Advances in Computational Mathematics· 2026Q1
Robust, randomized preconditioning for kernel ridge regression
- 1citations
- Q1SCImago
- 2026year
Short summary
Two new randomized preconditioners (RPCholesky and KRILL) significantly speed up kernel ridge regression for large datasets (N=10^4 to 10^7) compared to existing methods.
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Key points
- Introduces RPCholesky and KRILL, two randomized preconditioners for KRR.
- RPCholesky requires O(N^2) operations for full-data KRR with eigenvalue decay.
- KRILL requires O((N+k^2)k log k) operations for restricted KRR (k centers) without eigenvalue assumptions.
- Methods demonstrate robustness over existing preconditioners in experiments.
AI-generated from the title and abstract; the full text is not read.
Abstract
Abstract We investigate preconditioned conjugate gradient methods for kernel ridge regression (KRR) problems with a moderate to large number of data points ( $$10^4 \le N \le 10^7$$ 10 4 ≤ N ≤ 10 7 ). We develop and analyze two randomized preconditioners with complementary guarantees. For full-data KRR, RPCholesky preconditioning requires $$\mathcal {O}(N^2)$$ O ( N 2 ) arithmetic operations for fixed accuracy under sufficiently rapid eigenvalue decay of the kernel matrix. For restricted KRR with $$k\ll N$$ k ≪ N centers, KRILL preconditioning requires $$\mathcal {O}((N+k^2)k\log k)$$ O ( ( N + k 2 ) k log k ) operations with no eigenvalue-decay assumption. Experiments on benchmark and scientific data sets demonstrate the robustness of both methods relative to existing preconditioners.
The authors' abstract, as published at the source. Advances in Computational Mathematics, 2026 · DOI ↗
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Field: Computational Mechanics
Computational MechanicsEngineering