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quantile-guard

The quantile modeling toolkit with non-crossing guarantees.

Fit multiple quantiles jointly with monotonicity constraints that guarantee predictions never cross. Built-in inference, conformal calibration, evaluation metrics, and crossing diagnostics. Scikit-learn compatible.

Why Not Fit Quantiles Independently?

When you fit quantiles independently (as sklearn and statsmodels do), nothing prevents the 90th percentile prediction from falling below the 10th.

Crossing is common on real data

At n=500 with 13 quantile levels, 30% of test samples show crossed predictions when using sklearn or statsmodels. quantile-guard produces zero crossings by construction — and the joint formulation achieves comparable or better pinball loss in most benchmark settings. See Benchmarks for full results.

Workflows

This is a toolkit, not a single estimator. It covers the pipeline from raw quantile regression through calibrated prediction intervals:

Workflow Module What it does
Joint Quantile Regression QuantileRegression Fit multiple quantiles with non-crossing guarantees, inference, and regularization
Conformalized QR conformal Calibrate intervals for finite-sample coverage guarantees
Censored QR CensoredQuantileRegression Right- or left-censored (survival) quantile models
Evaluation & Metrics metrics Pinball loss, coverage, interval score, crossing rate
Calibration Diagnostics calibration Coverage by group/bin, nominal vs empirical, sharpness
Crossing Detection & Repair postprocess Diagnose and fix crossings from any quantile model
Feature comparison vs sklearn & statsmodels
Feature quantile-guard sklearn statsmodels
Multiple quantiles (joint fit) Yes No No
Non-crossing guarantee Yes No No
Multi-output regression Yes No No
Analytical / kernel / cluster / bootstrap SEs Yes No Partial
L1 / Elastic Net / SCAD / MCP Yes L1 only No
Conformal calibration (CQR) Yes No No
Calibration diagnostics Yes No No
Evaluation metrics suite Yes Partial No
Crossing detection + fix Yes No No
Censored QR Yes No No
Prediction intervals Yes No No
Pseudo R-squared Yes No Yes
Formula interface Yes No Yes
Sklearn pipeline compatible Yes Yes No

Who Is This For

Data scientists building prediction intervals for production systems where crossed quantiles break downstream logic.

Researchers & econometricians who need valid statistical inference — SEs, p-values, confidence intervals — on quantile regression coefficients.

ML engineers who want a drop-in sklearn-compatible estimator with monotone quantile guarantees.

Risk analysts & actuaries modeling conditional tail distributions with censored or survival data.

Anyone evaluating quantile models — the metrics and diagnostics modules work with predictions from XGBoost, LightGBM, or any other source.

Installation

pip install quantile-guard

With optional extras:

pip install quantile-guard[all]

pip install quantile-guard[plot]

pip install quantile-guard[formula]

Migrating from quantile-regression-pdlp?

For the core estimator, the import path changes but the call pattern stays the same: 

# before
from quantile_regression_pdlp import QuantileRegression
# after
from quantile_guard import QuantileRegression

Quick Example

import numpy as np
from quantile_guard import QuantileRegression

X = np.random.default_rng(0).normal(size=(200, 3))
y = X @ [2.0, -1.5, 0.8] + np.random.default_rng(1).normal(scale=0.5, size=200)

# Fit 3 quantiles jointly — guaranteed non-crossing
model = QuantileRegression(tau=[0.1, 0.5, 0.9], se_method='analytical')
model.fit(X, y)

print(model.summary()[0.5]['y'])
print(model.pseudo_r_squared_)

Benchmark Evidence

Independent fitters produce 4-30% crossing rates on challenging data; quantile-guard produces zero — while matching pinball loss and improving it in the hardest small-sample settings:

n features quantiles Crossing (quantile-guard) Crossing (sklearn) Pinball (quantile-guard) Pinball (sklearn)
500 10 13 0% 30.0% 0.5095 0.5240
1,000 10 13 0% 16.5% 0.5048 0.5071
2,000 20 13 0% 11.0% 0.5599 0.5611

Speed tradeoff: the joint LP is slower than fitting quantiles independently. The value is the guarantee and the richer downstream workflows.

Full benchmark results | Reproduce locally

Next Steps

  • Usage Guide — fit, predict, inference, regularization, formulas
  • Benchmarks — crossing rates, pinball loss, timing, coverage
  • Conformal — calibrated prediction intervals
  • Calibration — coverage diagnostics by group, bin, and feature
  • Crossing — detection, diagnostics, rearrangement
  • Evaluation — pinball loss, coverage, interval score
  • API Reference — full parameter and method documentation
  • Theory — LP formulation, non-crossing constraints, SE estimation