  Many data are naturally modeled by an unobserved hierarchical structure. In
this paper we propose a flexible nonparametric prior over unknown data
hierarchies. The approach uses nested stick-breaking processes to allow for
trees of unbounded width and depth, where data can live at any node and are
infinitely exchangeable. One can view our model as providing infinite mixtures
where the components have a dependency structure corresponding to an
evolutionary diffusion down a tree. By using a stick-breaking approach, we can
apply Markov chain Monte Carlo methods based on slice sampling to perform
Bayesian inference and simulate from the posterior distribution on trees. We
apply our method to hierarchical clustering of images and topic modeling of
text data.
