Statistical Inference in Graphical Models
Kevin Gimpel, Daniel Rudoy · 2008
Graphical models fuse probability theory and graph theory in such a way as to permit efficient representation and computation with probability distributions. They intuitively capture statistical relationships among random variables in a distribution and exploit these relationships to permit tractable algorithms for statistical inference. In recent years, certain types of graphical models, particularly undirected graphical models, Bayesian networks, and dynamic Bayesian networks (DBNs), have been shown to be applicable to various problems in air and missile defense that involve decision making under uncertainty and estimation in dynamic systems. While the scope of problems addressed by such systems is quite diverse, all require mathematically-sound machinery for dealing with uncertainty. Graphical models provide a robust, flexible framework for representing and computationally handling uncertainty in real-world problems. While the graphical model regime is relatively new, it has deep roots in many fields, as the formalism generalizes many commonly-used stochastic models, including Kalman filters [25] and hidden Markov models [47]. Statistical inference on a graphical model is NP-Hard, but there have been extensive efforts aimed