Inference Using Message Propagation and Topology Transformation in
  Vector Gaussian Continuous Networks
  We extend Gaussian networks - directed acyclic graphs that encode
probabilistic relationships between variables - to its vector form. Vector
Gaussian continuous networks consist of composite nodes representing
multivariates, 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 Kalman filter. This work unifies concepts from artificial intelligence
and modern control theory.
