Not All Mislabels Are Equal: Efficient Task-Aware Auditing with Confidence Sequences

An initial high-recall stage in an empirical pipeline decides which items pass to later review, labelling, or modelling, and relevant items it misses are lost to every subsequent stage. We study how many audit labels are needed to certify, with finite-sample validity, that this missed relevant mass is small, and our main results characterise the label complexity of this problem. We first show that no procedure using only labels from inside the candidate set can certify any non-trivial bound on the missed mass: the audit must sample the excluded pool, the only region where unrecovered relevant items can lie. We then prove a matching finite-corpus lower bound. Any valid audit that certifies fewer than $m$ missed relevant items with high probability when none are present, even if adaptive and permitted to label the entire included pool, must inspect on the order of $N_0/m$ excluded-pool labels. Excluded-pool auditing is therefore minimax rate-optimal, not merely convenient, for missed-mass certification in the zero-miss regime. Building on this characterisation, we develop an exact finite-sample toolkit, using binomial and hypergeometric inversion rather than asymptotic approximation, that certifies missed mass, converts it to recall through a two-pool design, certifies pre-specified families of nested candidate generators simultaneously, and produces stress-test certificates against declared perturbation mechanisms. These certificates can be paired with observable review burden to select the least burdensome pre-specified candidate generator meeting a missed-mass target. Every guarantee holds under one discipline: the candidate generator, or the pre-specified family from which it is selected, and the audit rule are fixed before the certification labels are examined.

AI systems increasingly search among candidate answers and deploy the highest-scoring one. Increasing search changes which errors matter, so a precise evaluation at one computation budget can leave another budget unresolved. We connect this information gap to the cost of closing it. For independent best-of-n search, aggregate reliability measurements identify deployment only through the directions they observe; we derive an exact ambiguity frontier when only small search widths are audited. Retaining candidate ranks and truth labels enables a constructive alternative: one audit can estimate reliability across all widths up to N. With known score percentiles, the minimax worst-coordinate mean squared error scales as (1 + log N)/T + N/M, capped at a constant, for expected budgets of T truth labels and M candidate observations. Matching lower bounds allow adaptive label acquisition, establishing that the distinct label and candidate costs are intrinsic to this experiment. An explicit design attains this order; a complementary record-based procedure supplies simultaneous guarantees without a known score distribution. Retrospective mathematical-reasoning and code-generation analyses show why search-dependent validation matters. In held-out CodeRM pools, a shared audit reduces the 95th-percentile maximum error across 100 widths by 58% and 40% relative to uniform labeling. These results turn structural ambiguity into a quantitative prescription for reusable validation.

Limited expert annotation capacity is a pervasive constraint in biodiversity monitoring. Passive acoustic recorders and camera traps generate data faster than experts can analyse them. Machine learning (ML) models can process these data at scale, but their reliability depends on the quality, quantity, and coverage of labelled samples, so expert time remains a constraint. Active learning (AL) eases this bottleneck by selecting, under a fixed annotation budget, the samples expected to improve a model most, and published evidence shows it can reduce the labels needed to reach a target performance. Monitoring programmes, however, face a broader question: how should a limited expert budget be divided so that model training, validation, and the ecological estimates built on model outputs all remain reliable? Because AL selects samples non-randomly, its labels are unsuitable for validation, calibration, or threshold selection, a tension rarely acknowledged. We synthesise AL research across acoustic and image modalities and identify gaps and opportunities. Most studies evaluate query strategies on pre-labelled benchmarks with simulated annotators; deployments in real monitoring workflows are rare and concentrate on birds and cetaceans. Bats, insects, amphibians, and fish are underrepresented, and multimodal applications remain largely unexplored. Evaluation centres on headline reductions in annotation effort, often without random-sampling baselines, per-class results, or calibration analysis, and rarely accounts for the labels required for validation. We provide a tutorial treatment of the AL loop that makes these budget decisions explicit, and a roadmap towards AL methods that support label-efficient training, validation, and trustworthy downstream ecological inference.