This package provides a framework for the method ANOVAapprox to approximate high-dimensional functions with a low superposition dimension or a sparse ANOVA decomposition from scattered data. The method has been dicussed and applied in the following articles/preprints:
- D. Potts and M. Schmischke
Interpretable transformed ANOVA approximation on the example of the prevention of forest fires
arXiv, PDF - F. Bartel, D. Potts und M. Schmischke
Grouped transformations and Regularization in high-dimensional explainable ANOVA approximation
SIAM Journal on Scientific Computing (accepted)
arXiv, PDF - D. Potts and M. Schmischke
Interpretable approximation of high-dimensional data
SIAM Journal on Mathematics of Data Science (accepted)
arXiv, PDF, Software - D. Potts and M. Schmischke
Learning multivariate functions with low-dimensional structures using polynomial bases
Journal of Computational and Applied Mathematics 403, 113821, 2021
DOI, arXiv, PDF - D. Potts and M. Schmischke
Approximation of high-dimensional periodic functions with Fourier-based methods
SIAM Journal on Numerical Analysis 59 (5), 2393-2429, 2021
DOI, arXiv, PDF - L. Lippert, D. Potts and T. Ullrich
Fast Hyperbolic Wavelet Regression meets ANOVA
ArXiv: 2108.13197
arXiv, PDF
ANOVAapprox.jl provides the following functionality:
- approximation of high-dimensional periodic and nonperiodic functions with a sparse ANOVA decomposition
- analysis tools for interpretability (global sensitvitiy indices, attribute ranking, shapley values)
In Julia you can get started by typing
] add ANOVAapproxthen checkout the documentation.