🤖 AI Summary
This paper addresses the poor interpretability of black-box models in spatial prediction. We propose a graph-partitioning-based spatial segmentation method that minimizes the sum of intra-segment prediction variance. Innovatively, we formulate interpretability as a variance-constrained graph partitioning problem and introduce, for the first time, a mixed-integer quadratic programming (MIQP) formulation to capture this objective. To tackle the prohibitive computational complexity on large-scale data, we design an efficient approximation algorithm that exploits intrinsic graph structural properties, ensuring high segmentation quality while drastically improving runtime efficiency. Experiments demonstrate that our method achieves 1–2 orders of magnitude speedup over exact MIQP solvers while reducing intra-segment variance by up to 37%. The approach thus establishes a new paradigm for scalable, interpretable spatial modeling—balancing fidelity, transparency, and computational tractability.
📝 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.