Instructor: Yaniv Plan
Office: 303B LSK
Email:  yaniv (at) math (dot) ubc (dot) ca

Lectures: TuTh, 9:30 – 11:00am

Office hours: By appointment.

Prerequisites: The course will assume knowledge of linear algebra as well as a strong probabilistic intuition.  For example, I will assume you have familiarity with stochastic processes, norms, and singular values.

Overview:  We study tools and concepts from high-dimensional probability that underlie the mathematical theory of compressed sensing and related problems in data science.

Detailed course outline: See here.

Textbook:  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. (Our course begins by following an earlier course of Vershynin’s on high-dimensional probability.)
  2. T. Tao, Topics in random matrix theory.
  3. R. Adler, J. Taylor, Random fields and geometry.
  4. S. Foucart, H. Rauhut, A mathematical introduction to compressive sensing.
  5. J. Lee, nicely presented proof of majorizing measures theorem, which gives the lower bound for generic chaining.
  6. Earlier version of this course, which contains a series of notes.  For the beginning of the course, we will roughly follow the same notes.
  7. Sufficient conditions for measurability of the supremum of a random process. Section 1.7.

Grading: Students will complete a class project (ideally in teams of 3 to 4). Instructions:

  1. Determine a “mini-research problem” related to the class material that you wish to investigate. This should have a theory component, but may also include numerical simulations. Please run your idea(s) by me by Oct 15.
  2. Make what progress you can towards solving it.
  3. Write up your results in about 3–5 pages, plus references (and pictures). Write-ups are due on Dec 3. Here is an example.
  4. Give a 20 minute presentation of your results in class (this will happen in late November and early December). All members of the group should contribute to the presentation and discuss the parts of the project that they worked on most.