S&DS 6020: High-Dimensional Probability and Applications

Description

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

Prerequisites: S&DS 3510/5510 or S&DS 4000/6000 (may be taken concurrently) or permission of instructor.

Lectures and office hours

Lecture: Wednesdays 4:00 - 6:30PM
Kline Tower 205

Office hours (Zhou Fan): Mondays 2:30 - 3:30PM
Kline Tower 1019

Office hours (Leda Wang): Tuesdays 3:00 - 4:00PM
Kline Tower 1149

Homework

Approximately weekly, due Wednesdays 3pm on Gradescope. Homework assignments will constitute 100% of your course grade. Late homeworks will not be accepted. Your lowest homework grade will be dropped.

Collaboration policy

You are strongly 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.

AI use policy

Use of LLMs and generative AI tools on the homework assignments is strongly discouraged. If such a tool is used, its use must be acknowledged in a citation that includes the prompt you submitted and the date and version of the tool used. You must write the solution yourself, and copy/paste from an LLM output is not permitted.

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