This short course will cover the following topics:

1. Trees, tree metrics and the space of trees.
I will introduce basic graph-theoretic tree concepts, tree metrics andother tree spaces that arise naturally in the study of latent treegraphical models.

2. Latent tree graphical models.
I will define the model and discuss the basic links to Bayesian networks and undirected graphical models on trees. I will present somebasic results concerning identifiability and moment structure.

3. Inference.
In many application the main interest is in learning the underlying tree. I will give an overview of some methods of learning the tree and show how the idea of tree metrics provides a natural estimator.

4. Parameter estimation.
I will introduce the structural EM algorithm for the MLE estimation and discuss some other approximate methods.

5. Special submodels: Hidden Markov model, symmetric models and models
used in phylogenetics.
Many popular models arise as special cases of latent tree Graphicalmodels. In this lecture I discuss these examples.