A Rank-Based Bernstein Additive Logistic Model with Spearman-Informed Regularisation for Interpretable Binary Classification
- 1Department of Biostatistics and Medical Informatics, Hamidiye Faculty of Medicine, University of Health Sciences Turkey, 34668 Istanbul, Türkiye
Abstract
Binary classification is judged on two axes: discrimination, the ability to rank cases, and calibration, the reliability of the predicted probabilities. Flexible ensembles often rank well while producing overconfident probabilities, whereas transparent models remain readable but may be too rigid. We propose B-RCM++, a single penalised logistic model in which each continuous predictor enters through a smooth Bernstein expansion of its mid-rank empirical distribution and each categorical predictor through a centred contrast; the ridge penalty is weighted by each predictor’s Spearman association with the outcome; and pure pairwise interaction surfaces are admitted only on out-of-fold evidence. Centring and orthogonalisation make the fitted object exactly decomposable: the displayed components reproduce the model’s own probabilities. Across 216 synthetic scenarios, crossing eight data-generating processes with three predictor counts (4, 10 and 20), three sample sizes and three prevalences, with 1000 planned replications per scenario, B-RCM++ attained the best mean discrimination, precision–recall, Brier score and logarithmic loss among the eighteen methods compared in simulation, the best mean rank on discrimination, and a median calibration slope of 1.07 against 0.34 to 0.67 for the uncalibrated tree ensembles. Its advantage was retained at every predictor count. The method is proposed for problems in which the predictor count is moderate relative to the sample; on five public benchmark datasets it was competitive on the lower-dimensional problems but did not lead overall, although it was ahead of the explainable boosting machine, its closest published relative, on both discrimination and calibration on those datasets, which are the only setting in which that comparison was run: on the four-dataset common-support comparison, among the methods completing all four, the mean AUC was 93.5% for B-RCM++ against 94.1% for the strongest competitor.
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BibTeX
@article{baydili2026rankbased,
title = {{A Rank-Based Bernstein Additive Logistic Model with Spearman-Informed Regularisation for Interpretable Binary Classification}},
author = {Kürşad Nuri Baydili},
journal = {Mathematics},
year = {2026},
month = oct,
doi = {10.3390/math14193588},
url = {https://www.mdpi.com/2227-7390/14/19/3588},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - A Rank-Based Bernstein Additive Logistic Model with Spearman-Informed Regularisation for Interpretable Binary Classification
AU - Kürşad Nuri Baydili
PY - 2026
DA - 2026/10/02
JO - Mathematics
DO - 10.3390/math14193588
UR - https://www.mdpi.com/2227-7390/14/19/3588
AB - Binary classification is judged on two axes: discrimination, the ability to rank cases, and calibration, the reliability of the predicted probabilities. Flexible ensembles often rank well while producing overconfident probabilities, whereas transparent models remain readable but may be too rigid. We propose B-RCM++, a single penalised logistic model in which each continuous predictor enters through a smooth Bernstein expansion of its mid-rank empirical distribution and each categorical predictor through a centred contrast; the ridge penalty is weighted by each predictor’s Spearman association with the outcome; and pure pairwise interaction surfaces are admitted only on out-of-fold evidence. Centring and orthogonalisation make the fitted object exactly decomposable: the displayed components reproduce the model’s own probabilities. Across 216 synthetic scenarios, crossing eight data-generating processes with three predictor counts (4, 10 and 20), three sample sizes and three prevalences, with 1000 planned replications per scenario, B-RCM++ attained the best mean discrimination, precision–recall, Brier score and logarithmic loss among the eighteen methods compared in simulation, the best mean rank on discrimination, and a median calibration slope of 1.07 against 0.34 to 0.67 for the uncalibrated tree ensembles. Its advantage was retained at every predictor count. The method is proposed for problems in which the predictor count is moderate relative to the sample; on five public benchmark datasets it was competitive on the lower-dimensional problems but did not lead overall, although it was ahead of the explainable boosting machine, its closest published relative, on both discrimination and calibration on those datasets, which are the only setting in which that comparison was run: on the four-dataset common-support comparison, among the methods completing all four, the mean AUC was 93.5% for B-RCM++ against 94.1% for the strongest competitor.
SN - 2227-7390
ER -