Embrace rejection: Kernel matrix approximation by accelerated randomly pivoted Cholesky

Code

• github.com/eepperly/randomly-pivoted-cholesky
  OfficialIn papernone★ 32

Abstract

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 develops an accelerated version of RPCholesky that employs block matrix computations and rejection sampling to efficiently simulate the execution of the original algorithm. For the task of approximating a kernel matrix, the accelerated algorithm can run over 40 faster. The paper contains implementation details, theoretical guarantees, experiments on benchmark data sets, and an application to computational chemistry.

Tasks

Reproductions