We present the nested Chinese restaurant process (nCRP), a stochastic process that assigns probability distributions to ensembles of inÞnitely deep, inÞnitely branching trees. We show how this stochastic process can be used as a prior distribution in a Bayesian nonparametric model of document collections. SpeciÞcally, we present an application to information retrieval in which documents are modeled as paths down a random tree, and the preferential attachment dynamics of the nCRP leads to clustering of documents according to sharing of topics at multiple levels of abstraction. Given a corpus of documents, a posterior inference algorithm Þnds an approximation to a posterior distribution over trees, topics and allocations of words to levels of the tree. We demonstrate this algorithm on collections of scientiÞc abstracts from several journals. This model exempliÞes a recent trend in statistical machine learning-the use of Bayesian nonparametric methods to infer distributions on ßexible data structures.
The nested Chinese Restaurant Process (nCRP) REF extends the Chinese Restaurant Process analogy of the Dirichlet Process to an infinitely-branched tree structure over restaurants to define a distribution over finite length paths of trees.
The nested chinese restaurant process and bayesian nonparametric inference of topic hierarchies
JACM
Mathematics Computer Science