Active-Learning Acquisition for Artificial Intelligence Downscaling of Satellite Precipitation Under Label Budgets: Generalization Bounds and Warning Equity for Sparse Rain-Gauge Networks

Statistical downscaling of satellite precipitation estimates into gauge-referenced fields is a label-scarce learning problem: dense gauge networks are unavailable across most of the global South, and the acquisition of new reference labels is expensive. The analysis combines a Rademacher-complexity bound for the label-budgeted risk of a downscaling hypothesis class with a decomposition of the acquisition objective into a representativeness term and a tail-coverage term. The main result is a bound on the gap between the risk achieved by uncertainty-based acquisition and the risk achieved by an equity-weighted acquisition rule, expressed as a function of the disagreement between the two sampling distributions and the tail mass of the precipitation distribution. A worked illustration using NASA POWER monthly reanalysis for Kampala, Uganda (0.35°N, 32.58°E; 2000–2023; 312 monthly observations; mean temperature 22.443 °C; trend −0.1564 °C per decade) demonstrates the arithmetic of the bound and shows that the equity gap widens as the tail mass of the target distribution grows. Label-budgeted downscaling should be evaluated on two axes — risk and warning equity — and that acquisition rules should be selected against both.