In this paper we apply the previously introduced approximation method based on the analysis of variance (ANOVA) decomposition and Grouped Transformations to synthetic and real data. The advantage of this method is the interpretability of the approximation, i.e., the ability to rank the importance of the attribute interactions or the variable couplings. Moreover, we are able to generate an attribute ranking to identify unimportant variables and reduce the dimensionality of the problem. We compare the method to other approaches on publicly available benchmark datasets.


  1. ANOVA
  2. high-dimensional
  3. approximation
  4. intrepretability
  5. fast Fourier methods

MSC codes

  1. 65T
  2. 42B05
  3. 62-07
  4. 65D15

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Supplementary Material

PLEASE NOTE: These supplementary files have not been peer-reviewed.

Index of Supplementary Materials

Title of paper: Interpretable Approximation of High-Dimensional Data

Authors: D. Potts and M. Schmischke

File: code.zip

Type: Compressed Code Files

Contents: The zip files contains several folders with code to replicate our numerical experiments.


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Information & Authors


Published In

cover image SIAM Journal on Mathematics of Data Science
SIAM Journal on Mathematics of Data Science
Pages: 1301 - 1323
ISSN (online): 2577-0187


Submitted: 25 March 2021
Accepted: 7 September 2021
Published online: 30 November 2021


  1. ANOVA
  2. high-dimensional
  3. approximation
  4. intrepretability
  5. fast Fourier methods

MSC codes

  1. 65T
  2. 42B05
  3. 62-07
  4. 65D15



Funding Information

Bundesministerium für Bildung und Forschung https://doi.org/10.13039/501100002347 : 01|S20053A
Deutsche Forschungsgemeinschaft https://doi.org/10.13039/501100001659 : 416228727 - SFB 1410

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