Active-Labeling Evaluation for Computer Agriculture Nematode-Cyst Detection Under Sparse Soil-Sample Ground Truth: An Artificial Intelligence Annotation-Efficiency Bound

Active learning promises to reduce the annotation burden of training nematode-cyst detection models for precision agriculture, but the size of that reduction is not known when ground truth comes from sparse soil samples rather than exhaustive visual inspection. the present analysis derives an annotation-efficiency bound for pool-based active learning under sparse soil-sample ground truth. The detection task is formalised as a two-stage process in which a classifier selects candidate cysts from soil imagery and a laboratory assay confirms a small labelled subset. Under a declared variance structure with between-cluster standard deviation 6.0, residual standard deviation 4.5 and intraclass correlation 0.64, the bound is evaluated across a design grid of 8, 16, 24 and 32 clusters and effect sizes of 3, 5 and 8 percentage points, with 2000 replications per cell. The annotation-efficiency gain is bounded by the ratio of label noise to cluster-level variance, and that 52 clusters are required to detect a 5-percentage-point improvement at 80% power. The bound provides a design rule for allocating annotation effort between active selection and confirmatory soil sampling.