Robust performance metrics for imbalanced classification problems

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.

Class-imbalance handling is routinely evaluated on a single benchmark dataset, and the resulting conclusions are reported as if they were properties of the method. We show this practice is unsafe. On the public Kaggle credit-card fraud dataset, under a leakage-free nested cross-validation protocol in which the decision threshold is selected on a held-out inner validation fold, a plain Random Forest at the default 0.5 threshold attains F1 = 0.861 +/- 0.021, and threshold tuning yields it no benefit (delta-F1 = -0.002). Read alone, this supports an appealing conclusion: for a well-calibrated ensemble, imbalance handling is unnecessary. We then apply the identical protocol to 45 binary tasks spanning imbalance ratios from 1:1.5 to 1:178 (2,025 model fits, four model families). The conclusion reverses. Random Forest benefits most from threshold tuning across the suite (delta-F1 = +0.101 +/- 0.134), not least, while three other families replicate their fraud-dataset behaviour almost exactly. SMOTE likewise harms the fraud dataset but helps across the suite (mean delta-F1 = +0.076; 138 wins, 39 losses; Wilcoxon p = 2.7e-17). Two further results. Threshold-tuning benefit is non-monotonic in the imbalance ratio: near zero below 1:5, peaking at +0.120 in the 1:15-1:40 band, declining to +0.045 beyond 1:100 - explaining why the fraud dataset, at 1:577, is an unrepresentative place to study the question. And we reject an intuitive heuristic: validation-set calibration error does not predict tuning benefit (expected calibration error r = -0.087; Brier r = +0.137), so calibration diagnostics cannot tell a practitioner whether tuning is worthwhile. We release the protocol, the 45-task harness, and all per-run metrics.

Class-level evaluation can conceal substantial performance disparities across subconcepts within the same class, causing models that perform well on average to fail on specific subpopulations. Prior work has shown that common evaluation measures for imbalanced classification are biased toward larger minority subconcepts and that utility-based reweighting using true subconcept labels can mitigate this bias; however, such labels are rarely available at test time. We introduce a practical utility-weighted evaluation that replaces unavailable subconcept labels with predicted posterior probabilities from a multiclass subconcept model. Evaluation weights are defined as the expected utility under this posterior, yielding a soft, uncertainty-aware metric we call predicted-weighted balanced accuracy (pBA). Experiments on tabular benchmarks as well as medical-imaging and text datasets show that unweighted scores can be misleading under within-class heterogeneity, while pBA provides more stable and interpretable assessments when subconcept distributions are uneven but not pathological. Our code is available at: https://anonymous.4open.science/r/correcting-bias-imbalance-9C6C/.