Continuous Time Bayesian Networks a Dissertation Submitted to the Department of Computer Science and the Committee on Graduate Studies of Stanford University in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy

Many domains require us to reason about system change. Examples include life history data analysis, financial risk modelling, fault diagnosis, and the study of evolution. Reasoning about such systems involves asking questions about event timing, e.g., when will a person find employment. Our answers, best expressed as probability distributions over time, must account for many factors that are, themselves, changing. Unfortunately, as the number of variables increases, the state space over which we must maintain a distribution grows exponentially. Such exponential growth makes modelling these domains difficult. We introduce the framework of continuous time Bayesian networks (CTBNs) to address this problem. The approach is based on the framework of finite state, homogeneous Markov processes, but uses ideas from Bayesian networks (BNs) to define continuous time models over a structured state space. The CTBN framework uses cyclic graphs that encode conditional independencies in the distribution over the evolution of the system. It explicitly represents temporal dynamics and allows us to query the network for distributions over the times when particular events of interest occur. We specify the class of processes representable by CTBNs and prove there is a unique minimal CTBN structure to encode any representable process. We provide algorithms for learning parameters and structure of CTBN models from both fully observed and partially observed data. We prove that the structure learning problem for CTBNs is easier than for traditional BNs or dynamic Bayesian networks (DBNs). We develop an inference algorithm for CTBNs which is a variant of expectation propagation and leverages domain structure and the explicit model of time for computational