High-Dimensional Probability for Big Data

This article is actually a summary of CS3936 Topic in Modern Algorithms Fall 2025. The focus here is on high-dimensional probability for big data algorithms, such as Machine Learning, which is indeed very modern.

The full text has been divided into multiple installments; this installment serves as the table of contents for the complete work.

Content

Here we won't discuss the old-style algorithms like Suffix Automatons or Network Flows, which might be pretty "Advanced" but not "Modern". In contrast, we'll introduce the most important math tools for today's most fashionable algorithms, Machine Learning. Concretely, We'll mainly foucs on Concentration, Stochastic Process and Suprema of Random Variables.