Bayesian Nonparametric Approaches for Modelling Stochastic Temporal Events

Abstract

Modelling stochastic temporal events is a classic machine learning problem that has drawn enormous research attentions over recent decades. Traditional approaches heavily focused on the parametric models that pre-specify model complexity. Comprehensive model comparison and selection are necessary to prevent over-fitting and under-fitting problems. The recently developed Bayesian nonparametric learning framework provides an appealing alternative to traditional approaches. It can automatically learn the model complexity from data. In this thesis, I propose a set of Bayesian nonparametric approaches for stochastic temporal event modelling with the consideration of event similarity, interaction, occurrence time and emitted observation. Specifically, I tackle following three main challenges in the modelling. 1. Data sparsity. Data sparsity problem is common in many real-world temporal event modelling applications, e.g., water pipes failures prediction. A Bayesian nonparametric model that allows pipes with similar behaviour to share failure data is proposed to attain a more effective failure prediction. It is shown that flexible event clustering can help alleviate the data sparsity problem. The clustering process is fully data-driven and it does not require predefining the number of clusters. 2. Event interaction. Stochastic events can interact with each other over time. One event can cause or repel the occurrence of other events. An unexplored theoretical bridge is established between interaction point processes and distance dependent Chinese restaurant process. Hence an integrated model, namely infinite branching model, is developed to estimate point event intensity, interaction mechanism and branching structure simultaneously. 3. Event correlation. The stochastic temporal events are correlated not only between arrival times but also between observations. A novel unified Bayesian nonparametric model that generalizes Hidden Markov model and interaction point processes is constructed to exploit two types of underlying correlation in a well-integrated way rather than individually. The proposed model provides a comprehensive insight into the interaction mechanism and correlation between events. At last, a future vision of Bayesian nonparametric research for stochastic temporal events is highlighted from both application and modelling perspectives.