### 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