**Graphical Models and****
Inference - Lecture 5**

**Decomposability**

This lecture is concerned with the case when there is an explicit formula for the MLE in log-linear models. This happens exactly when the generating class is the set of cliques of a chordal graph. Then the IPS-algorithm is in fact not iterative but converges in a finite number of steps.

We describe graph decompositions, chordal graphs and their properties, and algorithms for checking chordality of graphs. The most relevant reading for this lecture are the first six pages of Chapter 3 of my St Flour lecture notes.

**Links**

Last updated: Monday, 24 October 2011. Steffen L. Lauritzen