An overview on Graph Theory. Graph Theory with Applications. GTA. Heidelberg Graduate School Graphical Models: Research. Graphical Models. By Kevin Murphy, 1998. "Graphical models are a marriage between probability theory and graph theory. They provide a natural tool for dealing with two problems that occur throughout applied mathematics and engineering -- uncertainty and complexity -- and in particular they are playing an increasingly important role in the design and analysis of machine learning algorithms.
Fundamental to the idea of a graphical model is the notion of modularity -- a complex system is built by combining simpler parts. Probability theory provides the glue whereby the parts are combined, ensuring that the system as a whole is consistent, and providing ways to interface models to data. This tutorial We will briefly discuss the following topics. Note: Dan Hammerstrom has made a pdf version of this web page. Articles in the popular press The following articles provide less technical introductions. Other sources of technical information By using conditional independence relationships, we can rewrite this as where.