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Kernel Conjugate Gradient Methods with Random Projections
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- معلومة اضافية
- Publisher Information:
2018-11-05 2022-07-15
- نبذة مختصرة :
We propose and study kernel conjugate gradient methods (KCGM) with random projections for least-squares regression over a separable Hilbert space. Considering two types of random projections generated by randomized sketches and Nystr\"{o}m subsampling, we prove optimal statistical results with respect to variants of norms for the algorithms under a suitable stopping rule. Particularly, our results show that if the projection dimension is proportional to the effective dimension of the problem, KCGM with randomized sketches can generalize optimally, while achieving a computational advantage. As a corollary, we derive optimal rates for classic KCGM in the well-conditioned regimes for the case that the target function may not be in the hypothesis space.
Comment: Updating acknowledgments; Accepted version for Applied and Computational Harmonic Analysis
- الموضوع:
- الرقم المعرف:
10.1016.j.acha.2021.05.004
- Other Numbers:
COO oai:arXiv.org:1811.01760
Applied and Computational Harmonic Analysis 55(2021)223-269
doi:10.1016/j.acha.2021.05.004
1106319382
- Contributing Source:
CORNELL UNIV
From OAIster®, provided by the OCLC Cooperative.
- الرقم المعرف:
edsoai.on1106319382
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