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.

Recently, an increase in the availability and importance of relational datasets-such as social network data or protein interaction data-has lead to increased interest in modelling and learning from such data. Such data are often modelled as exchangeable arrays, yielding a particular representation due to Aldous and Hoover. We present a Bayesian nonparametric model based on this representation, which uses a novel process to generate a partition of the data. We present a Reversible Jump MCMC algorithm for inference in this model, and demonstrate the effectiveness of this approach on real-world data.

Stream mining has gained popularity in recent years due to the availability of numerous data streams from sources such as social media and sensor networks. Data mining on such continuous streams possess a variety of challenges including concept drift and unbounded stream length. Traditional data mining approaches to these problems have difficulty incorporating relational domain knowledge and feature relationships, which can be used to improve the accuracy of a classifier. In this work, we model large data streams using statistical relational learning techniques for classification, in particular, we use a Markov Logic Network to capture relational features in structured data and show that this approach performs better for supervised learning than current state-of-the-art approaches. Additionally, we evaluate our approach with semi-supervised learning scenarios, where class labels are only partially available during training.