Andrea Montanari: Denoising, compressed sensing and low-rank approximation.

Lecture 1:

Statistical estimation and linear models: Basic definitions. Examples and applications: Statistical learning, image denoising, etc. Linear smoothing.

Lecture 2:

Limitations of linear smoothing. Nonlinear denoising. Wavelet thresholding and some of its optimality properties. Sparsity.

Lecture 3:

Compressed sensing. Average case theory and phase transitions. Deterministic gurantees and oracle inequalities.

Lecture 4:

Approximate message passing algorithms and connections with statistical physics. Other convex optimization algorithms.

Lecture 5:

Low-rank matrix recovery. Matrix completion and hidden clique estimation.

Lecture 6:

Assessing uncertainty in high-dimensional statistical estimation. Theory and applications.