Nested Chinese Restaurant Franchise Process: Applications to User Tracking and Document Modeling.

Much natural data is hierarchical in nature. Moreover, this hierarchy is often shared between different instances. We introduce the nested Chinese Restaurant Franchise Process as a means to obtain both hierarchical tree-structured representations for objects, akin to (but more general than) the nested Chinese Restaurant Process while sharing their structure akin to the Hierarchical Dirichlet Process. Moreover, by decoupling the \emphstructure generating part of the process from the components responsible for the observations, we are able to apply the same statistical approach to a variety of user generated data. In particular, we model the joint distribution of microblogs and locations for Twitter for users. This leads to a 40% reduction in location uncertainty relative to the best previously published results. Moreover, we model documents from the NIPS papers dataset, obtaining excellent perplexity relative to (hierarchical) Pachinko allocation and LDA.