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Embrace rejection: Kernel matrix approximation by accelerated randomly pivoted Cholesky

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arxiv 2410.03969 v3 pith:HNBSJMTE submitted 2024-10-04 math.NA cs.NAstat.COstat.ML

Ethan N. Epperly , Joel A. Tropp , Robert J. Webber This is my paper · ORCID
classification math.NAcs.NAstat.COstat.ML
keywords matrixacceleratedalgorithmapproximationcholeskykernelpivotedrandomly
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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 $40\times$ faster. The paper contains implementation details, theoretical guarantees, experiments on benchmark data sets, and an application to computational chemistry.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Accelerated decomposition of bistochastic kernel matrices by low rank approximation

    math.NA 2025-10 conditional novelty 6.0 of 10

    A low-rank partial Cholesky factor of a kernel matrix can be used to compute the eigenvalue decomposition of its bistochastic normalization in O(N r^2) time with only O(Nr) kernel evaluations.

  2. Structured Column Subset Selection for Bayesian Optimal Experimental Design

    math.NA 2025-05 conditional novelty 5.0 of 10

    A tensor-based framework selects structured subsets of experimental design variables by applying column subset selection to mode unfoldings of the design matrix.

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