In Artificial Intelligence and Machine Learning, there is a need for flexible, expressive models of uncertainty. In the case of online classification, such models should be able to adapt to the dynamics of the data-generating system, i.e. they should be nonstationary. We introduce the Dynamic Pitman-Yor Diffusion Tree (DPYDT), a generalization of the Pitman-Yor Diffusion Tree (PYDT) [1] to nonstationary streaming data. These Bayesian nonparametric priors model hierarchical structure in the data, providing interpretable structural information about patterns in the data. Our model allows this structure to evolve over time in response to changes in the data distribution. We give a description of the generative process and derive closed form expressions for the joint density of a sequence of trees, and the predictive density of successive trees. We also discuss generalizations of the diffusion underlying the PYDT to bounded and unbounded discrete variables. Finally, we describe a Sequential Monte Carlo algorithm for inference in our model, and discuss its efficiency.
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