Mini Course

Lecture Series

Instructor: Aaradhya Pandey (Princeton University)

Content: In this course, we begin by introducing the basic information-theoretic objects and their natural appearances in large deviation principles. We discuss some of the key properties of these objects (all-most based on Jensen’s inequality), including convexity, continuity, chain rules, tensorization, variational representation, local expansion, as well as the data processing principle. We then turn to remarkable appearances of these objects in analysis, probability theory, statistics, combinatorics, graph theory, coding theory, theoretical computer science, mathematical physics, optimal transport, and partial differential equations.

Logistics: Many of the applications will appear in exercise sheets.

Pre-requisite: Jensen’s inequality

Motivation: Information-theoretic variational problems appear in the asymptotics of classical statistics at the level of large-deviation principles. The corresponding asymptotics of high-dimensional statistical problems are still in the making. We propose that Variational problems involving Wasserstein distance and  Wasserstein Gradient flow appear naturally in the asymptotics of a large collection of high-dimensional statistical problems, which are qualitatively different from the ones in information theory.