Abstract:Année de publication : 2014
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.