Multi-relational learning via hierarchical nonparametric Bayesian collective matrix factorization

Relational learning addresses problems where the data come from multiple sources and are linked together through complex relational networks. Two important goals are pattern discovery (e.g. by (co)-clustering) and predicting unknown values of a relation, given a set of entities and observed relations among entities. In the presence of multiple relations, combining information from different but related relations can lead to better insights and improved prediction. For this purpose, we propose a nonparametric hierarchical Bayesian model that improves on existing collaborative factorization models and frames a large number of relational learning problems. The proposed model naturally incorporates (co)-clustering and prediction analysis in a single unified framework, and allows for the estimation of entire missing row or column vectors. We develop an efficient Gibbs algorithm and a hybrid Gibbs using Newton's method to enable fast computation in high dimensions. We demonstrate the value of our framework on simulated experiments and on two real-world problems: discovering kinship systems and predicting the authors of certain articles based on article-word co-occurrence features.