JDS Journal of Data Science 1683-86021680-743X1680-743X School of Statistics, Renmin University of China JDS1210 10.6339/25-JDS1210 Statistical Data Science A Scalable Spatial Decorrelation Preprocessing Approach for Machine and Deep Learning https://orcid.org/0000-0003-4654-9827 HeatonMatthew J.mheaton@stat.byu.edu1∗ MillaneAndrew1 RhodesJake S.1 Department of Statistics, Brigham Young University, Provo, UT 84602, USA Corresponding author. Email: mheaton@stat.byu.edu. 2025912202500115 Supplementary Material

This material is based upon work supported by the National Aeronautics and Space Administration under Grant/Contract/Agreement No. 10053957-01 and by the National Science Foundation under Grant No. 2053188.

R and Python implementations of the proposed spatial whitening transformation are available as a zip file or at https://github.com/amillane/spatialtransform. The contents are organized as follows:

README.md: A brief overview of the repository structure and usage instructions.

R Function/

Functions/TransformFunctions.R: R implementation of the whitening and inverse-whitening transformations.

demo.R: Example code demonstrating use of the R transformation functions.

SimulatedData1.RData: Example simulated dataset for demonstration.

SimulatedData2.RData: Second example simulated dataset.

Python Function/

Functions/SpatialTransform.py: Python implementation of the whitening and inverse-whitening transformations.

Functions/matern.py: Matern covariance utility functions.

Functions/mknnIndx.py: Nearest-neighbor index construction for Vecchia approximation.

demo.ipynb: Jupyter notebook illustrating how to use the Python implementation.

NonLinSimDataSet17.json: Example nonlinear simulated dataset used in demonstrations.

 Together, these materials provide complete code and example data needed to reproduce the spatial whitening transformation and the analyses described in the manuscript.

136202525112025 2025 The Author(s). Published by the School of Statistics and the Center for Applied Statistics, Renmin University of China.2025 Open access article under the CC BY license.

Spatial data display correlation between observations collected at nearby locations. Generally, machine and deep learning methods either do not account for this correlation or do so indirectly through correlated features. To account for spatial correlation, we propose preprocessing the data using a spatial decorrelation transform motivated from properties of a multivariate Gaussian distribution and Vecchia approximations. The preprocessed, transformed data can then be ported into a machine or deep learning tool. After model fitting on the transformed data, the output can be spatially re-correlated via the corresponding inverse transformation. We show that including this spatial adjustment results in higher predictive accuracy on simulated and real spatial datasets.

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