基于流形-Hilbert核的一致插值系综
Consistent Interpolating Ensembles via the Manifold-Hilbert Kernel
摘要：
最近在过参数化学习理论中的研究试图在插值机制中建立泛化保证。这样的结果已经建立了几个常见的类的方法，但到目前为止还没有集成的方法。我们设计了一个集成分类方法，同时插值的训练数据，是一致的广泛的一类数据分布。为此，我们定义的流形希尔伯特核分布在黎曼流形上的数据。我们证明了在Devroye等人1998的设定下，使用流形-Hilbert核的核平滑回归是弱相容的。对于球，我们表明，流形希尔伯特内核可以实现为加权随机分区内核，这是作为一个无限的合奏分区为基础的分类。
英文摘要：
Recent research in the theory of overparametrized learning has sought to establish generalization guarantees in the interpolating regime. Such results have been established for a few common classes of methods, but so far not for ensemble methods. We devise an ensemble classification method that simultaneously interpolates the training data, and is consistent for a broad class of data distributions. To this end, we define the manifold-Hilbert kernel for data distributed on a Riemannian manifold. We prove that kernel smoothing regression using the manifold-Hilbert kernel is weakly consistent in the setting of Devroye et al. 1998. For the sphere, we show that the manifold-Hilbert kernel can be realized as a weighted random partition kernel, which arises as an infinite ensemble of partition-based classifiers.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
