Graphical Models and Inference  MT09

Overview of Lectures

This is the plan for the 16 lectures in MT09. 

1. Graphs and conditional independence
2. Markov properties for undirected graphs
3. Log-linear models
4. Maximum likelihood in log-linear models
5. Decomposability
6. Junction trees 
7. Markov properties for directed acyclic graphs
8. Bayesian networks and expert systems
9. Probability propagation
10. Probability propagation
11. The multivariate Gaussian distribution
12. Gaussian graphical models
13. Decomposable and directed Gaussian graphical models 
14. Graphical models for causal inference
15. Estimation of (causal?) structure
16. Bayesian graphical models

Most of the topics discussed can be found in similar form in at least one of the following books:

Cowell, R. G., Dawid, A. P., Lauritzen, S. L. and Spiegelhalter, D. J. (1999) Probabilistic Networks and Expert Systems. Springer-Verlag, New York.

Edwards, D. (2000). Introduction to Graphical Modelling (2nd ed). Springer-Verlag, New York.

Lauritzen, S. L. (1996). Graphical Models. Oxford University Press, Oxford

Whittaker, J. (1990). Graphical Models in Applied Multivariate Statistics. Wiley, Chicester.

You might also find my Aalborg lecture notes helpful. Many others have, even though they are somewhat dated, originally written in 1979.

S. L. Lauritzen. Lectures on Contingency Tables. Univ. Cop. Inst. Math. Stat., 1979. 2nd ed. Aalborg University Press 1982. 3rd ed. Department of Mathematics, Aalborg 1989. Electronic edition 2002 (pdf).

In 2006 I gave lectures at the summerschool at Saint Flour, France. My overheads for those lectures are here. Currently I am writing proper lecture notes for this course. An incomplete draft of these is available here, and you might find these helpful as well.

For graph-theoretic concepts, see either Lauritzen (1996) or the first chapter in

Bollobas, B. (1998). Modern Graph Theory. Springer, New York.

General course description.

Last updated: Friday 4 December 2009.  Steffen L. Lauritzen