论文标题
通过歧管 - 希尔伯特内核的一致插值合奏
Consistent Interpolating Ensembles via the Manifold-Hilbert Kernel
论文作者
论文摘要
过分兼容学习理论的最新研究试图在插值制度中建立概括保证。已经针对一些常见的方法建立了此类结果，但到目前为止，对于集成方法而言，这些结果尚未建立。我们设计了一种合奏分类方法，该方法同时插入培训数据，并且对于一系列数据分布是一致的。为此，我们为分布在Riemannian歧管上的数据定义了歧管 - 希尔伯特内核。我们证明，在Devroye等人的环境中，使用歧管 - 希尔伯特内核的内核平滑回归是微弱一致的。 1998年。对于球体，我们表明，歧管 - 希尔伯特内核可以被实现为加权随机分区内核，它是基于分区的分类器的无限合奏。
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.
