EE 378 B : Syllabus

Here is a rough syllabus (precise schedule will depend on the progress in class, and suggestions/feedback are welcome).

Jan 11, 13

Singular value decomposition; Matrix norms; Perturbation theory for eigenspaces; Applications to matrix estimation and matrix completion

Jan 18, 20

Subgaussian random variables, Epsilon-net method, Concentration of the norm of random matrices, Application to covariance estimation, Application to spectral clustering.

Jan 25, 27

Matrix concentration inequalities. Application to spectral matrix completion and to sparse graph community detection.

Feb 1, 3

Semidefinite programming relaxations. Analysis of nuclear norm-based matrix completion.

Feb 8, 10

Additional applications: dimensionality reduction, graph localization.

Feb 15, 17

Gaussian processes. Slepian and Gordon's inequalities. Application to bound the norm of random matrices. The BBAP phase transition and the spiked model.

Feb 22, 24

Analysis of community detection via SDP. Exact reconstruction threshold. Weak reconstruction via Grothendieck inequality.

Mar 1, 3

Approximate Message Passing. Analysis via Gaussian conditioning technique. Application to low-rank matrix reconstruction.

Mar 8, 10

Bayes optimal reconstruction in low-rank models. Phase diagram and computationally hard regime.

Mar 15, 17

Additional topics.

Homeworks will be assigned on Monday, due on Monday of the following week.
Each week, two-four students taking the class will be requested to discuss the solution to one of the problems in the homework.
1. This will take maximum 15 minutes of class time (strictly enforced).
2. The problems to presented will be indicated week-by-week.
3. Sign up with Qijia Jiang for the schedule (first come-first serve).
There will be a 24 hours take home final.