Decision-Target Reversal under Informative Label Missingness

Informative label missingness can improve classification efficiency because the pattern of label availability may itself contain information about the discriminant structure. We show that this advantage need not persist across deployment objectives: with the data-generating model and statistical experiments held fixed, informative partial classification can be favourable under one loss and unfavourable under another. We call this phenomenon decision-target reversal. For binary Gaussian discrimination, we derive a local cost-sensitive excess-risk expansion and, in one dimension, obtain explicit critical cost ratios at which the first-order risk ordering reverses. We show that the required covariance geometry arises under finite uncertainty-dependent missingness mechanisms with a fixed marginal missing-label proportion. We then extend the analysis to multiclass finite-action problems through loss-specific active-boundary curvature, yielding a general decision-target frontier. Monte Carlo experiments illustrate the predicted reversals, and a descriptive gastrointestinal-lesion application with agreement-defined label availability illustrates sensitivity to deployment costs. The results show that favourable informative missingness is a property of the statistical experiment relative to the deployment decision, rather than of the experiment alone.