# Topics in High-Dimensional Econometrics and ML Theory

Emory University, Spring 2024

## Table of contents

## About

Designed to be a Directed Study (a intensive reading in econometrics on a topic not covered in a regular course at Emory University), this course covers a variety of topics in high-dimensional econometrics and machine learning theory. The course is based on student presentations, and discussions among participants (students and faculty invited).

## Course Description

This course aims to be a in-depth exploration of the theoretical foundations and practical applications of high dimensional statistics and machine learning theory at the graduate level. Since this a topics course, the content is based on the interests of the participants and student presenter. The primary objective of this directed reading is to provide a comprehensive and self-contained overview of high-dimensional statistics, covering topics such as concentration inequalities, empirical processes, uniform laws, reproducing kernel Hilbert spaces, semiparametric theory, double/debiased machine learning and their applications in causal inference.

## Content

### Topic 1: Concentrations Inequalities

- Motivating examples
- Classical bounds

### Topic 2: Uniform law of large numbers

- Uniform convergence
- Rademacher complexity

### Topic 3: Sparse linear models in high-dimensions

- Different types of sparsity
- Shrinkage estimators and regularizers
- Regularization bias

### Topic 4: Reproducing Kernel Hilbert Spaces

- Hilbert spaces
- Kernels and operations
- Reproducing kernel Hilbert spaces
- Kernel Ridge regression

### Topic 5: Semiparametric Efficiency Theory

- Semiparametric efficiency
- Efficiency Influence Functions
- Pathwise Defferentiability and Distributional Taylor Expansion

### Topic 6: Double/Debiased Machine Learning

- Neyman Orthogonality
- Sample Splitting
- Cross-fitting
- Applications

## References

The content of the course will be based on the following references:

High-Dimensional Statistics: A Non-Asymptotic Viewpoint by Martin Wainwright.

Lectures Notes for Machine Learning Theory (CS229M/STATS214) by Tengyu Ma.

Introduction to RKHS, and some simple kernel algorithms by Arthur Gretton.

Machine Learning for Econometrics by Christophe Gaillac and Jeremy Lâ€™Hour.

## Acknowledgments

I thank Prof. David Jacho-Chavez for his guidance and serve as Faculty Sponsor to develop this course.