RCShift: Certifying When Partial Linkage Suffices for Finite-Sample Decisions

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.

A mean shift between two data sources can be easy to detect but hard to remove without substantially changing their representations. We cast its removal as a statistical decision problem: from noisy differences between paired calibration measurements in $\mathbb{R}^d$, learn one linear map, applied to both sources under a hard distortion budget, that leaves as little of the shift as possible on fresh data. We derive the exact finite-sample minimax risk over all such maps, $(d-k) \mathbb{E}[1/(d+2J)]$ with $J\sim\mathrm{Pois}(κ/2)$, where the budget allows deleting $k$ directions and $κ$ is the calibration signal-to-noise ratio. Projecting out the mean calibration difference attains it without knowing $κ$ or the noise scale. This exposes a detection-repair gap: detecting the shift needs only $κ\gg\sqrt d$, whereas removing a fixed fraction of it at constant distortion needs $κ\asymp d$, as for estimating its direction. Standard linear concept erasers (MP, SAL, LEACE) remove the same calibration difference, so the formula gives, before fitting, exactly how much shift they leave on fresh data and how much calibration a target requires. The limit is robust: pairing keeps it exact for non-Gaussian shared content, the projection keeps its guarantee under anisotropic noise, and selective abstention cannot close the gap. On paired clinical and wearable sleep EEG, where differences between participants act as calibration noise, the formula predicts the device shift left in new participants, and more recordings per person soon stop helping. Together, these results tell whether a correction that falls short needs a better method, more recordings, or more participants.

Matching repair after utility changes can reuse valid observations, but new evaluations must respect matching capacity and may return out of order. We study announced invalidations with bounded, possibly reward-dependent reporting delays and pending evaluations that do not occupy future matching capacity. Residualload repair (RLR) combines sound outcome certificates with batched matching schedules for unequal sample deficits. Its complete dyadic quota schedule admits a sharp issue-round bound with coefficient cb < 1.607 relative to the terminal residual endpoint load, together with separate delay and evidence-lifetime bounds. RLR-P monitors complete issue-order prefixes without changing the sampling plan before acceptance. With a deterministic pure oracle, a single-repair coupling from the same drained initial state guarantees no increase in certification time, issued observations, or time to a reusable checkpoint. We also derive an information-load lower bound. On fixed priority-star markets with unknown Bernoulli gaps, PrioritySearch attains the history-adjusted first-order constant for expected certification time as δ {\sim} 0, under hypothesis-independent linear history scaling and sublogarithmic reporting delays. Paired simulations and measured-feedback replay quantify the trade-offs: in the replay, RLR-P has lower mean capped update-certification time than a monitored width-based baseline, at higher oracle CPU cost.