36-771 Martingales 1: Concentration Inequalities, The Basics

6 units, Carnegie Mellon University

Martingales are a central topic in statistics, but are even more relevant today due to modern applications to sequential learning and decision making problems. This course will present a unified derivation of a widevariety of new and old concentration inequalities for martingales. We will prove inequalities for scalars and matrices, that hold under a wide variety of nonparametric assumptions. For example, we will encounter exponential concentration inequalities for martingales whose increments have heavytails, for continuoustime martingales, and for martingales in general Banach spaces. This course will be a prerequisite for the second mini, which focuses more on applications.

Prerequisites: none listed

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