Hierarchical Bayesian mixed-membership models and latent pattern discovery
Edoardo M. Airoldi, Stephen E. Fienberg, Cyrille J. Joutard, Tanzy Mae Tallapoosa Paz Love · 2005
Hierarchical Bayesian methods expanded markedly with the introduction of MCMC computation in the 1980s, and this was followed by the explosive growth of machine learning tools involving latent structure for clustering and classification. Nonetheless, model choice remains a major methodological issue, largely because competing models used in machine learning often have different parameterizations and very different specifications and constraints. Here, we utilize hierarchical Bayesian mixed-membership models and present several examples of model specification and variations, both parametric and nonparametric, in the context of learning the number of latent groups and associated patterns for clustering units. We elucidate strategies for comparing models and specifications by producing novel analyses of the following two data sets in both parametric and nonparametric settings: (1) a corpus of scientific publications from the Proceedings of the National Academy of Sciences where we use both text and references to narrow the choice of the number of latent topics in our publications data; (2) data on functional disabilities of the elderly from the National Long Term Care Survey. 1