Abstract
Accurate risk estimation under distribution shifts is critical for deploying machine learning models in real-world spatial applications, from ecological forecasting to medical image analysis. Conventional methods such as No Weighting (NW) and Importance Weighting (IW) fail in spatially structured data due to two challenges: (1) density ratio estimation in high-dimensional clustered distributions and (2) non-stationarity from environmental gradients or sampling biases. Classifier-based approaches offer partial improvements but often yield miscalibrated risk estimates by prioritizing discriminative accuracy over distribution alignment. We conduct a systematic evaluation of four risk estimation methods —NW, IW, Kernel Mean Matching (KMM), and classifier-based reweighting—across synthetic benchmarks (with controlled spatial clustering) and real-world datasets (species distributions and immune cell layouts). Results show that KMM achieves superior robustness, reducing Mean Absolute Percentage Error (MAPE) by 12.3–86.5% compared to alternatives in high-dimensional settings. This advantage stems from KMM’s direct minimization of distributional divergence via kernel embeddings, bypassing error-prone density ratio estimation. Our findings demonstrate that KMM is a principled solution for spatial risk estimation, particularly when source and target distributions exhibit complex clustering or sampling artifacts. Its consistency across ecological and biomedical domains suggests broad applicability for reliable model deployment in spatially heterogeneous environments.
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Data and code availability
For the data, preprocessing and modeling details to reproduce the calculations, we refer the reader to the repository of the project https://github.com/awesomeslayer/Importance-reweighting.
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Funding
The work was supported by the grant for research centers in the field of AI provided by the Ministry of Economic Development of the Russian Federation in accordance with the agreement 000000C313925P4F0002 and the agreement with Skoltech №139-10-2025-033.
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Conceptualization: A.Z., E.S. and D.K.; methodology: E.S., A.Z., D.K.; software: E.S.; validation: E.S., A.Z.; formal analysis: E.S., D.K.; investigation: A.Z., E.S.; data curation: D.K., E.S.; writing—original draft preparation: E.S., D.K.; writing—review and editing: D.K., E.S. and A.Z.; visualization: E.S., D.K.; supervision: A.Z.; project administration: A.Z., D.K. All authors have read and agreed to the published version of the manuscript.
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Serov, E., Koldasbayeva, D. & Zaytsev, A. Kernel mean matching enhances risk estimation under spatial distribution shifts.
Sci Rep (2026). https://doi.org/10.1038/s41598-026-36740-7
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DOI: https://doi.org/10.1038/s41598-026-36740-7
Keywords
- Kernel mean matching
- Spatial risk estimation
- Spatial modeling
- Importance reweighting
- Distribution shift robustness
Source: Ecology - nature.com
