Sketching for Linear Algebra - Basics of Dimensionality Reduction and CountSketch I

Explore the fundamentals of dimensionality reduction and CountSketch in this 59-minute lecture from the Foundations of Data Science Boot Camp. Delve into topics such as regression analysis, Moore-Penrose Pseudoinverse, and time complexity. Learn about sketching techniques for solving least squares regression and discover how to select the appropriate sketching matrix. Examine faster subspace embeddings and gain insights into the simple proof ANW. Investigate the matrix product result by Kane and Nelson, and understand the transition from vectors to matrices. Conclude by exploring how CountSketch satisfies the Johnson-Lindenstrauss property, providing a comprehensive overview of key concepts in linear algebra and data science.

Intro
Outline
Regression analysis
Moore-Penrose Pseudoinverse
Time Complexity
Sketching to solve least squares regression
How to choose the right sketching matrix S? [S]
Faster Subspace Embeddings S CW,MM,NN
Simple Proof ANW
Matrix Product Result [Kane, Nelson]
From Vectors to Matrices
CountSketch Satisfies the JL Property