# MIT 6.438: Algorithms for Inference

Intended for: MIT 6.438 students

Here is an overview of the topics covered in MIT's probabilistic graphical models course, 6.438. If you're a student taking the class, you may find this a helpful source of additional readings. If you're not taking the class, but want to learn about graphical models, this can help you identify some of the key topics.

This roadmap corresponds to how the class was taught in the fall of 2011 (the semester I TA'ed it), and the class has probably changed since then.

### Lecture 1: Introduction, overview, preliminaries

• Nothing specifically for this lecture, but you may want to learn about conditional independence now, since that gets used a lot early on in the course.

### Lecture 2: Directed probabilistic graphical models

• Bayesian networks, or Bayes nets, known in 438-land as directed graphical models
• d-separation, a way of analyzing conditional independence structure in Bayes nets
• Bayes Ball, an efficient algorithm for computing Bayes net conditional independencies. Note that while the course uses Bayes Ball to find conditional independencies, you may find it more intuitive to think directly in terms of the d-separation rules, as in the previous item.

### Lecture 4: Factor graphs; generating and converting graphs

• factor graphs. Note that factor graphs and undirected graphical models are two different ways to represent the structure of Boltzmann distributions, and the only real difference is that factor graphs are a more fine-grained notation.
• converting between graphical models

### Lecture 5: Perfect maps, chordal graphs, Markov chains, trees

• Nothing to go with this lecture, sorry.

### Lecture 8: Inference on trees: sum-product algorithm

• sum-product algorithm. Unfortunately, different sources differ in which version of this algorithm they present. Most of them use the factor graph version, which is covered in a later lecture. Koller and Friedman jump straight to the junction tree (clique tree) version, which is the most general, but it can be a lot to take in all at once. Start with whichever you like, and it should make the other versions easier to understand.

### Lecture 10: Sum-product algorithm with factor graphs

• See the references for lecture 8, since some of them use factor graphs.