S&DS 602: High-Dimensional Probability and Applications

Zhou Fan, Yale University, Fall 2024


Description

Non-asymptotic methods in high-dimensional probability that find common use in applications across statistics, computer science, data science, and engineering. Topics include tail bounds for i.i.d. sums and martingale differences, concentration inequalities for non-linear functions, matrix concentration, and suprema of stochastic processes.

Prerequisites: S&DS 351b/551b or S&DS 400/600 (may be taken concurrently) or permission of instructor.

Lectures

Wednesdays 4:00PM - 5:50PM
Kline Tower 101

Office hours: Mondays 2:30 - 3:30PM
Kline Tower 1019

Homework

Approximately weekly, due Wednesdays 2pm on Gradescope. Homework assignments will constitute 100% of your course grade. Late homeworks will not be accepted. Your lowest homework grade will be dropped.

You are encouraged to work on homework problems with your classmates, but you must write the solutions yourself. Please indicate at the top of your assignment the names of your collaborators.

Textbooks

High-Dimensional Probability: An Introduction with Applications in Data Science, Roman Vershynin

Concentration Inequalities: A Nonasymptotic Theory of Independence, Stephane Boucheron, Gabor Lugosi, Pascal Massart

Probability in High Dimension, Ramon van Handel