Course Syllabus

Stochastic Models in High Dimensions 

Class notes, announcements, and other information can be found here.

Instructor: Anastasios Matzavinos, amatzavinos@uc.cl 

Teaching assistant: Lucas Buvinic Meira, lbuvinic@uc.cl 

Class meeting times:  Tuesday & Thursday 11:00 am - 12:10 pm in room AP103

Instructor's office hours: By appointment.

TA's office hours: By appointment.

Course description: IMT 3420 is focused on the various tools and techniques of high-dimensional probability along with their applications in data science and statistical learning. Topics covered include basic concentration inequalities, concentration of measure via entropic techniques and isoperimetric inequalities, martingale methods and Poincaré-type inequalities, random matrices, random projection methods, generic chaining, VC dimension, and the Rademacher complexity. Various applications in statistical learning will be considered, including sparse linear models in high dimensions, compressed sensing, the LASSO algorithm, stochastic bandit algorithms, the slicing method, and approximation by neural networks. 

The official UC course description for IMT 3420 can be found here.

Grading policy: The final grade will be based on attendance (5% of the grade), homework assignments (35%), a mid-term exam (30%),  and a final take-home exam (30%).

Homework assignments: Homework problems will be handed out on a regular basis. Discussion of homework assignments with other students is encouraged, but what is handed in should be your own work. 

References: The following references will be used in different parts of the course. 

• R. Vershynin. High-Dimensional Probability: An Introduction with Applications in Data Science. 2nd Edition. Cambridge University Press, 2026.
• J. Wainwright. High-Dimensional Statistics: A Non-Asymptotic Viewpoint. Cambridge University Press, 2019.
• Boucheron, G. Lugosi, and P. Massart. Concentration Inequalities: A Non-asymptotic Theory of Independence. Oxford University Press, 2013.

Announcements and other information about the class can be found here. A PDF copy of the course program can be found here: IMT_3420.pdf