Topics in High-Dimensional Statistics

Department: 
MATH
Course Number: 
8803-KOL
Hours - Lecture: 
3
Hours - Lab: 
0
Hours - Recitation: 
0
Hours - Total Credit: 
3
Typical Scheduling: 
Not typically scheduled
Prerequisites: 
 
An advanced probability course (ideally, at the level 6241)
 
 
Course Text: 
 
R. Vershynin, High-Dimensional Probability: An introduction with applications in data science, Cambiridge University Press, 2018
 
C. Giraud, Introduction to High-Dimensional Statistics, CRC press, 2015
 
M. Ledoux, The concentration of measure phenomenon, AMS, 2001.
 
S. Boucheron, G. Lugosi and P. Massart. Concentration inequalities, Oxford Univ. Press, 2013.
 
A. van der Vaart and J. Wellner. Weak Convergence and Empirical Processes, Springer, 1996
 
Topic Outline: 
 
Methods of high-dimensional probability: 
 
- concentration inequalities;
- entropy and generic chaining bounds;
- symmetrization and multipliers inequalities;
- non-asymptotic theory of random matrices.
 
High-dimensional statistical inference and machine learning:
 
- generalization bounds in learning theory;
- model selection, aggregation and oracle inequalities;
- sparse recovery;
- low-rank matrix recovery;
- covariance estimation and principal component analysis in high dimensions;
- trace regression models and quantum state tomography.