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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