How do we find the maximum?

Abstract

By Yan Wang, Wayne State University

Given a bunch of real numbers, one can easily find the maximum. However, as a common assumption in machine learning, the dataset itself is random, and what really interests people is the expectation of the maximum. How can we estimate how large it is under reasonable conditions? We will introduce some basic mathematical principles that can help achieve this goal. Surprisingly, this seemingly simple problem turns out to be very deep.

One of the major contributions of Michel Talagrand (2024 Abel Prize winner) is the development of a technique that fully characterizes the maximum of a Gaussian process. Moreover, maximum-related inequalities play a fundamental role in analyzing the excess risk of machine learning algorithms. Although we won't be able to delve into the details in this talk, we will surely cover the most essential ideas that underlie such results. This talk is accessible to students who have taken basic courses in probability/statistics (such as STA 2210).

Pizza will be served.