Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Management Science
Planning and control
Artificial intelligence: a modern approach
Artificial intelligence: a modern approach
A bayesian decision-theoretic framework for real-time monitoring and diagnosis of complex systems: theory and application
Implementation of continuous Bayesian networks using sums of weighted Gaussians
UAI'95 Proceedings of the Eleventh conference on Uncertainty in artificial intelligence
Artificial Intelligence for Engineering Design, Analysis and Manufacturing
Space-efficient inference in dynamic probabilistic networks
IJCAI'97 Proceedings of the Fifteenth international joint conference on Artifical intelligence - Volume 2
A variational approximation for Bayesian networks with discrete and continuous latent variables
UAI'99 Proceedings of the Fifteenth conference on Uncertainty in artificial intelligence
UAI'00 Proceedings of the Sixteenth conference on Uncertainty in artificial intelligence
Nonuniform dynamic discretization in hybrid networks
UAI'97 Proceedings of the Thirteenth conference on Uncertainty in artificial intelligence
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We extend continuous Gaussian networks - directed acyclic graphs that encode probabilistic relationships between variables - to its vector form. Vector Gaussian continuous networks consist of composite nodes representing multivariables, that take continuous values. These vector or composite nodes can represent correlations between parents, as opposed to conventional univariate nodes. We derive rules for inference in these networks based on two methods: message propagation and topology transformation. These two approaches lead to the development of algorithms, that can be implemented in either a centralized or a decentralized manner. The domain of application of these networks are monitoring and estimation problems. This new representation along with the rules for inference developed here can be used to derive current Bayesian algorithms such as the Kalman filter, and provide a rich foundation to develop new algorithms. We illustrate this process by deriving the decentralized form of the Kalnaan filter. This work unifies concepts from artificial intelligence and modern control theory.