Statistically Aware Optimization for Resource-constrained and Geometrically-rich Data: Nigerian Agricultural Case Study

Modern machine learning, fueled by large datasets and complex models, faces a critical tension. The statistical principles underpinning learning (generalization, efficiency, robustness) often clash with the computational realities of optimization, especially in a resource constrained environment or when data exhibits inherent geometric structure. This work addresses the theme "Statistics Meets Optimization" by employing an optimization framework explicitly designed to leverage statistical data properties, particularly group invariances/equivariances common in real world data (e.g., spatial rotations in satellite imagery, temporal shifts in sensor data), to achieve significant gains in sample efficiency and convergence speed. We theoretically derive generalization bounds linking the exploitation of data geometry to reduced sample complexity. Empirically, we demonstrate the efficacy of our method on a challenging real world case study, i.e., on predicting crop yield anomalies in Delta State, Nigeria, using limited, noisy, and spatially heterogeneous satellite and meteorological data. Our optimizer achieved a significant performance with 40% less data compared to adaptive baselines (Adam, RMSProp), highlighting the practical impact of statistically-informed optimization, especially for regions facing data scarcity. This work provides a concrete bridge between statistical theory (data structure, efficiency) and optimization practice (algorithm design, scalability), demonstrating that geometry-aware algorithms can democratize effective ML for resource-limited applications.