Quantized Prediction Models (QPMs)

Output-Space Regularization for Stable and Interpretable Regression

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

---

Overview

This repository contains the complete, self-contained code to reproduce every experiment and claim in the paper. The implementation is written from scratch to be clean and readable — no proprietary dependencies.

QPMs constrain model output to a finite, ordered set of prediction levels (a "ladder") by learning a supervised quantizer on top of any continuous latent scorer. The quantizer is fully model-agnostic: it works with XGBoost, LightGBM, scikit-learn GBMs, neural networks, or any scorer that produces a 1-D array of continuous predictions.

from qpm import QPMQuantizer

# Train any backbone first
F_train = xgb_model.predict(X_train)   # or lgb, sklearn, torch, ...
F_test  = xgb_model.predict(X_test)

# Fit the output-space quantizer
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)

# Discrete PD predictions on a monotone ladder
y_hat = qpm.predict(F_test)

---

Installation

git clone <this-repo>
cd QPM_PAPER
pip install -e .

Python ≥ 3.9 required.

---

Notebooks

Run the notebooks in order. Each is fully self-contained.

Notebook	Experiment	What it reproduces
notebooks/01_uci_default.ipynb	Exp 1 — UCI Credit Card	Table 1, Table 2, Figure 1, churn analysis
notebooks/02_home_credit.ipynb	Exp 2 — Home Credit	Table 3, churn (3.4× factor)
notebooks/03_framingham.ipynb	Exp 3 — Framingham CHD	AUC CIs, DeLong test (p=0.46), 13-strata ladder

---

Data Setup

See data/README.md for download instructions.

• Exp 1 (UCI): downloaded automatically via ucimlrepo — no action needed.
• Exp 2 (Home Credit): requires Kaggle API token.
• Exp 3 (Framingham): requires Kaggle API token.

---

Package Structure

qpm/
├── quantizer.py     # QPMQuantizer — optimizer-driven supervised binning
├── calibration.py   # AnchoredCalibration + residual stacking
├── metrics.py       # AUC, KS, MSE, bootstrap BCa CIs, DeLong test, churn
└── scorecard.py     # WoE logistic scorecard baseline

---

Key Claims Reproduced

Experiment 1 — UCI Default (30k accounts, 22.1% default rate)

Model	MSE	AUC	KS
Scorecard (LR, 10 bands)	0.1389	0.7599	0.4018
GBM (continuous)	0.1359	0.7727	0.4203
QPM (latent F(x))	0.1359	0.7773	0.4289
QPM (quantized PD)	0.1359	0.7750	0.4225

• QPM produces a 14-bin bank-style score ladder (Table 2) with monotone PD centers.
• Fixed-edge fine-tuning reduces native band churn by >4× vs independent retraining.
• Anchored Calibration achieves 0.00% rank-order churn (Proposition 1).

Experiment 2 — Home Credit (~300k accounts, 8.0% default rate)

Model	MSE	AUC	KS
GBM (continuous)	0.0683	0.7517	0.3784
QPM (quantized PD)	0.0683	0.7487	0.3740

• QPM fine-tuning reduces churn by 3.4× vs GBM retrain (0.001067 vs 0.003635).

Experiment 3 — Framingham CHD (15.2% incidence)

• GBM AUC: 0.683 [0.633–0.729] vs QPM latent AUC: 0.666 [0.616–0.712]
• DeLong test: p = 0.46 (no statistically significant difference)
• 13-strata risk ladder from ~2% to ~55% event rate

---

Citation

@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}
}

---

License

MIT