A statistical learning framework for explainable forest disturbance-agent attribution with provable guarantees and theoretical foundations for spatial transfer
Abstract
We develop the mathematical foundations of a framework that attributes a disturbance agent, namely wildfire, harvest, insect defoliation, windthrow, or drought, to each disturbance event detected in standardized satellite time-series change metrics. The attribution task is posed as a statistical decision problem on a feature space built from spectral-temporal descriptors, object geometry, terrain, and climate. Within this formulation we prove the Bayes optimality of the posterior-maximizing rule and of its cost-sensitive counterpart, a finite-sample generalization bound for the empirical-risk minimizer over a finite class, the variance-reduction identity that governs ensemble estimators together with a bias-variance decomposition, an ordering between the Gini and entropy impurities, the convexity and second-order optimality conditions of gradient-boosted trees, the gradient identities of the softmax and focal objectives, the efficiency, symmetry, and null-player properties of the Shapley attribution used for explanation, the order preservation of temperature scaling, and the distribution-free lower and upper coverage bounds of the marginal and class-conditional conformal predictors used for uncertainty. We further prove an unbiasedness and variance result for the design-based accuracy estimator and a decomposition of the cross-region transfer gap, together with an estimable form of that decomposition. Many of these results are specializations of established statistical-learning theory to the attribution setting; the contribution lies in their unified formulation on a standardized metric product, in the explicit statement of the assumptions under which each guarantee holds, and in a small number of new corollaries. The paper is theoretical: all results are established by proof and illustrated with synthetic numerical examples, no empirical forest-disturbance dataset is analysed, and the empirical transferability, calibration, and accuracy of an implemented system remain to be evaluated.
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BibTeX
@article{ahmad2026statistical,
title = {{A statistical learning framework for explainable forest disturbance-agent attribution with provable guarantees and theoretical foundations for spatial transfer}},
author = {Khaleel Ahmad and Walid Abdelfattah and Malick Sallah and Jawaher Saud Alrashood},
journal = {Scientific Reports},
year = {2026},
month = oct,
doi = {10.1038/s41598-026-72550-7},
url = {https://www.nature.com/articles/s41598-026-72550-7},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - A statistical learning framework for explainable forest disturbance-agent attribution with provable guarantees and theoretical foundations for spatial transfer
AU - Khaleel Ahmad
AU - Walid Abdelfattah
AU - Malick Sallah
AU - Jawaher Saud Alrashood
PY - 2026
DA - 2026/10/12
JO - Scientific Reports
DO - 10.1038/s41598-026-72550-7
UR - https://www.nature.com/articles/s41598-026-72550-7
AB - We develop the mathematical foundations of a framework that attributes a disturbance agent, namely wildfire, harvest, insect defoliation, windthrow, or drought, to each disturbance event detected in standardized satellite time-series change metrics. The attribution task is posed as a statistical decision problem on a feature space built from spectral-temporal descriptors, object geometry, terrain, and climate. Within this formulation we prove the Bayes optimality of the posterior-maximizing rule and of its cost-sensitive counterpart, a finite-sample generalization bound for the empirical-risk minimizer over a finite class, the variance-reduction identity that governs ensemble estimators together with a bias-variance decomposition, an ordering between the Gini and entropy impurities, the convexity and second-order optimality conditions of gradient-boosted trees, the gradient identities of the softmax and focal objectives, the efficiency, symmetry, and null-player properties of the Shapley attribution used for explanation, the order preservation of temperature scaling, and the distribution-free lower and upper coverage bounds of the marginal and class-conditional conformal predictors used for uncertainty. We further prove an unbiasedness and variance result for the design-based accuracy estimator and a decomposition of the cross-region transfer gap, together with an estimable form of that decomposition. Many of these results are specializations of established statistical-learning theory to the attribution setting; the contribution lies in their unified formulation on a standardized metric product, in the explicit statement of the assumptions under which each guarantee holds, and in a small number of new corollaries. The paper is theoretical: all results are established by proof and illustrated with synthetic numerical examples, no empirical forest-disturbance dataset is analysed, and the empirical transferability, calibration, and accuracy of an implemented system remain to be evaluated.
SN - 2045-2322
ER -