  Learning by integrating multiple heterogeneous data sources is a common
requirement in many tasks. Collective Matrix Factorization (CMF) is a technique
to learn shared latent representations from arbitrary collections of matrices.
It can be used to simultaneously complete one or more matrices, for predicting
the unknown entries. Classical CMF methods assume linearity in the interaction
of latent factors which can be restrictive and fails to capture complex
non-linear interactions. In this paper, we develop the first deep-learning
based method, called dCMF, for unsupervised learning of multiple shared
representations, that can model such non-linear interactions, from an arbitrary
collection of matrices. We address optimization challenges that arise due to
dependencies between shared representations through Multi-Task Bayesian
Optimization and design an acquisition function adapted for collective learning
of hyperparameters. Our experiments show that dCMF significantly outperforms
previous CMF algorithms in integrating heterogeneous data for predictive
modeling. Further, on two tasks - recommendation and prediction of gene-disease
association - dCMF outperforms state-of-the-art matrix completion algorithms
that can utilize auxiliary sources of information.
