Output-Space Regularization for Stable and Interpretable Regression

Carlos R. Ortiz-Gomez, Independent Researcher, December 2025
DOI: 10.5281/zenodo.17785949

This repository contains the reference implementation and reproducibility notebooks for the QPM paper.

QPM is a post-hoc output quantizer: you first train any continuous scorer F(x), then fit QPMQuantizer on top of those scores to produce an ordered, discrete PD ladder. The method is model-agnostic and works with XGBoost, LightGBM, scikit-learn models, neural networks, or any source of 1-D scores.

from qpm import QPMQuantizer

# 1) Train any backbone model and obtain latent scores
F_train = model.predict(X_train)
F_test = model.predict(X_test)

# 2) Fit QPM post-hoc
qpm = QPMQuantizer(
    focus_pd=(0.05, 0.20),
    n_low_max=6, n_mid_max=6, n_high_max=6,
    min_band_size=300, pd_cap=0.80,
)
qpm.fit(F_train, y_train)

# 3) Quantized predictions (discrete PD ladder)
y_hat = qpm.predict(F_test)

git clone https://github.com/orgoca/qpm-paper.git
cd qpm-paper
pip install -e .

Python 3.9+ required.

Run notebooks in order:

Each notebook writes canonical outputs to:

• artifacts/exp01/report.json
• artifacts/exp02/report.json
• artifacts/exp03/report.json

An executed reference notebook for Exp 3 is also included at notebooks/03_framingham_executed.ipynb.

See data/README.md for details.

• Exp 1 (UCI): downloaded automatically via ucimlrepo
• Exp 2 (Home Credit): Kaggle API token required
• Exp 3 (Framingham): Kaggle API token required

qpm/
|- quantizer.py     # QPMQuantizer: supervised output quantization
|- calibration.py   # AnchoredCalibration + residual_stack
|- metrics.py       # AUC, KS, MSE, BCa bootstrap, DeLong, churn
`- scorecard.py     # WoE logistic scorecard baseline

The values below come from artifacts/*/report.json in this repository.

• QPM bins: 14
• Churn reduction (scenario B vs A): 4.40x
• Anchored calibration native churn (scenario C): 0.00

• QPM bins: 22
• Native churn reduction vs GBM retrain: 4.84x

• GBM AUC: 0.6897 (95% BCa CI: 0.6401-0.7348)
• QPM quantized AUC: 0.6866 (95% BCa CI: 0.6369-0.7312)
• DeLong test p-value: 0.4675 (no significant AUC difference)
• QPM bins: 9
• PD range across bins: 3.7% to 53.0%

These current runs preserve the core paper conclusions: QPM maintains most discriminative power while producing a stable, interpretable discrete risk ladder and materially improving update stability.

@article{ortizgomez2025qpm,
  title   = {Quantized Prediction Models: Output-Space Regularization
             for Stable and Interpretable Regression},
  author  = {Ortiz-G{\'o}mez, Carlos R.},
  year    = {2025},
  month   = {December},
  doi     = {10.5281/zenodo.17785949},
  note    = {Independent Researcher}
}

MIT