We propose two algorithms for boosting random Fourier feature models for approximating high-dimensional functions. These methods utilize the classical and generalized analysis of variance (ANOVA) decomposition to learn low-order functions, where there are few interactions between the variables. Our algorithms are able to find an index set of important input variables and variable interactions reliably. Furthermore, we generalize already existing random Fourier feature models to an ANOVA setting, where terms of different order can be used. Our algorithms have the advantage of interpretability, meaning that the influence of every input variable is known in the learned model, even for dependent input variables. We give theoretical as well as numerical results that our algorithms perform well for sensitivity analysis. The ANOVA-boosting step reduces the approximation error of existing methods significantly.
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