Four lectures on probabilistic methods for data science

TL;DR

This paper introduces key probabilistic tools like Bernstein's inequalities and their applications in data science tasks such as dimension reduction, network analysis, and matrix recovery, aimed at graduate students.

Contribution

It provides an accessible presentation of high-dimensional probability tools and demonstrates their use in various data science applications.

Findings

Effective dimension reduction techniques demonstrated

Network analysis applications illustrated

Covariance estimation and matrix completion results shown

Abstract

Methods of high-dimensional probability play a central role in applications for statistics, signal processing theoretical computer science and related fields. These lectures present a sample of particularly useful tools of high-dimensional probability, focusing on the classical and matrix Bernstein's inequality and the uniform matrix deviation inequality. We illustrate these tools with applications for dimension reduction, network analysis, covariance estimation, matrix completion and sparse signal recovery. The lectures are geared towards beginning graduate students who have taken a rigorous course in probability but may not have any experience in data science applications.