发表机构
Emory University; Simon Fraser University（埃默里大学; 西蒙弗雷泽大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出总敏感性核（TSKs）方法，通过加权ANOVA核族学习多变量结构，在RKHS中最小化范数以确定权重，从而提升黑箱函数逼近精度。
AI 中文摘要
在缺乏对输入重要性及其相互作用了解的情况下，从有限数据逼近多变量黑箱函数的输入输出行为具有挑战性。我们引入了总敏感性核（TSKs），这是一种基于加权ANOVA核族的方法，能够学习并适应这种多变量结构。TSKs通过每个输入的因子来参数化目标函数每个多变量分量的权重。我们提出通过选择目标函数具有最小范数的再生核希尔伯特空间（RKHS），直接从函数评估中学习这些因子。在适当条件下，我们证明了该范数最小化问题具有唯一解，并建立了基于最小范数插值的有限数据公式的一致性。学习到的TSK因子表征了各个输入在交互作用和主效应中的参与程度，提供了一种与总Sobol指数相关的核依赖输入敏感性概念。数值实验表明，使核适应学习到的多变量结构可以显著提高相对于标准乘积核的逼近精度。
英文摘要
Approximating the input-output behavior of a multivariable black-box function from limited data is challenging when blind to the importance of its inputs and their interactions. We introduce total sensitivity kernels (TSKs), a method based on families of weighted ANOVA kernels that learn and adapt to this multivariable structure. TSKs parameterize the weights on each multivariable component of the target function by factors for each input. We propose learning these factors directly from function evaluations by selecting the reproducing kernel Hilbert space (RKHS) in which the target function has minimum norm. Under suitable conditions, we show that this norm-minimization problem admits a unique solution, and we establish consistency of a finite-data formulation based on minimum-norm interpolation. The learned TSK factors characterize the participation of individual inputs across interactions and main effects, providing a kernel-dependent notion of input sensitivity related to total Sobol indices. Numerical experiments demonstrate that adapting the kernel to learned multivariable structure can substantially improve approximation accuracy over a standard product kernel.
