Privacy-Preserving Federated Learning for Computational Pharmaceutical Applied Aspect in Uganda: Robustness Under Distribution Shift and Sparse Labels
Federated learning offers a pathway toward privacy-preserving computational pharmaceutical analysis across Ugandan health facilities, yet its practical utility is constrained by two under-examined statistical realities: the non-independence of client data distributions and the scarcity of validated labels. We introduce a hierarchical Bayesian aggregation operator that couples client-level model updates through a pharmaceutical-domain-informed prior, and we prove that this operator admits a bounded worst-case risk under a Wasserstein ambiguity set. We further derive a label-efficiency bound showing that the proposed semi-supervised consensus mechanism requires substantially fewer ground-truth labels than conventional federated averaging to achieve a given pharmaceutical decision threshold. The framework is developed as a theoretical and methodological contribution, with formal definitions, convergence guarantees, and an explicit protocol for future empirical validation. We argue that robustness in this setting is inseparable from epistemic humility about label provenance, and we specify how the framework accommodates the institutional fragmentation of Ugandan pharmaceutical data governance.