** Course**: STAT 946 — Mathematics of Data Science (Adv. Topics)

** Section**: TBA — Winter 2021

** Location/Medium: ** TBA

** Office Hours: ** TBA

**(Tentative) 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:

- Dimension reduction
- Sparse models
- Low-rank models: the spiked matrix model for PCA and the BBP transition
- Community detection
- Mean-field methods: approximate message passing, belief propagation, et al
- Neural networks: mean-field limits and NTK for shallow networks, related kernel methods, approximation theory
- Stochastic approximation algorithms, Markov processes, and their mixing properties
- Random optimization problems
- Statistical phase transitions: Statistical—to—computational gaps

**Suggested Background:** This will be an advanced topics course and will be mathematically rigorous. That is, 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.

**Evaluation:** *[Tentative]* The evaluation for this course will be based on problem sets and a project, either a literature review or original work. The project will have 3 components: (1) A brief proposal justifying your planned project, (2) A brief presentation with a Q+A, (3) A final paper.