Approximation Package for High-Dimensional Functions in Julia
Author NFFT
0 Stars
Updated Last
10 Months Ago
Started In
October 2020


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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)

Getting started

In Julia you can get started by typing

] add ANOVAapprox

then checkout the documentation.

Used By Packages

No packages found.