Scikit-Learn mean_pinball_loss() Metric

Evaluating regression models can be enhanced by using the mean_pinball_loss() metric, which quantifies the accuracy of quantile regression models by penalizing overestimations and underestimations differently based on a specified quantile.

The mean_pinball_loss() function in scikit-learn measures this accuracy by calculating the weighted absolute error. The weight is the quantile level for underestimates and one minus the quantile level for overestimates, making it a useful metric for quantile regression problems where predicting a specific quantile of the target distribution is desired.

Lower values of this metric indicate better model performance, though there is no fixed threshold for good or bad values as it depends on the specific problem and data. This metric is not suitable for classification tasks and is designed specifically for regression problems focusing on predicting quantiles.

from sklearn.datasets import make_regression
from sklearn.model_selection import train_test_split
from sklearn.linear_model import QuantileRegressor
from sklearn.metrics import mean_pinball_loss

# Generate synthetic dataset
X, y = make_regression(n_samples=1000, n_features=1, noise=0.1, random_state=42)

# Split into train and test sets
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)

# Train a Quantile Regressor for the 50th percentile (median)
quantile = 0.5
model = QuantileRegressor(quantile=quantile, alpha=0)
model.fit(X_train, y_train)

# Predict on test set
y_pred = model.predict(X_test)

# Calculate mean pinball loss
pinball_loss = mean_pinball_loss(y_test, y_pred, alpha=quantile)
print(f"Mean Pinball Loss: {pinball_loss:.4f}")

Running the example gives an output like:

Mean Pinball Loss: 0.0407

• Generate a synthetic regression dataset using make_regression().
• Split the dataset into training and test sets using train_test_split().
• Train a QuantileRegressor model on the training set for the 50th percentile (median).
• Use the trained model to predict on the test set with predict().
• Calculate the mean pinball loss using mean_pinball_loss() by comparing the predicted values to the true values and specifying the quantile.

This example demonstrates how to use the mean_pinball_loss() function from scikit-learn to evaluate the performance of a quantile regression model.