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Kernel mean matching enhances risk estimation under spatial distribution shifts.

Egor Serov1, Diana Koldasbayeva2, Alexey Zaytsev1,3

  • 1Skolkovo Institute of Science and Technology, Moscow, Russia.

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Summary

Kernel Mean Matching (KMM) improves machine learning risk estimation in spatial data, outperforming traditional methods like No Weighting (NW) and Importance Weighting (IW). KMM offers robust and accurate predictions, crucial for ecological and medical applications facing distribution shifts.

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Distribution shift robustnessImportance reweightingKernel mean matchingSpatial modelingSpatial risk estimation

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Area of Science:

  • Spatial statistics
  • Machine learning
  • Data science

Background:

  • Accurate risk estimation is vital for deploying machine learning in spatial applications like ecology and medicine.
  • Conventional methods (No Weighting, Importance Weighting) struggle with spatially structured data due to density estimation challenges and non-stationarity.
  • Classifier-based methods show limited success, often miscalibrating risk estimates.

Purpose of the Study:

  • To systematically evaluate risk estimation methods for spatially structured data under distribution shifts.
  • To identify a robust method that overcomes challenges in high-dimensional clustered distributions and non-stationarity.
  • To demonstrate the effectiveness of Kernel Mean Matching (KMM) in spatial risk estimation.

Main Methods:

  • Evaluated four risk estimation methods: No Weighting (NW), Importance Weighting (IW), Kernel Mean Matching (KMM), and classifier-based reweighting.
  • Utilized synthetic benchmarks with controlled spatial clustering and real-world datasets (species distributions, immune cell layouts).
  • Focused on minimizing distributional divergence using kernel embeddings in KMM.

Main Results:

  • Kernel Mean Matching (KMM) demonstrated superior robustness across diverse spatial datasets.
  • KMM reduced Mean Absolute Percentage Error (MAPE) by 12.3-86.5% compared to other methods in high-dimensional settings.
  • KMM effectively bypassed density ratio estimation issues inherent in conventional approaches.

Conclusions:

  • Kernel Mean Matching (KMM) provides a principled and effective solution for spatial risk estimation, especially with clustered or artifact-prone data.
  • KMM's direct minimization of distributional divergence ensures more reliable risk estimates.
  • The method's broad applicability across ecological and biomedical domains highlights its potential for robust model deployment in heterogeneous environments.