Faster linear algebra for data analysis and machine learning

Abstract

We study fast algorithms for linear algebraic problems that are ubiquitous in data analysis and machine learning. Examples include singular value decomposition and low-rank approximation, several varieties of linear regression, data clustering, and nonlinear kernel methods. To scale these problems to massive datasets, we design new algorithms based on random sampling and iterative refinement, tools that have become an essential part of modern computational linear algebra. We focus on methods that are provably accurate and efficient, while working well in practical applications. Open source code for many of the methods discussed in this thesis can be found at https://github.com/cpmusco.