# Estimating the Prediction Performance of Spatial Models via Spatial k-Fold Cross Validation

arXiv: https://arxiv.org/abs/2005.14263 · HTML: https://mlsanity.com/paper/2005.14263/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 May 2020.

## Built on by (most cited first, 14 of 14)

- [Mission Critical -- Satellite Data is a Distinct Modality in Machine Learning](https://mlsanity.com/paper/2402.01444/) (2024)
- [Evaluation Challenges for Geospatial ML](https://mlsanity.com/paper/2303.18087/) (2023)
- [mlr3spatiotempcv: Spatiotemporal resampling methods for machine learning in R](https://mlsanity.com/paper/2110.12674/) (2021)
- [Foundation for unbiased cross-validation of spatio-temporal models for species distribution modeling](https://mlsanity.com/paper/2502.03480/) (2025)
- [Spatial machine-learning model diagnostics: a model-agnostic distance-based approach](https://mlsanity.com/paper/2111.08478/) (2021)
- [Geostatistical Learning: Challenges and Opportunities](https://mlsanity.com/paper/2102.08791/) (2021)
- [Using Machine Learning to generate an open-access cropland map from satellite images time series in the Indian Himalayan Region](https://mlsanity.com/paper/2203.14673/) (2022)
- [Challenges in data-based geospatial modeling for environmental research and practice](https://mlsanity.com/paper/2311.11057/) (2023)
- [At the junction between deep learning and statistics of extremes: formalizing the landslide hazard definition](https://mlsanity.com/paper/2401.14210/) (2024)
- [On the use of adversarial validation for quantifying dissimilarity in geospatial machine learning prediction](https://mlsanity.com/paper/2404.12575/) (2024)
- [Towards physics-informed neural networks for landslide prediction](https://mlsanity.com/paper/2407.06785/) (2024)
- [Temporal Validation Changes the Apparent Public-Health Utility of Under-Five Mortality Prediction in Bangladesh: A Four-Round DHS Machine-Learning Study](https://mlsanity.com/paper/2602.03957/) (2026)
- [Spatiotemporal Heterogeneity of AI-Driven Traffic Flow Patterns and Land Use Interaction: A GeoAI-Based Analysis of Multimodal Urban Mobility](https://mlsanity.com/paper/2603.05581/) (2026)
- [Aligning Validation with Deployment in Spatial Prediction: Target-Weighted Cross-Validation](https://mlsanity.com/paper/2603.29981/) (2026)

## Abstract (arXiv)

In machine learning one often assumes the data are independent when evaluating model performance. However, this rarely holds in practise. Geographic information data sets are an example where the data points have stronger dependencies among each other the closer they are geographically. This phenomenon known as spatial autocorrelation (SAC) causes the standard cross validation (CV) methods to produce optimistically biased prediction performance estimates for spatial models, which can result in increased costs and accidents in practical applications. To overcome this problem we propose a modified version of the CV method called spatial k-fold cross validation (SKCV), which provides a useful estimate for model prediction performance without optimistic bias due to SAC. We test SKCV with three real world cases involving open natural data showing that the estimates produced by the ordinary CV are up to 40% more optimistic than those of SKCV. Both regression and classification cases are considered in our experiments. In addition, we will show how the SKCV method can be applied as a criterion for selecting data sampling density for new research area.