately. The HeMF can determine the number of communities automatically and
exploit the latent linear structure for each bicluster efficiently. We propose
a Variational Bayesian method to estimate the parameters and missing data. We
further develop a novel online learning approach for Variational inference and
use it for the online learning of HeMF, which can efficiently cope with the
important large-scale DDP problem. We evaluate the performance of our method on
the EachMoive, MovieLens and Netflix Prize collaborative filtering datasets.
The experiment shows that, our model outperforms state-of-the-art methods on
all benchmarks. Compared with Stochastic Gradient Method (SGD), our online
learning approach achieves significant improvement on the estimation accuracy
and robustness.
