# Interpretable Graph Partitioning for Spatial Prediction

arXiv: https://arxiv.org/abs/2610.16063 · HTML: https://mlsanity.com/paper/2610.16063/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 32 references that are in the map.
- First posted on arXiv 12 Oct 2026.

## Builds on (most cited first, 9 of 9)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Gaussian Processes for Big Data](https://mlsanity.com/paper/1309.6835/) (2013)
- [Kriging Convolutional Networks](https://mlsanity.com/paper/2306.09463/) (2023)
- [Recent Advances in Graph Partitioning](https://mlsanity.com/paper/1311.3144/) (2013)
- [DeepKriging: Spatially Dependent Deep Neural Networks for Spatial Prediction](https://mlsanity.com/paper/2007.11972/) (2020)
- [Variational Learning on Aggregate Outputs with Gaussian Processes](https://mlsanity.com/paper/1805.08463/) (2018)
- [Spatially Aggregated Gaussian Processes with Multivariate Areal Outputs](https://mlsanity.com/paper/1907.08350/) (2019)
- [Learning from Summarized Data: Gaussian Process Regression with Sample Quasi-Likelihood](https://mlsanity.com/paper/2412.17455/) (2024)

## Abstract (arXiv)

Spatial prediction estimates unobserved values from spatially distributed observations. Although flexible predictive models are increasingly available, their practical use remains limited when interpretability is essential. In this study, we formulate a graph partitioning problem to construct a global surrogate model that approximates black-box predictions with simpler representations. Specifically, we select connected subgraphs to minimize within-cluster residuals in vertex-level predictions. Although this formulation can be viewed as a variant of spatial regionalization, it operates on model-based predictions at individual locations rather than predefined areal units. With many locations, this point-level formulation may produce artificial connections between regions, reducing interpretability. We therefore introduce a constraint that excludes such connections while retaining flexible partition boundaries. We theoretically analyze how this constraint affects the resulting partition. We also develop a computational procedure for adjusting partition boundaries. Experimental results show that the proposed method yields spatially coherent partitions with flexible boundaries.