Winter 2021 STAT 33611

Course: STAT 33611

Title: Gaussian Processes with Applications to Modern Statistical Problems

Instructor(s): Yandi Shen

Teaching Assistant(s): TBA

Class Schedule: Sec 1: TR 2:00 PM-3:20 PM in Hinds 180

Textbook(s): TBA

Description: Gaussian processes play a fundamental role in modern statistics, machine learning, and probability theory. In the first part of the course, we will cover several essential techniques related to the Gaussian distribution, including Gaussian concentration, Gaussian comparison theorems, and Poincare type inequalities. We will then detail the applications of these theoretical tools in a series of modern statistical and mathematical problems, including sharp spectral bounds of Gaussian matrices, exact characterization of the least squares estimator, and the free energy of the Sherrington-Kirkpatrick model in statistical physics.

Prerequisites: Graduate student in Statistics, Computer Science, or Computational and Applied Mathematics, or consent of instructor.