Basic measurement concentration results. Gaussian and sub-Gaussian processes. Chaining and the Dudley and Sudakov quotas. Applications: VC dimension and learning theory; sparse linear regression in high dimension; matrix completion; the LASSO analysis; oracle inequalities and non-parametric statistics.

References:
VERSHYNIN, R. – High-Dimensional Probability: An Introduction with Applications in Data Science (Cambridge Series in Statistical and Probabilistic Mathematics). Cambridge: Cambridge University Press, 2018.

Other books:
BOUCHERON, S., LUGOSI, G., MASSART, P. – Concentration Inequalities: A Nonasymptotic Theory of Independence. Oxford: Oxford University, 2013.
WAINWRIGHT, M. – High-Dimensional Statistics: A Non-Asymptotic Viewpoint (Cambridge Series in Statistical and Probabilistic Mathematics). Cambridge: Cambridge University Press, 2019.

 

* Basic syllabus. The teacher has the autonomy to make any changes.