Graphical Models for Categorical Data

Recently, I have been interested in developing methods for categorical data with a known (or unknown) graphical dependence structure. The main challenge in this problem is to specify an appropriate prior for the probability tensor describing the relationships between features. In “Hierarchical Directed Dirichlet Networks for Discrete Graphical Modeling” (working paper), we introduce the Hierarchical Directed Dirichlet Network (HiDDeN) as one such prior. We establish a framework for posterior computation with HiDDeN and hypothesis testing (e.g., evaluating an edge between nodes).