用图划分方法生成可解释的空间预测分段，提升工业应用中的透明度。
Surrogate Graph Partitioning for Spatial Prediction
- 基于图划分构建空间分段，最小化段内预测方差。
- 提出近似算法，计算效率远高于精确解法。
- 适合需要可解释性的空间数据分析场景。
空间预测旨在从空间分布的观测数据中估计未观测值。尽管近期研究提升了对多种观测类型建模的能力，但实际工业应用仍受限于对可解释性的需求。为此，我们提出一种图划分问题，用于构建空间片段，以最小化各片段内预测值的总方差。数据点分配至片段的问题可建模为混合整数二次规划问题。虽然该公式理论上能识别精确片段，但随着数据点数量增加，计算复杂度急剧上升。针对此挑战，我们设计了一种利用图划分结构特性的近似方案。实验表明，该近似方法在识别空间片段时具有显著的计算效率优势。
原文摘要 · Abstract (English)
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.
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