High dimensional probability and applications
High dimensional Probability investigates the behavior of high
dimensional random objects, such as random vectors, random
matrices with the emphasis upon quantifying the role of the
dimension. In this course some of the basic techniques required
for applications in Data Sciences will be presented. In particular,
basic theory of concentration of measure, random projection
methods and dimension reduction, stochastic processes including
chaining as well as combinatorial tools such as the VC dimension.
Applications on statistical learning theory, compressed sensing,
approximation algorithms and estimation in high dimensions will be
presented.