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Title: Sketching the Krylov subspace: faster computation of the entire ridge regularization path
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 efciency. 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 efectiveness of the proposed method compared to standard baselines which require super-linear computational time.  more » « less
Award ID(s):
2134248
PAR ID:
10433853
Author(s) / Creator(s):
;
Date Published:
Journal Name:
The Journal of Supercomputing
ISSN:
0920-8542
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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