4.5 Article

Sketching the Krylov subspace: faster computation of the entire ridge regularization path

期刊

JOURNAL OF SUPERCOMPUTING
卷 79, 期 16, 页码 18748-18776

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SPRINGER
DOI: 10.1007/s11227-023-05309-w

关键词

Ridge regression; Randomized algorithms; Kernel ridge regression

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We propose a fast algorithm for computing the entire ridge regression regularization path in nearly linear time. Our method constructs a basis on which the solution of ridge regression can be computed instantly for any value of the regularization parameter. Consequently, linear models can be tuned via cross-validation or other risk estimation strategies with substantially better efficiency.
We propose a fast algorithm for computing the entire ridge regression regularization path in nearly linear time. Our method constructs a basis on which the solution of ridge regression can be computed instantly for any value of the regularization parameter. Consequently, linear models can be tuned via cross-validation or other risk estimation strategies with substantially better efficiency. The algorithm is based on iteratively sketching the Krylov subspace with a binomial decomposition over the regularization path. We provide a convergence analysis with various sketching matrices and show that it improves the state-of-the-art computational complexity. We also provide a technique to adaptively estimate the sketching dimension. This algorithm works for both the over-determined and under-determined problems. We also provide an extension for matrix-valued ridge regression. The numerical results on real medium and large-scale ridge regression tasks illustrate the effectiveness of the proposed method compared to standard baselines which require super-linear computational time.

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