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SLACE: A Monotone and Balance-Sensitive Loss Function for Ordinal Regression
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Proposes SLACE, a convex, monotone and balance-sensitive ordinal loss that accumulates soft-label-weighted probabilities over proximity-aware class dominance, and shows gains over CE, SORD and OLL with XGBoost on tabular ordinal and binned regression benchmarks.
Problem
Existing ordinal regression losses assume constant distances between classes and ignore class imbalance, so they fail to satisfy desired properties such as ordinal monotonicity and balance-sensitivity.
Approach
SLACE combines soft labels weighted by proximity-aware distances with an accumulating cross-entropy over a class dominance matrix, so a class never contributes more loss than classes closer to the true class, and class sizes enter through the proximity measure.
Key results
- On ordinal datasets, SLACE-prox reaches 0.687 accuracy and 0.402 MAE versus 0.667 (OLL) and 0.405 (OLL), with statistically significant gains over all baselines.
- On binned regression datasets, SLACE-prox improves AMAE to 0.715 versus 0.767 for OLL and Ma Acc to 0.524 versus 0.497.
- SLACE-prox is equal or better than the baselines on over 70% of datasets for CEM, Ma Acc and AMAE, and over 59% for Acc and MAE.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use SLACEprox instead of the strongest baseline, SORD | XGBoost ordinal regression · Ordinal datasets | Acc: 0.68 -> 0.687†‡‡‡ | Helped |
| Use SLACEprox instead of the strongest baseline, OLL | XGBoost ordinal regression · Ordinal datasets | MAE: 0.405 -> 0.402†‡ | Helped |
| Use SLACEprox instead of the strongest baseline, SORD | XGBoost ordinal regression · Ordinal datasets | CEM: 0.797 -> 0.807†‡‡‡ | Helped |
| Use SLACEprox instead of the strongest baseline, OLL | XGBoost ordinal regression · Ordinal datasets | τ: 0.686 -> 0.687†‡ | Helped |
| Use SLACEprox instead of the strongest baseline, OLL | XGBoost ordinal regression · Ordinal datasets | QWK: 0.7 -> 0.702†‡ | Helped |
| Use SLACEprox instead of the strongest baseline, SORD | XGBoost ordinal regression · Ordinal datasets | Ma Acc: 0.534 -> 0.562†‡‡‡ | Helped |
| Use SLACEprox instead of the strongest baseline, OLL | XGBoost ordinal regression · Ordinal datasets | AMAE: 0.622 -> 0.594†‡‡‡ | Helped |
| Use SLACEprox instead of the strongest baseline, SORD | XGBoost ordinal regression · Regression datasets | Acc: 0.605 -> 0.607†‡‡‡ | Helped |
| Use SLACEprox instead of the strongest baseline, SORD | XGBoost ordinal regression · Regression datasets | MAE: 0.548 -> 0.542†‡‡‡ | Helped |
| Use SLACEprox instead of the strongest baseline, OLL | XGBoost ordinal regression · Regression datasets | CEM: 0.775 -> 0.781†‡‡‡ | Helped |
| Use SLACEprox instead of the strongest baseline, SORD | XGBoost ordinal regression · Regression datasets | τ: 0.73 -> 0.731†‡‡ | Helped |
| Use SLACEprox instead of the strongest baseline, OLL | XGBoost ordinal regression · Regression datasets | QWK: 0.796 -> 0.813†‡‡‡ | Helped |
Surprising findings
- SORD is not monotone for any distance metric and OLL also fails monotonicity on a toy example, despite both being common ordinal losses.
Limitations
- Evaluation limited to tabular data; other modalities left for future work.
- Experiments use only XGBoost as the classifier.
Experimental setup
Datasets: 10 inherently ordinal tabular datasets from Gutiérrez et al. 9 regression datasets binned into 5, 7, and 10 classes
Benchmarks: tabular ordinal regression benchmarks (Gutiérrez et al.) binned regression datasets
Metrics: Accuracy MAE CEM Kendall's tau QWK Macro Accuracy AMAE
Baselines: Cross Entropy SORD OLL
Builds on: SORD ordinal log-loss (OLL) accumulating cross-entropy CEM closeness metric
Closest papers by meaning
- Nonparametric Regression with Comparisons: Escaping the Curse of Dimensionality with Ordinal Information (ICML 2018 · similarity 0.89)
- Adversarial Surrogate Losses for Ordinal Regression (NeurIPS 2017 · similarity 0.88)
- Soft Labels for Ordinal Regression (CVPR 2019 · similarity 0.88)
- GoR: A Unified and Extensible Generative Framework for Ordinal Regression (ICLR 2026 · similarity 0.86)
- Gradient Aligned Regression via Pairwise Losses (ICML 2025 · similarity 0.84)
- Improved Balanced Classification with Theoretically Grounded Loss Functions (NeurIPS 2025 · similarity 0.83)
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