A Simple and General Exponential Family Framework for Partial Membership and Factor Analysis
In this chapter we show how mixture models, partial membership models, factor analysis, and their extensions to more general mixed membership models, can be unified under a simple framework using the exponential family of distributions and variations in the prior assumptions on the latent variables that are used. We describe two models within this common latent variable framework: a Bayesian partial membership model and a Bayesian exponential family factor analysis model. Accurate inferences can be achieved within this framework that allow for prediction, missing value imputation, and data visualization, and importantly, allow us to make a broad range of insightful probabilistic queries of our data. We emphasize the adaptability and flexibility of these models for a wide range of tasks, characteristics that will continue to see such models used at the core of modern data analysis paradigms.