6 papers · 1 filter
Linear algebra at exponential scale via tensor network dimension reduction
Chris Camaño, Ethan N. Epperly, Raphael A. Meyer +1
Many problems in modern scientific computing are challenging because of a \emph{curse of dimension}, where their mathematical formulation involves objects whose dimension is \emph{…
Robust, randomized preconditioning for kernel ridge regression
Mateo DÃaz, Mateo Díaz, Ethan N. Epperly +3
We investigate preconditioned conjugate gradient methods for kernel ridge regression (KRR) problems with a moderate to large number of data points (). We dev…
Randomized matrix computations: Themes and variations
Anastasia Kireeva, Joel A. Tropp
This short course offers a new perspective on randomized algorithms for matrix computations. It explores the distinct ways in which probability can be used to design algorithms for…
Embrace rejection: Kernel matrix approximation by accelerated randomly pivoted Cholesky
Ethan N. Epperly, Joel A. Tropp, Robert J. Webber
Randomly pivoted Cholesky (RPCholesky) is an algorithm for constructing a low-rank approximation of a positive-semidefinite matrix using a small number of columns. This paper devel…
Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations
Yifan Chen, Ethan N. Epperly, Joel A. Tropp +1
The randomly pivoted partial Cholesky algorithm (RPCholesky) computes a factorized rank-k approximation of an N x N positive-semidefinite (psd) matrix. RPCholesky requires only (k…
Efficient error and variance estimation for randomized matrix computations
Ethan N. Epperly, Joel A. Tropp
Randomized matrix algorithms have become workhorse tools in scientific computing and machine learning. To use these algorithms safely in applications, they should be coupled with p…