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.