论文标题
通过随机梯度下降对Nyström样品的局部优化
Local optimisation of Nyström samples through stochastic gradient descent
论文作者
论文摘要
我们研究了内核矩阵NyStröm近似的柱采样问题的放松版本，其中从环境空间中的地标点的多组定义了近似值；这样的多组称为NyStröm样品。我们将径向平方内核差异（SKD）标准的未加权变化视为用于评估NyStröm近似准确性的经典标准的替代物；在这种情况下，我们讨论了如何通过随机梯度下降如何有效地优化Nyström样品。我们执行数值实验，表明径向SKD的局部最小化可产生具有提高NyStröm近似精度的Nyström样品。
We study a relaxed version of the column-sampling problem for the Nyström approximation of kernel matrices, where approximations are defined from multisets of landmark points in the ambient space; such multisets are referred to as Nyström samples. We consider an unweighted variation of the radial squared-kernel discrepancy (SKD) criterion as a surrogate for the classical criteria used to assess the Nyström approximation accuracy; in this setting, we discuss how Nyström samples can be efficiently optimised through stochastic gradient descent. We perform numerical experiments which demonstrate that the local minimisation of the radial SKD yields Nyström samples with improved Nyström approximation accuracy.
