Energy-based sequential sampling for low-rank PSD-matrix approximation - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2023

Energy-based sequential sampling for low-rank PSD-matrix approximation

Résumé

We introduce a pseudoconvex differentiable relaxation of the column-sampling problem for the Nyström approximation of positive-semidefinite (PSD) matrices. The relaxation is based on the interpretation of PSD matrices as integral operators, and relies on the supports of measures to characterise samples of columns. We describe a class of gradient-based sequential sampling strategies which leverages the properties of the considered framework, and demonstrate and its ability to produce accurate Nyström approximations. The time-complexity of the stochastic variants of the discussed strategies is linear in the number of columns of the considered matrices, and the underlying computations can be easily parallelised.
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Dates et versions

hal-04102664 , version 1 (22-05-2023)
hal-04102664 , version 2 (18-12-2023)

Identifiants

  • HAL Id : hal-04102664 , version 2

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Matthew Hutchings, Bertrand Gauthier. Energy-based sequential sampling for low-rank PSD-matrix approximation. 2023. ⟨hal-04102664v2⟩
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