The FANOVA (or "Sobol'-Hoeffding") decomposition of multivariate functions
has been used for high-dimensional model representation and global sensitivity
analysis. When the objective function f has no simple analytic form and is
costly to evaluate, a practical limitation is that computing FANOVA terms may
be unaffordable due to numerical integration costs. Several approximate
approaches relying on random field models have been proposed to alleviate these
costs, where f is substituted by a (kriging) predictor or by conditional
simulations. In the present work, we focus on FANOVA decompositions of Gaussian
random field sample paths, and we notably introduce an associated kernel
decomposition (into 2^{2d} terms) called KANOVA. An interpretation in terms of
tensor product projections is obtained, and it is shown that projected kernels
control both the sparsity of Gaussian random field sample paths and the
dependence structure between FANOVA effects. Applications on simulated data
show the relevance of the approach for designing new classes of covariance
kernels dedicated to high-dimensional kriging.

本文研究高维函数的表征和全局敏感性分析的 FANOVA 分解，阐述了一种基于高斯随机场样本路径 KANOVA 的核分解方法，以及相关联的张量积投影和协方差核的设计。