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