Hierarchical Topic Modeling for Analysis of Time-Evolving Personal Choices

The nested Chinese restaurant process is extended to design a nonparametric topic-model tree for representation of human choices. Each tree branch corresponds to a type of person, and each node (topic) has a corresponding probability vector over items that may be selected. The observed data are assumed to have associated temporal covariates (corresponding to the time at which choices are made), and we wish to impose that with increasing time it is more probable that topics deeper in the tree are utilized. This structure is imposed by developing a new “change point"" stick-breaking model that is coupled with a Poisson and product-of-gammas construction. To share topics across the tree nodes, topic distributions are drawn from a Dirichlet process. As a demonstration of this concept, we analyze real data on course selections of undergraduate students at Duke University, with the goal of uncovering and concisely representing structure in the curriculum and in the characteristics of the student body.