Imbalanced Classification under Capacity Constraints
Authors: Daniel Fraiman, Ricardo Fraiman
Organizations: Departamento de Matem´atica y Ciencias, Universidad de San Andr´es, Buenos Aires, Argentina · CONICET, Argentina. · PEDECIBA, Matem´atica, Uruguay.
Abstract
Detecting observations from a minority class under severe class imbalance is a central challenge in applications such as fraud detection, medical screening, and industrial quality control. In these settings, each positive prediction triggers a costly follow-up action, an MRI scan, a transaction audit, whose execution is subject to real operational constraints. This paper proposes a formal classification framework under capacity constraints: given a user-defined bound limit b on the proportion of observations that can be labeled as belonging to the minority class, the goal is to find the classifier that maximizes sensitivity on that class. We characterize the optimal classifier under this constraint and establish its equivalence with the classical Bayes classifier under a reweighting of the prior probabilities. We also introduce a capacity-adjusted performance metric M that accounts for the effective detection rate when the capacity constraint is binding. The framework is implemented on top of standard learning methods, k-NN, SVM, random forests, and neural networks, and statistical consistency is established for each. We further show that these methods reduce to post-hoc thresholding when no hyperparameters are oriented toward the capacity-constrained objective, and introduce a capacity-aware support vector machine that exploits the constraint during training and achieves the strongest empirical performance. Experiments on the Taiwanese credit card default dataset confirm that capacity-constrained classifiers substantially outperform both classical approaches and SMOTE under high imbalance regimes. The framework extends naturally to multiclass settings and online environments.
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.
Class imbalance poses a fundamental challenge in risk-sensitive applications such as fraud detection and medical diagnosis, where minority-class samples are scarce yet critical for accurate classification. Existing oversampling methods generate synthetic samples to rebalance class distributions; however, they often produce large numbers of low-quality candidates that distort decision boundaries or introduce artifacts, leading to overfitting and degraded generalization. In this work, we introduce RUBRIC, a generator-agnostic filtering framework that formulates synthetic sample selection as a quality-over-quantity optimization problem. RUBRIC ranks candidates using a realism-utility trade-off: realism is quantified by a learned discriminator that distinguishes real samples from synthetic samples, while utility captures proximity to the decision boundary through a concave margin-based scoring function. We show that, under mild regularity conditions, the proposed filtering strategy monotonically tightens the generalization bound for margin-based classifiers by jointly reducing distribution shift and suppressing near-negative tail contributions. Through extensive experiments on credit-card fraud detection and other imbalanced benchmarks, we demonstrate that RUBRIC improves F1-macro and recall while maintaining comparable ROC-AUC across several generators. We also provide explicit lambda-sensitivity analysis to show how users can recover AUPRC when ranking quality is prioritized.
Deep learning models using traditional softmax classifiers have achieved remarkable success in various classification tasks. However, their performance degrades significantly on imbalanced datasets. Although Balanced Softmax is widely adopted as a state-of-the-art rebalancing method, it possesses inherent limitations, such as yielding disproportionately lower testing accuracy for tail classes. To mitigate these shortcomings, we propose the Class-Balanced Softmax (CBS). Rooted in a theoretical Bayesian framework and a heuristic power-law assumption, the CBS is a simple logit adjustment that is computationally inexpensive and easily integrated into existing pipelines. Furthermore, we characterise a fundamental phenomenon in models trained on imbalanced data, termed the preference issue, wherein models exhibit higher training error and a larger generalisation gap for classes with limited data. To quantify this issue, we introduce a novel metric and demonstrate that CBS effectively mitigates the preference issue. Extensive experiments on large-scale benchmarks show that CBS is highly scalable and outperforms existing methods, including Balanced Softmax.