On the usability of continuous time bayesian networks: improving scalability and expressiveness

Abstract

The Continuous Time Bayesian Network (CTBN) is a model capable of compactly representing the behavior of discrete state systems that evolve in continuous time. This is achieved by factoring a Continuous Time Markov Process using the structure of a directed graph. Although CTBNs have proven themselves useful in a variety of applications, adoption of the model for use in real-world problems can be difficult. We believe this is due in part to limitations relating to scalability as well as representational power and ease of use. This dissertation attempts to address these issues. First, we improve the expressiveness of CTBNs by providing procedures that support the representation of non-exponential parametric distributions. We also propose the Continuous Time Decision Network (CTDN) as a framework for representing decision problems using CTBNs. This new model supports optimization of a utility value as a function of a set of possible decisions. Next, we address the issue of scalability by providing two distinct methods for compactly representing CTBNs by taking advantage of similarities in the model parameters. These compact representations are able to mitigate the exponential growth in parameters that CTBNs exhibit, allowing for the representation of more complex processes. We then introduce another approach to managing CTBN model complexity by introducing the concept of disjunctive interaction for CTBNs. Disjunctive interaction has been used in Bayesian networks to provide significant reductions in the number of parameters, and we have adapted this concept to provide the same benefits within the CTBN framework. Finally, we demonstrate how CTBNs can be applied to the real-world task of system prognostics and diagnostics. We show how models can be built and parameterized directly using information that is readily available for diagnostic models. We then apply these model construction techniques to build a CTBN describing a vehicle system. The vehicle model makes use of some of the newly introduced algorithms and techniques, including the CTDN framework and disjunctive interaction. This extended application not only demonstrates the utility of the novel contributions presented in this work, but also serves as a template for applying CTBNs to other real-world problems.