High-Dimensional Statistics Notes

Published: May 01, 2023

High-dimensional statistics is the branch of statistics concerned with obtaining bounds on how random variables differ from their expectations, especially as the number of dimensions in the data increases. These notes will tackle three topics: (1) basic concentration inequalities and properties of sub-Gaussian random variables, (2) sparse linear regression, and (3) Dudley’s theorem and its applications.

Numerical Analysis Notes

Published: October 02, 2023

This page relates notes from MATH 269A at UCLA, numerical analysis.

Introduction to Reinforcement Learning Notes

Published: January 06, 2025

Table of Contents

• Lecture 1/30: Algorithms for Policy Evalation
  • Policy Evaluation via the Temporal Difference Algorithm
  • Policy Iteration via the Every Visit Monte Carlo Method
• Lecture 2/5: More on Policy Evaluation
  • Convergence of Policy Evaluation

Real Analysis III

Published: March 31, 2025

Lecture 3/31: Measure and Integration on Topological Spaces in General

We construct a chain of concepts in real analysis, beginning with the Borel $\sigma$-algebra $\mathbb{B}$ which is the $\sigma$-algebra on $\mathbb{R}^n$ generated by all open sets.