On generative models for sequential formation of clusters

In the literature of machine learning, a class of unsupervised approaches is based on Dirichlet process mixture models. These approaches fall into the category of nonparametric Bayesian methods, and they find a wide range of applications including in biology, computer science, engineering, and finance. An important assumption of the Dirichlet process mixture models is that the data are exchangeable. This is a restriction for many types of data whose structures vary over time or space or some other independent variables. In this paper, we address generative models that remove the restriction of exchangeability of the Dirichlet process model, which allows for creation of mixtures with time-varying structures. We also address how these models can be applied to sequential estimation of clusters.