Lecture 1:

• Motivational examples of inference problems: module detection in networks and compressed sensing.
• Optimal Bayes inference and solving statistical mechanical models.
• Factor graphs.
• Derivation of belief propagation algorithm on trees.

Lecture 2:

• Random graphs and their tree-like property.
• Potts antiferromagnet, graph coloring and planted graph coloring.
• How to find planted coloring using belief propagation and associated phase transition.
• Phase diagram of inference models and physics on the Nishimori line.

Lecture 3:

• The phase diagram of mean field glassy system and inference with mismatching prior distribution.
• On the presence or absence of replica symmetry breaking.
• Message passing for module detection in networks, associated phase diagram.
• Comparison with other inference techniques - Monte Carlo, naive mean field inference and spectral methods.

Lecture 4:

• Solving compressed sensing.
• The approximate message passing technique.
• The phase diagram of compressed sensing.
• Optimal inference by introducing spatial coupling and connection to nucleation.