Machine learning models should be robust, in the sense of remaining predictively consistent under permissible variations. A model's predictions should ideally remain unchanged when it is replaced by a functionally equivalent one, or when its inputs are subject to minor, admissible perturbations. If such changes alter a prediction significantly, then the prediction is "ambiguous" with respect to the model. Models should abstain from making such ambiguous predictions and/or should flag them for human inspection, especially in high-stakes decision-making scenarios. However, in practice, such ambiguity is not easy to identify once a model is deployed. Here, the Robust Ambiguity Detection (RAD) framework is advanced for quantifying predictive ambiguity using two complementary metrics: Model-Space Consistency and Feature-Space Consistency. These two scores, the RAD Score-Pair, visualised through the RAD Plot, provide an interpretable characterisation of the sources of ambiguity and the actions a user may consider in response. RAD is evaluated on synthetic datasets with systematically controlled overlap, as well as several real-world datasets where the level of ambiguity cannot be directly inspected. Finally, we demonstrate a downstream application of RAD where samples are ranked by their RAD Pareto-Rank and the most ambiguous are abstained from prediction, achieving performance comparable to existing rejection-based approaches.
Javier Fumanal-Idocin, Javier Andreu-Perezcs.LG cs.AI
Interpretable classification often requires more than accurate predictions for real-life deployment: models should be transparent about the evidence behind their decisions and abstain when they cannot decide reliably. We introduce Fast Evidential Rule Learning (FERL), a method that learns interpretable, accurate fuzzy rule models whose outputs are evidential. Unlike post-hoc calibration, FERL's belief, plausibility, and abstention capabilities arise directly from the fuzzy memberships in a single deterministic pass, with no auxiliary head, held-out set, or repeated inference. Our theoretical analysis further shows that FERL is Lipschitz stable, which means that its evidential outputs vary smoothly with the input. Against state-of-the-art rule learners, FERL is statistically significantly more accurate across a 30 tabular-dataset benchmark ($+2.6\%$ average accuracy over the second best). Its native set predictions attain the best utility-discounted accuracy among credal classifiers ($u_{65}/u_{80}=0.80/0.83$ vs.\ $0.79/0.80$ for the naive credal classifier), at higher set coverage ($0.92$ vs.\ $\le0.82$). FERL also matches dedicated out-of-distribution detectors on tabular near-OOD detection ($77.7$ vs.\ $77.4$ AUROC for the strongest baseline). Under detector-class-disjoint concept-bottleneck evaluation, its it is within $2.3$ AUROC points of the strongest dedicated detector on both CUB and AwA2, while attaining the best AwA2 AUPR-Out ($68.3$) and novel-class rejection ($57.2$), while being able to name which attributes are anomalous.
High-stakes decision systems in credit scoring, fraud detection, healthcare, and industrial safety require reliable uncertainty quantification under severe class imbalance and asymmetric error costs. Standard marginal conformal prediction (CP) provides valid overall coverage guarantees; however, we show that it severely under-covers rare, costly minority classes, with minority-class coverage dropping to as low as 0.5% on certain datasets. To characterize and address this limitation, we conduct a comprehensive benchmark comparing marginal CP, class-conditional (Mondrian) CP, and cost-controlled abstention mechanisms across 15 real-world imbalanced tabular datasets, 7 classification models, 3 probability calibration techniques, and 10 random seeds, resulting in 3,150 experimental runs. Our results show that Mondrian CP restores valid minority-class coverage, achieving an average minority-coverage improvement of 61.7 percentage points over marginal CP (p < 1e-80). Furthermore, combining Mondrian CP with cost-controlled abstention significantly reduces expected decision cost compared with standard decision boundaries, confidence-based rejectors, and risk-controlled rejectors under realistic human review budgets. We further quantify dataset-specific break-even thresholds at which deferring ambiguous instances to human experts becomes cost-effective. These findings provide practical guidance for deploying distribution-free, cost-aware uncertainty quantification in high-stakes decision support systems.
Model merging combines independently trained or fine-tuned models, but pairwise alignability does not imply globally consistent alignment. We formulate merging as a finite descent problem in which checkpoints are local objects, alignment maps are transitions, and cycle products are residuals. TwistedMerge is a conservative certification pipeline that separates fixed-chart averaging, synchronization-removable gauge inconsistency, a certified central obstruction on a specified comparison complex, and nonabelian holonomy. A residual is promoted to a cohomology class only after inverse-consistency, coefficient-identification, centrality, and closure tests; otherwise the method abstains and returns an ordinary or synchronized fallback. We prove a constant-edge no-go result, frozen-complex three-way and predeclared-family error-control theorems, and a refinement test for comparison-complex sensitivity. A planted neural alignment defect is removed by cycle-consistent synchronization, showing that a nonzero cycle score alone is not a higher obstruction. Controlled central systems recover the predicted non-coboundary and projective-rank behavior, while noisy estimates move from certification to abstention without false lifts on the tested controls. A trained low-rank-adapter audit shows that naive factor averaging depends on the chosen GLr representative, whereas global factor synchronization and dense-delta SVD are stable. On natural checkpoint collections, cycle residuals do not predict merge degradation and no natural central or period-index class is certified. The results position descent theory as a falsifiable certification and abstention framework.
Deep learning methods have achieved state-of-the-art in time series forecasting, yet their accuracy varies considerably across samples, as some instances remain inherently difficult to predict. Reject option mechanisms, which allow models to abstain from high-risk predictions, are well established in classification and regression but underexplored in forecasting. Existing abstention strategies typically rely on proxies, such as the width of the prediction interval or learned confidence scores derived from forecasts. However, these approaches are inherently tied to the training domain, limiting their ability to generalize. We propose a selective forecasting framework that addresses this limitation by modeling the empirical percentile of forecasting errors, that is, a scale-invariant statistic, based on structural characteristics extracted from recent lags via metalearning. By decoupling the rejection decision from the forecast itself and grounding it in domain-agnostic features, the framework enables effective abstention transfer across heterogeneous time series. Experiments in both in-domain and transfer learning settings show that rejecting samples predicted as challenging consistently improves forecasting accuracy across coverage levels.
ML classifiers deployed in high-stakes domains produce predictions whose quality varies systematically across subgroups. For granular subgroups defined by intersections of multiple features, predictions are often inconsistent with the observed data: the model's outputs contradict the evidence available for that subgroup. This problem is exacerbated by regularisation, which improves aggregate performance by collapsing small subgroups into larger groups, disproportionately affecting demographic minorities. We define two requirements for consistent prediction: determinism (identical individuals receive identical predictions) and statistical consistency (we cannot reject, at significance level alpha, the hypothesis that the predictions for a subgroup were drawn from the Bayesian optimal target distribution inferred for that subgroup). From these requirements we derive the Fair Bayesian classifier, which enforces both across every group and subgroup simultaneously and abstains whenever no consistent deterministic prediction is possible. On three benchmark datasets (Adult, COMPAS, and Bank Marketing), standard classifiers produce statistically inconsistent predictions for a substantial proportion of subgroups. Our classifier achieves zero consistency error by construction while exceeding baseline accuracy and multicalibration on every dataset tested. Statistical consistency provides a principled foundation for prediction quality with direct implications for algorithmic fairness. Minority demographics are disproportionately concentrated in small subgroups, precisely where frequentist inference is least reliable; addressing this inference problem is therefore a necessary step toward fair ML. By enforcing Bayesian consistency at the finest resolution the data supports, the our classifier demonstrates that exhaustive subgroup fairness with principled abstention is achievable in practice.
We consider selective classification with abstention in the fixed-pool (or transductive) setting, where the unlabeled pool is given beforehand and only a subset of points can be queried for labels. Our main insight is to view selective prediction through agreement: given queried labels and Lipschitz margin constraints in an embedding space, the version space of Lipschitz-consistent classification heads is well defined. We obtain upper and lower Lipschitz margin bounds that define, for each pool point, a set of certified valid labels containing the prediction of every head in the version space. The model therefore predicts only when the label is forced (i.e., all consistent heads agree), and abstains otherwise. We also propose a monotone submodular geometric proxy for budgeted querying, and show that a greedy algorithm retains the standard approximation factor.