The paper introduces an ANOVA boosting approach for random Fourier feature models to address high-dimensional function approximation tasks. The key highlights are:
The authors generalize the classical ANOVA decomposition to handle dependent input variables, allowing the decomposition of the function into hierarchical terms that capture variable interactions.
They propose two algorithms that leverage the ANOVA decomposition to identify important input variables and their interactions, and use this information to construct an initial approximation of the function.
This ANOVA-boosting step is then combined with existing random Fourier feature models, such as SHRIMP and HARFE, to further improve the approximation accuracy while maintaining interpretability.
The theoretical analysis generalizes the theory of sparse random Fourier features to handle functions of low order, where the Fourier transform only exists in a distributional sense.
Numerical examples demonstrate the power of the ANOVA-boosting approach, showing that it can significantly reduce the approximation error compared to existing random Fourier feature methods.
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by Daniel Potts... lúc arxiv.org 04-05-2024
https://arxiv.org/pdf/2404.03050.pdfYêu cầu sâu hơn