SoftMCC: An MCC-Brier Calibration Bridge for Threshold-Free Model Selection under Class Imbalance

The Brier score conflates two distinct properties of probabilistic predictions: reliability (calibration error) and resolution (discriminatory power). We introduce the Manokhin Probability Matrix, a BCG-style two-dimensional diagnostic framework that separates them. Classifiers are placed on a 2x2 grid by Spiegelhalter Z-statistic and AUC-ROC expected rank, then assigned to one of four archetypes: Eagle (good on both axes), Bull (strong discrimination, poor calibration), Sloth (well-calibrated, weak discriminator), and Mole (poor on both). Each archetype carries a distinct prescription. We populate the matrix from a large-scale empirical study spanning 21 classifiers, 5 post-hoc calibrators, and 30 real-world binary classification tasks from the TabArena-v0.1 suite. The assignment is unambiguous. CatBoost, TabICL, EBM, TabPFN, GBC, and Random Forest are Eagles. XGBoost, LightGBM, and HGB are Bulls; Venn-Abers calibration cuts log-loss by 6.5 to 12.6% on Bulls but degrades Eagles by 2.1%. SVM, LR, LDA, and the empirical base-rate predictor are Sloths. MLP, KNN, Naive Bayes, and ExtraTrees are Moles. A theoretical asymmetry follows: no order-preserving post-hoc calibrator can add discriminatory power (Proposition 1), so calibration is the fixable part and discrimination is the hard part. The practical rule is direct: do not optimise aggregate Brier score without first decomposing it; optimise discrimination first, then fix calibration post-hoc. Code and raw experimental data are available at https://github.com/valeman/classifier_calibration.

Recent work has argued normatively, on synthetic data, that evaluating survival models by discrimination alone (concordance index) yields systematically misleading model comparisons, because the metric ignores calibration and time-dependent accuracy. Whether this matters for real, published, non-clinical models has not been tested. We reproduce three published survival-ML models across three structurally distinct domains -- hard-drive failure prediction, peer-to-peer credit default, and user disengagement on digital platforms -- validate our instrument against the anchor paper's own synthetic experiment, and test five pre-registered hypotheses under a Holm-corrected family-wise error rate. Three of five reject (though one pre-registered threshold clears by a narrow margin). A model reproducing the published literature's discrimination almost exactly (C = 0.9595 vs. 0.958 reported) fails a formal calibration test at p < 0.001; a broad feature-ablation search finds no single attribute responsible for its discrimination, so the calibration failure is not a trivial shortcut artifact. A lender's estimated default risk is biased upward by roughly two percentage points, growing to nearly four in the riskiest segment, when loan prepayment is treated as non-informative censoring rather than a competing risk. A platform's churn model shows probability estimates that degrade with the horizon even as global discrimination stays within the pre-registered C-index band. A direct test of whether metric choice inverts model preference does not reject, though with limited power given two to three models per domain; the failure mode we document is better characterized as misplaced confidence in a chosen model than as choosing the wrong one. We release a pre-registered evaluation harness with full code and an annotated notebook, so these results can be verified independently and the audit extended.

Cervical cytology classification models are typically evaluated on curated, class-balanced benchmarks, but real-world liquid-based cytology (LBC) collections are often small and class-imbalanced. This paper presents a class-imbalance-aware and calibration-aware ensemble classification study on the Mendeley LBC dataset, using its native four-class Bethesda taxonomy (NILM, LSIL, HSIL, SCC) rather than a collapsed binary formulation. Three lightweight architectures (Swin-Tiny, TinyViT-5M, DenseNet121) are trained directly on Mendeley LBC using weighted random sampling to counteract class imbalance, and compared against two soft-voting ensembles (Hybrid-2, Hybrid-3). Post-hoc temperature scaling is fit on a held-out calibration subset carved out of the training portion of each cross-validation fold, distinct from both the training data used to fit model weights and the evaluation fold used for final metrics, avoiding the optimistic calibration estimates that result when the same data is used for both purposes. Calibration substantially reduces expected calibration error, Brier score, and negative log-likelihood for every model and ensemble configuration tested, while discrimination metrics (accuracy, macro-F1, macro-AUROC) remain essentially unchanged. Ensemble size shows no consistent additional reliability benefit over the best individual model once all configurations are properly calibrated. Confusion matrices show that all classification errors, across every configuration, are confined to the boundary between high-grade lesions (HSIL) and carcinoma (SCC); no errors involve the negative (NILM) or low-grade (LSIL) categories. These results suggest that, for this dataset, calibration is the dominant lever for reliability, not ensemble size, though this conclusion should be read in light of the dataset's modest size.