Statistical physics of inference

Florent Krzakala (ENS Paris)

2014-05-16 10:00, Salle Itzykson, IPhT
2014-05-23 10:00, Salle Itzykson, IPhT
2014-05-28 10:00, Salle Itzykson, IPhT
2014-06-06 10:00, Salle Itzykson, IPhT
Approved by the École Doctorale ED 107
Abstract: 

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.
Series: 
IPhT Courses
Short course title: 
Statistical physics of inference
Arxiv classes: