Aukosh Jagannath


Course: STAT 946 — Mathematics of Data Science (Adv. Topics)
Section: Lec 001— Winter 2021
Location/Medium: Live-stream
Live-stream Times: TTh 1-2.20pm EST (GMT-5)
Office Hours: By appointment
Course website: See Learn.

Syllabus: The goal of this course is to quickly orient you toward mathematical problems at the heart of data science. This course will focus on the statistical and computational limits of high-dimensional problems. The first third of the course will serve as an introduction to the basic tools of the course, namely high-dimensional probability and random matrix theory. We will then cover a broad range of applications. Depending on interest, applications may include:

Suggested Background: This will be an advanced topics course and will be mathematically rigorous. We will focus on theoretical results regarding both statistical and computational limits. It is strongly recommended that the student have successfully completed at least one advanced course in probability, stochastic processes, or mathematical statistics, as well as courses in analysis and linear algebra. Please contact the instructor to confirm if your background is sufficient.

Lectures

Part I: Fundamentals

Week 1: High-dimensional probability Week 2: High-dimensional probability Week 3: PCA and spiked matrix models Week 4: Spiked matrix models Week 5: Gaussian processes and the M* bound Week 6: The escape theorem and exact recovery
Part II: Selected recent results

Week 6: Mean-field methods I Week 7: Mean-field methods II Week 8: Neural Networks Week 9: Neural Networks and Presentations Week 10: Presentations Week 11: Presentations Week 12: Wrap-up