Implementation:Scikit learn Scikit learn QuantileRegressor

Knowledge Sources	Scikit_learn Scikit-learn Docs
Domains	Machine Learning, Quantile Regression
Last Updated	2026-02-08 15:00 GMT

Overview

Concrete tool for linear regression that predicts conditional quantiles using the pinball loss, robust to outliers, provided by scikit-learn.

Description

QuantileRegressor optimizes the pinball loss for a desired quantile, producing a linear model that predicts conditional quantiles rather than the conditional mean. It uses L1 regularization (similar to Lasso) and solves the optimization via linear programming using scipy's linprog. By default it predicts the median (quantile=0.5), but can predict any quantile between 0 and 1. The model is inherently robust to outliers since the pinball loss grows linearly rather than quadratically for large residuals.

Usage

Use QuantileRegressor when you need to predict specific quantiles of the response distribution (e.g., the 90th percentile for risk assessment), when you need robust regression that is not sensitive to outliers, or when you want to understand the full conditional distribution of the target rather than just its mean. It is commonly used in financial risk modeling, weather forecasting, and any domain requiring prediction intervals.

Code Reference

Source Location

• Repository: scikit-learn
• File: sklearn/linear_model/_quantile.py

Signature

class QuantileRegressor(LinearModel, RegressorMixin, BaseEstimator):
    def __init__(
        self,
        *,
        quantile=0.5,
        alpha=1.0,
        fit_intercept=True,
        solver="highs",
        solver_options=None,
    ):

Import

from sklearn.linear_model import QuantileRegressor

I/O Contract

Inputs

Name	Type	Required	Description
quantile	float	No	Target quantile to predict, strictly between 0 and 1 (default=0.5)
alpha	float	No	L1 regularization constant (default=1.0)
fit_intercept	bool	No	Whether to fit the intercept (default=True)
solver	str	No	Linear programming solver: 'highs-ds', 'highs-ipm', 'highs', 'interior-point', 'revised simplex' (default='highs')
solver_options	dict	No	Additional parameters passed to scipy.optimize.linprog (default=None)

Outputs

Name	Type	Description
coef_	ndarray of shape (n_features,)	Estimated coefficients for the features
intercept_	float	The intercept of the model (bias term)
n_features_in_	int	Number of features seen during fit
feature_names_in_	ndarray of shape (n_features_in_,)	Names of features seen during fit

Usage Examples

Basic Usage

from sklearn.linear_model import QuantileRegressor
from sklearn.datasets import make_regression

X, y = make_regression(n_samples=200, n_features=5, noise=20, random_state=42)

# Predict the median
model_median = QuantileRegressor(quantile=0.5, alpha=0.0)
model_median.fit(X, y)

# Predict the 90th percentile
model_upper = QuantileRegressor(quantile=0.9, alpha=0.0)
model_upper.fit(X, y)

print("Median prediction:", model_median.predict(X[:3]))
print("90th percentile prediction:", model_upper.predict(X[:3]))

Related Pages

• Principle:Scikit_learn_Scikit_learn_Robust_Regression