# Valid model-free spatial prediction

arXiv: https://arxiv.org/abs/2006.15640 · HTML: https://mlsanity.com/paper/2006.15640/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Jun 2020.

## Built on by (most cited first, 19 of 19)

- [Conformal Contextual Robust Optimization](https://mlsanity.com/paper/2310.10003/) (2023)
- [Conformal Prediction: A Data Perspective](https://mlsanity.com/paper/2410.06494/) (2024)
- [Spatio-temporal DeepKriging for Interpolation and Probabilistic Forecasting](https://mlsanity.com/paper/2306.11472/) (2023)
- [Conformal Prediction under Levy-Prokhorov Distribution Shifts: Robustness to Local and Global Perturbations](https://mlsanity.com/paper/2502.14105/) (2025)
- [Relational Conformal Prediction for Correlated Time Series](https://mlsanity.com/paper/2502.09443/) (2025)
- [Conformal Approach To Gaussian Process Surrogate Evaluation With Coverage Guarantees](https://mlsanity.com/paper/2401.07733/) (2024)
- [Spatial Conformal Inference through Localized Quantile Regression](https://mlsanity.com/paper/2412.01098/) (2024)
- [Distribution-Free Finite-Sample Guarantees and Split Conformal Prediction](https://mlsanity.com/paper/2210.14735/) (2022)
- [Adaptive Conformal Anomaly Detection with Time Series Foundation Models for Signal Monitoring](https://mlsanity.com/paper/2604.20122/) (2026)
- [Uncertainty quantification in automated valuation models with spatially weighted conformal prediction](https://mlsanity.com/paper/2312.06531/) (2023)
- [Bivariate DeepKriging for Large-scale Spatial Interpolation of Wind Fields](https://mlsanity.com/paper/2307.08038/) (2023)
- [Bin-Conditional Conformal Prediction of Fatalities from Armed Conflict](https://mlsanity.com/paper/2410.14507/) (2024)
- [GeoConformal prediction: a model-agnostic framework of measuring the uncertainty of spatial prediction](https://mlsanity.com/paper/2412.08661/) (2024)
- [Flow-Based Conformal Predictive Distributions](https://mlsanity.com/paper/2602.07633/) (2026)
- [STACI: Spatio-Temporal Aleatoric Conformal Inference](https://mlsanity.com/paper/2505.21658/) (2025)
- [DANCE: Doubly Adaptive Neighborhood Conformal Estimation](https://mlsanity.com/paper/2602.20652/) (2026)
- [Conformal PM2.5 Mapping Under Spatial Covariate Shift: Satellite-Reanalysis Fusion for Africa's Green Industrial Transition](https://mlsanity.com/paper/2604.22787/) (2026)
- [Conflict Forecasting via Conformal Prediction for Markov Processes](https://mlsanity.com/paper/2604.25139/) (2026)
- [GeoDose-CP: Graph-Local Conformal Inference for Continuous-Treatment Earth Observation](https://mlsanity.com/paper/2609.28895/) (2026)

## Abstract (arXiv)

Predicting the response at an unobserved location is a fundamental problem in spatial statistics. Given the difficulty in modeling spatial dependence, especially in non-stationary cases, model-based prediction intervals are at risk of misspecification bias that can negatively affect their validity. Here we present a new approach for model-free nonparametric spatial prediction based on the conformal prediction machinery. Our key observation is that spatial data can be treated as exactly or approximately exchangeable in a wide range of settings. In particular, under an infill asymptotic regime, we prove that the response values are, in a certain sense, locally approximately exchangeable for a broad class of spatial processes, and we develop a local spatial conformal prediction algorithm that yields valid prediction intervals without strong model assumptions like stationarity. Numerical examples with both real and simulated data confirm that the proposed conformal prediction intervals are valid and generally more efficient than existing model-based procedures for large datasets across a range of non-stationary and non-Gaussian settings.