论文标题
通过签署的措施在复制核心核素空间中快速学习
Fast Learning in Reproducing Kernel Krein Spaces via Signed Measures
论文作者
论文摘要
在本文中，我们试图解决机器学习社区中非阳性确定（非PD）内核的持久开放问题：是否可以将给定的非PD内核分解为两个PD内核的差异（称为阳性分解）？我们通过引入\ emph {签名度量}将这个问题作为分配视图，该问题将正分解转换为测量分解：一系列非PD内核可以与特定有限的疏水岩测量的线性组合相关联。通过这种方式，我们基于分配的框架提供了一个足够和必要的条件来回答这个开放问题。具体而言，该解决方案在实践中也可以在计算上实现，以在大型样本案例中扩展非PD内核，这使我们可以设计第一个随机特征算法以获得无偏的估计器。几个基准数据集的实验结果验证了我们算法对现有方法的有效性。
In this paper, we attempt to solve a long-lasting open question for non-positive definite (non-PD) kernels in machine learning community: can a given non-PD kernel be decomposed into the difference of two PD kernels (termed as positive decomposition)? We cast this question as a distribution view by introducing the \emph{signed measure}, which transforms positive decomposition to measure decomposition: a series of non-PD kernels can be associated with the linear combination of specific finite Borel measures. In this manner, our distribution-based framework provides a sufficient and necessary condition to answer this open question. Specifically, this solution is also computationally implementable in practice to scale non-PD kernels in large sample cases, which allows us to devise the first random features algorithm to obtain an unbiased estimator. Experimental results on several benchmark datasets verify the effectiveness of our algorithm over the existing methods.
