Concentration of Measure

What it is about

You will learn fundamental inequalities and techniques of Concentration of Measure (e.g., Chernoff, Hoeffding, Bernstein inequalities, isoperimetry, Johnson–Lindenstrauss, Martingale methods, Poincaré and Gromov–Milman theorems). In the end you will be able to understand these inequalities and apply them to simple examples from applications.

What you will be able to do

• Understanding central Concentration of Measure inequalities
• Application of Chernoff, Hoeffding, and Bernstein inequalities to examples
• Use of Martingale methods and Azuma's inequality
• Knowledge of isoperimetric and functional inequalities (Poincaré, Gromov–Milman)
• Understanding the Johnson–Lindenstrauss property and its consequences

What the module consists of

• LecturesConveying the content in lectures with demonstrative examples and discussions
• Übung/Practice sessionsAccompanying session to each lecture for deepening and application

Teaching method

• Lecture with examplesPresentation of the content and demonstration of typical applications
• Discussion with studentsPromotes understanding and motivates personal analysis
• Self-study of literatureComplements lectures and enables deep engagement
• Practice tasks/Practice sessionsPracticing the techniques on examples