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Kernel Conjugate Gradient Methods with Random Projections

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اقرأ أكثر حفظ في قائمتي
  • المؤلفون: Lin, Junhong; Cevher, Volkan
  • نوع التسجيلة:
    Electronic Resource
  • الدخول الالكتروني :
    http://arxiv.org/abs/1811.01760
  • 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:
      Statistics - Machine Learning; Computer Science - Machine Learning; Mathematics - Functional Analysis; Mathematics - Optimization and Control; Mathematics - Statistics Theory; 68T05, 94A20, 41A35; text
    • 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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