36-761 Concentration of Measure

6 units, Carnegie Mellon University

In the second part of the course, we will discuss concentration inequalities for functions of independent and dependent random variables. The same intuition as for the CLTs holds here as well. After a detailed discussion of Hoeffding, Bernstein, and Bennett inequalities for independent bounded random variables, we focus on concentration inequalities for general statistics of independent heavytailed random variables, with applications to empirical process theory. Finally, we consider concentration inequalities for functions of dependent data, including empirical processes. We will pay some attention to the optimality of concentration inequalities. Once again, there is no single book we follow. We will follow the works of Hoeffding, Bentkus, Pinelis, Boucheron, Massart, Pollard, Bercu, Shen, and Chen.

Prerequisites: none listed

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