Probability in high dimensions

Instructor: Yaniv Plan
Office: 1219 Math Annex
Email:  yaniv (at) math (dot) ubc (dot) ca

Lectures: MWF 10:00 am – 11:00 am,  MATX 1102.

Office hours: Wednesday 11:30 am – 12:30 pm, MATX 1219 and by request.

Prerequisites: Graduate probability, undergraduate linear algebra, undergraduate functional analysis.  For example, I will assume you have familiarity with stochastic processes, probability spaces, norms, singular values, and Lipschitz functions.

Overview:  See here.

Detailed course outline: See here.

Textbook:  This course is based on a similar course from Roman Vershynin.  There is no required textbook.  The following references cover some of the material, and they are available online:

  1. R. Vershynin, High-dimensional probability.  This book has the most overlap with our course.
  2. T. Tao, Topics in random matrix theory.
  3. D. Chafai, O. Guedon, G. Lecue, A. Pajor, Interactions between compressed sensing, random matrices and high dimensional geometry, preprint.
  4. R. Vershynin, Lectures in geometric funcitonal analysis.
  5. R. Adler, J. Taylor, Random fields and geometry.
  6. S. Foucart, H. Rauhut, A mathematical introduction to compressive sensing.
  7. J. Lee, notes on generic chaining and majorizing measures theorem.
  8. Earlier version of this course, which contains a series of notes.  For the beginning of the course, we will roughly follow the same notes.
  9. Compressed sensing using generative models.  We will do a project as a class trying to improve results in this paper!

Grading: 50% bi-weekly homework, 50% project.  The project may be a literature review or a mini-research problem.

Homework:

Homework 1:  Due Feb 9 (extended)