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MA3K0 Content


  • Preliminaries on Random Variables (limit theorems, classical inequalities, Gaussian models, Monte Carlo)
  • Basic Information theory (entropy; Kull-Back Leibler information divergence)
  • Concentrations of Sums of Independent Random Variables
  • Random Vectors in High Dimensions
  • Random Matrices
  • Concentration with Dependency structures
  • Deviations of Random Matrices and Geometric Consequences
  • Graphical models and deep learning


  • Concentration of measure problem in high dimensions
  • Three basic concentration inequalities
  • Application of basic variational principles
  • Concentration of the norm
  • Dependency structures
  • Introduction to random matrices


By the end of the module the student should be able to:

  • Understand the concentration of measure problem in high dimensions
  • Distinguish three basic concentration inequalities
  • Distinguish between concentration for independent families as well as for various dependency structures
  • Understand the basic concentrations of the norm
  • Be familiar with random matrices (main properties)
  • Be able to understand basic variational problems
  • Be familiar with some application of graphical models


We won't follow a particular book and will provide lecture notes. The course is based on the following three books where the majority is taken from [1]:

[1] Roman Vershynin, High-Dimensional Probability: An Introduction with Applications in Data Science, Cambridge Series in Statistical and Probabilistic Mathematics, (2018).

[2] Kevin P. Murphy, Machine Learning - A Probabilistic Perspective, MIT Press (2012).

[3] Simon Rogers and Mark Girolami, A first course in Machine Learning, CRC Press (2017).

[4] Alex Kulesza and Ben Taskar, Determinantal point processes for machine learning, Lecture Notes (2013).