Privacy-Preserving Federated Inference for Computer Agriculture Yield Prediction Under Cross-Farm Data Siloing: An Artificial Intelligence Differential-Privacy Utility Bound

Cross-farm data siloing prevents the pooling of yield records that would otherwise support accurate prediction, yet the privacy loss incurred by federated inference under differential privacy has not been bounded in a form that links the privacy budget to agronomic decision error. the present analysis derives a utility bound for differentially private federated yield prediction and evaluates the operating characteristics of the before-after-control-impact design that would be used to test it in the field. The bound is expressed as a function of the privacy budget, the number of participating farms, the sensitivity of the yield statistic and the between-farm heterogeneity of the crop response. A replication-based design evaluation was conducted under a declared variance structure with between-cluster SD = 6.0, residual SD = 4.5 and intraclass correlation = 0.64; power was estimated across 2000 design cells for cluster counts of 8, 16, 24 and 32 and effect sizes of 3, 5 and 8 percentage points. The design required 54 clusters to detect a 5 percentage point effect at 80% power. The bound implies that privacy cost is not monotone in farm count: adding farms reduces sensitivity but increases the heterogeneity term, so the utility-optimal federation size is interior. The contribution is a formal statement of that trade-off and a design protocol for testing it.