Course: STAT 41500
Title: High-Dimensional Statistics I
Instructor(s): Chao Gao
Teaching Assistant(s): Fengshuo Zhang
Class Schedule: Sec 01: MW 9:30 AM–10:50 AM in Jones 226
Description: These courses treat statistical problems where the number of variables is very large. Classical statistical methods and theory often fail in such settings. Modern research has begun to develop techniques that can be effective in high dimensions, and that can be understood theoretically. The first quarter introduces a range of statistical frameworks for finding low-dimensional structure in high-dimensional data, such as sparsity in regression, sparse graphical models, or low-rank structure. This quarter emphasizes methods for estimation and inference developed in these areas, along with theoretical analysis of their properties. The second quarter emphasizes foundational aspects of high-dimensional statistics, focusing on principles that are used across a range of problems and are likely to be relevant for methods developed in the future. Topics include "the curse of dimensionality," elements of random matrix theory, properties of high-dimensional covariance matrices, concentration of measure, dimensionality reduction techniques, and handling mis-specified models. The courses may be taken separately.
Prerequisite(s): STAT 30100 and STAT 30400 and STAT 31015, or consent of instructor