Metadata Dependent Mondrian Processes

Stochastic partition processes in a product space play an important role in modeling relational data. Recent studies on the Mondrian process have introduced more flexibility into the block structure in relational models. A side-effect of such high flexibility is that, in data sparsity scenarios, the model is prone to overfit. In reality, relational entities are always associated with meta information, such as user profiles in a social network. In this paper, we propose a metadata dependent Mondrian process (MDMP) to incorporate meta information into the stochastic partition process in the product space and the entity allocation process on the resulting block structure. MDMP can not only encourage homogeneous relational interactions within blocks but also discourage meta-label diversity within blocks. Regularized by meta information, MDMP becomes more robust in data sparsity scenarios and easier to converge in posterior inference. We apply MDMP to link prediction and rating prediction and demonstrate that MDMP is more effective than the baseline models in prediction accuracy with a more parsimonious model structure.