Workshop "High-Dimensional Covariance Matrices, Networks and Concentration Inequalities''
General Information
The aim of this workshop is to provide an opportunity for training and interaction among researchers in operator theory, random matrices, approximation theory, probability, statistics, computer science and related areas of the emerging "Data Science". The workshop is sponsored by National Science Foundation CAREER grant DMS-1554456.
The workshop was planned to take place at Texas A&M University on May 22-23 of 2020, but is postponed until further notice as a part of COVID-19 preventive measures.
Mini-course
Speaker: Stanislav Minsker (University of Southern California)
Title: Concentration inequalities for the sums of random matrices and their applications.
Suggested mathematics background for the audience:
Good
knowledge of probability theory (upper undergraduate level) and linear
algebra, including the notions of trace, matrix norms, positive definite
matrices, singular value/eigenvalue decompositions.
Tentative Topics:
The theory part would include an overview of the classical moment and
concentration inequalities for real-valued random variables (Rosenthal,
Hoeffding, and Bennett/Bernstein inequalities) and their extensions to
the sums of random matrices. The applications part would address, time
permitting, the estimation of covariance matrices/masked covariance
estimation, spectra of random graphs, low-rank matrix completion problem
and sparse linear regression.
Additional Topic-Featured Lectures
Speaker: Anirban Bhattacharya (Texas A&M University)
Title: Statistical and algorithmic guarantees for variational Bayes.
Speaker: Simon Foucart (Texas A&M University)
Title: Restricted isometry properties and their role in compressive sensing.
Speaker: Kshitij Khare (University of Florida)
Title of lecture 1: Gaussian graphical models beyond decomposable graphs.
Title of lecture 2: Generalized likelihood approaches for scalable covariance selection.
Speaker: Elina Robeva (University of British Columbia)
Title: Estimating totally positive densities.
Tentative Schedule
Day 1
8:30 - 9:00 registration, coffee
9:00 - 9:50 Stas, I
10:00 - 10:50 Stas, II
10:50 - 11:10 coffee
11:10 - 12:00 Kshitij, I
12:00 - 14:00 lunch
14:00 - 14:50 Stas, III
15:00 - 15:50 Simon, I
15:50 - 16:10 coffee
16:10 - 17:00 Simon, II
Day 2
8:30 - 9:00 registration, coffee
9:00 - 9:50 Stas, IV
10:00 - 10:50 Stas, V
10:50 - 11:10 coffee
11:10 - 12:00 Kshitij, II
12:00 - 14:00 lunch
14:00 - 14:50 Elina
15:00 - 15:50 Anirban, I
15:50 - 16:10 coffee
16:10 - 17:00 Anirban, II