Marc Mézard, ENS Paris, France

Statistical physics of inference (13.5h)

1. A short introduction to statistical inference:

Examples. Information, noise

Bayesian statistics

Large dimensions: algorithmic issues

2. Statistical physics formulation

Statistical physics of disordered systems. "Planted" ensembles

Examples: community detection, error-correcting codes

The generic phase-diagram

Relations to glasses

3. Cavity method and algorithms

Belief propagation, TAP equations

Examples: perceptron, compressed sensing

4. Phase diagrams: replica approach

The "generic" phase diagram and replica symmetry breaking

The replica-cavity connection