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Non-asymptotic analysis of random matrices - NMMA587

Title:	Neasymptotická analýza náhodných matic
Guaranteed by:	Department of Mathematical Analysis (32-KMA)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2016 to 2016
Semester:	winter
E-Credits:	3
Hours per week, examination:	winter s.:2/0, Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	not taught
Language:	English, Czech
Teaching methods:	full-time
Teaching methods:	full-time

Guarantor:	doc. RNDr. Dr. rer. nat. Jan Vybíral, Ph.D.
Class:	DS, matematická analýza DS, pravděpodobnost a matematická statistika M Mgr. MA > Volitelné M Mgr. PMSE > Volitelné

Opinion survey results Examination dates Schedule Noticeboard

Annotation -

Last update: T_KMA (16.04.2015)

We will introduce basic non-asymptotic methods and concepts in random matrix theory. The students will learn tools for the analysis of the extreme singular values of random matrices with independent rows or columns. They results have applications in several fields, most notably in theoretical computer science, statistics and signal processing.

Literature -

Last update: doc. RNDr. Dr. rer. nat. Jan Vybíral, Ph.D. (28.07.2015)

Roman Vershynin, Introduction to the non-asymptotic analysis of random matrices, 2011

Joel Tropp, User-friendly tail bounds for sums of random matrices, 2012

Joel Tropp, An Introduction to Matrix Concentration Inequalities, 2015

Terry Tao, Topics in random matrix theory, 2012

Syllabus -

Last update: T_KMA (16.04.2015)

1. Introduction: matrices, singular values, sub-gaussian random variables, sub-exponential random variables, isotropic random vectors

2. Sums of independent random matrices

3. Random matrices with independent entries

4. Random matrices with independent rows and columns

5. Restricted isometries