bc-cpit

Conditional generators (diffusion, ensembles, simulators) often return a finite sample vector

\hat{\mathbf{Y}}(x)
=
\left(
\hat{Y}^{(1)}(x),
\ldots,
\hat{Y}^{(m)}(x)
\right)
\sim
\hat{Q}^{(m)}_x

with no tractable likelihood. Those sample clouds can be biased and poorly calibrated, and standard conformal tools mainly return a fixed-level set—not a predictive CDF you can query for arbitrary quantiles, exceedance probabilities, or tail losses.

bc-cpit is a split-sample post-processing pipeline:

1. Bias correction — fit an affine location–scale map on a held-out bias split (global, or x-dependent via GAM).
2. Conformal PIT calibration — calibrate randomized PITs on a calibration split; represent the corrected law as a weighted empirical distribution on the generator order statistics.

From the calibrated law you get threshold-coherent probabilities, quantiles, central / highest-density intervals, and calibrated resamples. An optional PIT-centrality wrapper adds nested intervals with finite-sample marginal coverage under exchangeability.

This package does not retrain the generator; it recalibrates whatever samples you already have.

Install

pip install bc-cpit

Development:

git clone https://github.com/egpivo/bc-cpit.git
cd bc-cpit
pip install -e ".[dev]"

Quick start

from cpit.bc import fit_global_affine, apply_affine
from cpit import fit_conformal_calibrator, get_weighted_samples_at_x
from cpit import quantile_from_weighted_samples, central_interval_from_weighted_samples

# 1. Bias correction
params = fit_global_affine(y_bias, y_bias_samples)

# 2. Conformal calibration
cal_samples_adj = [apply_affine(s, params) for s in cal_samples]
_, c_hat = fit_conformal_calibrator(cal_samples_adj, y_cal)

# 3. Inference
y_pts, weights = get_weighted_samples_at_x(y_test_samples, params, c_hat)
q80 = quantile_from_weighted_samples(y_pts, weights, 0.80)
lo, hi = central_interval_from_weighted_samples(y_pts, weights, alpha=0.10)

x-dependent (GAM) correction:

from cpit.bc import fit_x_dependent_affine_gam

params_gam = fit_x_dependent_affine_gam(x_bias, y_bias, y_bias_samples)
y_pts, weights = get_weighted_samples_at_x(y_test_samples, params_gam, c_hat, x=x_test)

High-level pipeline:

from cpit.pipeline import run_pipeline, predict_interval

state = run_pipeline(X, y, generator_fn)
lo, hi = predict_interval(state, X_test, y_samples_test, alpha=0.10)

Reproduce paper results

make test          # unit tests
make run-sim       # Designs 1/2/3 simulations (§5)
make pit-figures   # PIT histogram figures
make run-wb2       # WB2 application: Taiwan + Europe (§6)

Citation

If you use this package, please cite:

Wang, W.-T., Tzeng, S., Fan, Y.-T., & Huang, H.-C. (2026). Calibrated Predictive Distributions from Sample-Based Generators. arXiv:2609.19035.

@article{wang2026calibrated,
  title   = {Calibrated Predictive Distributions from Sample-Based Generators},
  author  = {Wang, Wen-Ting and Tzeng, ShengLi and Fan, Yu-Ting and Huang, Hsin-Cheng},
  journal = {arXiv preprint arXiv:2609.19035},
  year    = {2026},
  url     = {https://arxiv.org/abs/2609.19035}
}

License

MIT — see LICENSE.