Graphical models, a marriage between probability theory and graph theory, provide anatural tool for dealing with two problems that occur throughout applied mathematics and engineering-- uncertainty and complexity. In particular, they play an increasingly important role in the designand analysis of machine learning algorithms. Fundamental to the idea of a graphical model is thenotion of modularity: a complex system is built by combining simpler parts. Probability theoryserves as the glue whereby the parts are combined, ensuring that the system as a whole is consistentand providing ways to interface models to data. Graph theory provides both an intuitively appealinginterface by which humans can model highly interacting sets of variables and a data structure thatlends itself naturally to the design of efficient general-purpose algorithms.
Thisbook presents an in-depth exploration of issues related to learning within the graphical modelformalism. Four chapters are tutorial chapters -- Robert Cowell on Inference for Bayesian Networks,David MacKay on Monte Carlo Methods, Michael I. Jordan et al. on Variational Methods, and DavidHeckerman on Learning with Bayesian Networks. The remaining chapters cover a wide range of topics ofcurrent research interest.
