2014/09/21 by David Ginsbourger, Ginsbourger, David, Olivier Roustant +7 · 1 citation
Computer Science · Decision Sciences · Physics and Astronomy · #FOS: Mathematics #Gaussian Processes and Bayesian Inference #Model Reduction and Neural Networks #Probabilistic and Robust Engineering Design #Probability (math.PR) #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1409.6008
openalex publication_date 2014/09/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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 22d 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.