# GeoShapley: A Game Theory Approach to Measuring Spatial Effects in Machine Learning Models

arXiv: https://arxiv.org/abs/2312.03675 · HTML: https://mlsanity.com/paper/2312.03675/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 66 references that are in the map.
- First posted on arXiv 6 Dec 2023.

## Builds on (most cited first, 14 of 14)

- [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)
- [Tabular Data: Deep Learning is Not All You Need](https://mlsanity.com/paper/2106.03253/) (2021)
- [European Union regulations on algorithmic decision-making and a "right to explanation"](https://mlsanity.com/paper/1606.08813/) (2016)
- [Interpretable machine learning: definitions, methods, and applications](https://mlsanity.com/paper/1901.04592/) (2019)
- [Opportunities and Challenges in Explainable Artificial Intelligence (XAI): A Survey](https://mlsanity.com/paper/2006.11371/) (2020)
- [Feature relevance quantification in explainable AI: A causal problem](https://mlsanity.com/paper/1910.13413/) (2019)
- [Improving KernelSHAP: Practical Shapley Value Estimation via Linear Regression](https://mlsanity.com/paper/2012.01536/) (2020)
- [ETA Prediction with Graph Neural Networks in Google Maps](https://mlsanity.com/paper/2108.11482/) (2021)
- [Causal Shapley Values: Exploiting Causal Knowledge to Explain Individual Predictions of Complex Models](https://mlsanity.com/paper/2011.01625/) (2020)
- [A Review of Location Encoding for GeoAI: Methods and Applications](https://mlsanity.com/paper/2111.04006/) (2021)
- [Machine Learning Estimation of Heterogeneous Treatment Effects with Instruments](https://mlsanity.com/paper/1905.10176/) (2019)
- [Advances in Hyperspectral Image Classification: Earth monitoring with statistical learning methods](https://mlsanity.com/paper/1310.5107/) (2013)
- [Joint Shapley values: a measure of joint feature importance](https://mlsanity.com/paper/2107.11357/) (2021)

## Built on by (most cited first, 5 of 5)

- [Can Moran Eigenvectors Improve Machine Learning of Spatial Data? Insights from Synthetic Data Validation](https://mlsanity.com/paper/2504.12450/) (2025)
- [The Geography of Transportation Cybersecurity: Visitor Flows, Industry Clusters, and Spatial Dynamics](https://mlsanity.com/paper/2505.08822/) (2025)
- [Improving the Computational Efficiency and Explainability of GeoAggregator](https://mlsanity.com/paper/2507.17977/) (2025)
- [SX-GeoTree: Self-eXplaining Geospatial Regression Tree Incorporating the Spatial Similarity of Feature Attributions](https://mlsanity.com/paper/2511.19845/) (2025)
- [Evaluating the Alignment Between GeoAI Explanations and Domain Knowledge in Satellite-Based Flood Mapping](https://mlsanity.com/paper/2604.26051/) (2026)

## Abstract (arXiv)

This paper introduces GeoShapley, a game theory approach to measuring spatial effects in machine learning models. GeoShapley extends the Nobel Prize-winning Shapley value framework in game theory by conceptualizing location as a player in a model prediction game, which enables the quantification of the importance of location and the synergies between location and other features in a model. GeoShapley is a model-agnostic approach and can be applied to statistical or black-box machine learning models in various structures. The interpretation of GeoShapley is directly linked with spatially varying coefficient models for explaining spatial effects and additive models for explaining non-spatial effects. Using simulated data, GeoShapley values are validated against known data-generating processes and are used for cross-comparison of seven statistical and machine learning models. An empirical example of house price modeling is used to illustrate GeoShapley's utility and interpretation with real world data. The method is available as an open-source Python package named geoshapley.