Syllabus

Course Meeting Times

Lectures: 2 sessions / week, 1.5 hours / session

Prerequisites

• 18.100C Real Analysis
• 18.700 Linear Algebra
• 18.440 Probability and Random Variables (Conditional Expectations, Random Vectors)
• 18.466 Mathematical Statistics (Statistical Model, Exponential Families, Estimation, Confidence Intervals)

Course Description

This course offers an introduction to the finite sample analysis of high-dimensional statistical methods. The goal is to present various proof techniques for state-of-the-art methods in regression, matrix estimation and principal component analysis (PCA) as well as optimality guarantees. The course ends with research questions that are currently open.

Schedule

• Sub-Gaussian Random Variables - 2 weeks
• Linear Regression - 3 weeks
• Misspecified Linear Models and Nonparametric Regression - 2 weeks
• Matrix Estimation - 3 weeks
• Minimax Lower Bounds - 3 weeks

Notes

This course has no required or recommended textbooks but notes are provided.

Problem Sets

There will be two problem sets.

Grading Policy