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This paper proposes a graph partitioning method to enhance the interpretability of spatial prediction models by segmenting data points based on prediction variance. The authors develop an approximation scheme to address the prohibitive computational complexity of exact mixed-integer quadratic programming formulations for large datasets. However, the manuscript has been withdrawn by the authors, indicating that this specific research direction is no longer being pursued as a joint effort.
Surrogate Graph Partitioning for Spatial Prediction
arXiv:2510.07832v2 Announce Type: replace-cross Abstract: Spatial prediction refers to the estimation of unobserved values from spatially distributed observations. Although recent advances have improved the capacity to model diverse observation types, adoption in practice remains limited in industries that demand interpretability. To mitigate this gap, surrogate models that explain black-box predictors provide a promising path toward interpretable decision making. In this study, we propose a graph partitioning problem to construct spatial segments that minimize the sum of within-segment variances of individual predictions. The assignment of data points to segments can be formulated as a mixed-integer quadratic programming problem. While this formulation potentially enables the identification of exact segments, its computational complexity becomes prohibitive as the number of data points increases. Motivated by this challenge, we develop an approximation scheme that leverages the structural properties of graph partitioning. Experimental results demonstrate the computational efficiency of this approximation in identifying spatial segments.
Abstract:Spatial prediction refers to the estimation of unobserved values from spatially distributed observations. Although recent advances have improved the capacity to model diverse observation types, adoption in practice remains limited in industries that demand interpretability. To mitigate this gap, surrogate models that explain black-box predictors provide a promising path toward interpretable decision making. In this study, we propose a graph partitioning problem to construct spatial segments that minimize the sum of within-segment variances of individual predictions. The assignment of data points to segments can be formulated as a mixed-integer quadratic programming problem. While this formulation potentially enables the identification of exact segments, its computational complexity becomes prohibitive as the number of data points increases. Motivated by this challenge, we develop an approximation scheme that leverages the structural properties of graph partitioning. Experimental results demonstrate the computational efficiency of this approximation in identifying spatial segments.
The authors have mutually agreed to withdraw this manuscript, as they no longer intend to pursue it as a joint work. The subsequent research will be pursued under a different authorship arrangement
Machine Learning (stat.ML); Machine Learning (cs.LG)
arXiv:2510.07832 [stat.ML]
(or arXiv:2510.07832v2 [stat.ML] for this version)
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