# Kriging prior Regression: A Case for Kriging-Based Spatial Features with TabPFN in Soil Mapping

arXiv: https://arxiv.org/abs/2509.09408 · HTML: https://mlsanity.com/paper/2509.09408/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 85 references that are in the map.
- First posted on arXiv 11 Sep 2025.

## Builds on (most cited first, 11 of 11)

- [Shortcut Learning in Deep Neural Networks](https://mlsanity.com/paper/2004.07780/) (2020)
- [TabPFN: A Transformer That Solves Small Tabular Classification Problems in a Second](https://mlsanity.com/paper/2207.01848/) (2022)
- [Transformers Can Do Bayesian Inference](https://mlsanity.com/paper/2112.10510/) (2021)
- [Predictive inference with the jackknife+](https://mlsanity.com/paper/1905.02928/) (2019)
- [TabArena: A Living Benchmark for Machine Learning on Tabular Data](https://mlsanity.com/paper/2506.16791/) (2025)
- [DeepKriging: Spatially Dependent Deep Neural Networks for Spatial Prediction](https://mlsanity.com/paper/2007.11972/) (2020)
- [Over-optimism in benchmark studies and the multiplicity of design and analysis options when interpreting their results](https://mlsanity.com/paper/2106.02447/) (2021)
- [Neural networks for geospatial data](https://mlsanity.com/paper/2304.09157/) (2023)
- [Modern Neural Networks for Small Tabular Datasets: The New Default for Field-Scale Digital Soil Mapping?](https://mlsanity.com/paper/2508.09888/) (2025)
- [An Efficient Model-Agnostic Approach for Uncertainty Estimation in Data-Restricted Pedometric Applications](https://mlsanity.com/paper/2409.11985/) (2024)
- [LimeSoDa: A Dataset Collection for Benchmarking of Machine Learning Regressors in Digital Soil Mapping](https://mlsanity.com/paper/2502.20139/) (2025)

## Built on by (most cited first, 3 of 3)

- [TabPFN-2.5: Advancing the State of the Art in Tabular Foundation Models](https://mlsanity.com/paper/2511.08667/) (2025)
- [TabPFN-3: Technical Report](https://mlsanity.com/paper/2605.13986/) (2026)
- [From field-scale to large-scale spectral libraries: Tabular foundation models in soil spectroscopy](https://mlsanity.com/paper/2608.00608/) (2026)

## Abstract (arXiv)

Machine learning and geostatistics are two fundamentally different frameworks for predicting and spatially mapping soil properties. Geostatistics leverages the spatial structure of soil properties, while machine learning captures the relationship between available environmental features and soil properties. We propose a hybrid framework that enriches ML with spatial context through engineering of 'spatial lag' features from ordinary kriging. We call this approach 'kriging prior regression' (KpR), as it follows the inverse logic of regression kriging. To evaluate this approach, we assessed both the point and probabilistic prediction performance of KpR, using the TabPFN model across six fieldscale datasets from LimeSoDa. These datasets included soil organic carbon, clay content, and pH, along with features derived from remote sensing and in-situ proximal soil sensing. KpR with TabPFN demonstrated reliable uncertainty estimates and more accurate predictions in comparison to several other spatial techniques (e.g., regression/residual kriging with TabPFN), as well as to established non-spatial machine learning algorithms (e.g., random forest). Most notably, it significantly improved the average R2 by around 30% compared to machine learning algorithms without spatial context. This improvement was due to the strong prediction performance of the TabPFN algorithm itself and the complementary spatial information provided by KpR features. TabPFN is particularly effective for prediction tasks with small sample sizes, common in precision agriculture, whereas KpR can compensate for weak relationships between sensing features and soil properties when proximal soil sensing data are limited. Hence, we conclude that KpR with TabPFN is a very robust and versatile modelling framework for digital soil mapping in precision agriculture.