## Topics in High-Dimensional Probability and Statistics

Department:
MATH
Course Number:
8803 KOL
Hours - Lecture:
3
Hours - Lab:
0
Hours - Recitation:
0
Hours - Total Credit:
3
Typical Scheduling:
Not regularly scheduled
Description:
Special Topics Course "Topics in High-Dimensional Probability and Statistics" offered in Spring 2013 by Vladimir Koltchinskii.
Prerequisites:

TBA

Course Text:
TBA
Topic Outline:
• The focus of this course will be on several topics in probability in Banach spaces and empirical processes theory that found a number of applications in high-dimensional statistics, signal processing (compressed sensing) and machine learning.

This includes Talagrand's concentration inequalities for empirical processes, entropy bounds and generic chaining bounds for Gaussian and empirical processes, matrix versions of Bernstein exponential inequalities and several other results from nonasymptotic theory of random matrices.

Other topics will be closer to applications of these methods in high-dimensional statistics, including problems of sparse recovery (compressed sensing) and low rank matrix recovery (matrix completion, quantum state tomography, etc). In particular, oracle inequalities for the methods of sparse recovery based on $\ell_1$-norm penalization and for the methods of low rank matrix estimation based on nuclear norm penalization will be discussed.