Label-Noise-Robust Weak Supervision for Artificial Intelligence Agriculture Crop Disease Annotation Under Rater Disagreement: A Computer Noise-Transition Identifiability Evaluation

Weak supervision for crop-disease annotation in artificial-intelligence agriculture routinely pools labels from plant pathologists, extension officers and untrained field staff whose diagnostic reliability differs systematically. The pooled label is then treated as a noisy observation of a latent disease state, and the noise process is assumed identifiable from the agreement structure alone. It formalises rater disagreement as a class-conditional noise-transition matrix and derives identifiability conditions for the transition probabilities under weak supervision, showing that the transition matrix is identifiable up to permutation only when at least three conditionally independent raters with non-degenerate pairwise agreement are available, and that with two raters only the product of the off-diagonal transition probabilities is recoverable. A before-after-control-impact design was evaluated by replication to characterise the operating characteristics of the identifiability test under a declared variance structure (between-cluster SD = 6.0, residual SD = 4.5, intraclass correlation = 0.64). Power was estimated across 2000 design cells spanning 8, 16, 24 and 32 clusters and 3, 5 and 8 percentage-point effects. The analysis indicates that 54 clusters are required for 80% power at a 5 percentage-point effect, and that the identifiability test is severely underpowered at the smaller cluster counts that characterise most published crop-disease annotation studies. The contribution is a formal statement of when weak-supervision noise transitions can and cannot be recovered from rater disagreement, together with a design-power characterisation that bounds what annotation studies in this setting can support.