| Many real-world systems are naturally modeled as hybrid stochastic processes, i.e., stochastic processes that contain both discrete and continuous variables. Examples include speech recognition, target tracking, and monitoring of physical systems. The task is usually to perform probabilistic inference, i.e., infer the hidden state of the system given some noisy observations. For example, we can ask what is the probability that a certain word was pronounced given the readings of our microphone, what is the probability that a submarine is trying to surface given our sonar data, and what is the probability of a valve being open given our pressure and flow readings.; Bayesian networks are a compact way to represent a probability distribution. They can be extended to dynamic Bayesian networks which represent stochastic processes. In this thesis we concentrate on hybrid (dynamic) Bayesian networks. Our contributions are three-fold: theoretical, algorithmic, and practical.; From a theoretical perspective, we provide a novel complexity analysis for inference in hybrid models and show that there is a fundamental difference between the complexity of inference in discrete models and in hybrid ones. In particular, we provide the first NP-hardness results for inference in very simple hybrid models. From an algorithmic perspective, we provide a suite of new inference algorithms, designed to deal with non-linearities present in many real-world systems, and to scale up to large hybrid models. We show that our algorithms often outperform the current state of the art inference algorithms for hybrid models. Finally, from a practical perspective, we apply our techniques to the task of fault diagnosis in a complex real-world physical system, designed to extract oxygen from the Martian atmosphere. We demonstrate the feasibility of our approach using data collected during actual runs of the system. |
