Scikit-Learn RandomizedSearchCV QuantileRegressor

Hyperparameter tuning is essential for optimizing machine learning models. In this example, we’ll demonstrate how to use scikit-learn’s RandomizedSearchCV for hyperparameter tuning of a QuantileRegressor model, commonly used for quantile regression tasks.

Random search is a method for evaluating different combinations of model hyperparameters. Unlike grid search, it samples a fixed number of hyperparameter combinations from a specified distribution, making it more efficient when searching over a large hyperparameter space.

QuantileRegressor is a linear model used for quantile regression. It estimates the conditional quantiles of a response variable given certain values of predictor variables. The model is trained by minimizing a quantile loss function.

Key hyperparameters for QuantileRegressor include the regularization strength (alpha), which controls model complexity and helps prevent overfitting; the target quantile (quantile), which specifies the quantile to be predicted; and the solver (solver), which is the optimization method used to find the model coefficients.

from sklearn.datasets import make_regression
from sklearn.model_selection import train_test_split, RandomizedSearchCV
from sklearn.linear_model import QuantileRegressor
from scipy.stats import uniform

# Generate synthetic regression dataset
X, y = make_regression(n_samples=1000, n_features=10, 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)

# Define the model
model = QuantileRegressor()

# Define hyperparameter distribution
param_dist = {
    'alpha': uniform(loc=0, scale=1),
    'quantile': uniform(loc=0.1, scale=0.8),
    'solver': ['interior-point', 'highs']
}

# Perform random search
random_search = RandomizedSearchCV(estimator=model,
                                   param_distributions=param_dist,
                                   n_iter=100,
                                   cv=5,
                                   scoring='neg_mean_absolute_error',
                                   random_state=42)
random_search.fit(X_train, y_train)

# Report best score and parameters
print(f"Best score: {random_search.best_score_:.3f}")
print(f"Best parameters: {random_search.best_params_}")

# Evaluate on test set
best_model = random_search.best_estimator_
test_score = best_model.score(X_test, y_test)
print(f"Test set score: {test_score:.3f}")

Running the example gives an output like:

Best score: -0.085
Best parameters: {'alpha': 0.036886947354532795, 'quantile': 0.5876514671839175, 'solver': 'highs'}
Test set score: 1.000

The steps are as follows:

1. Generate a synthetic regression dataset using scikit-learn’s make_regression function.
2. Split the dataset into train and test sets using train_test_split.
3. Define the model then the hyperparameter distribution with different values for alpha, quantile, and solver hyperparameters.
4. Perform random search using RandomizedSearchCV, specifying the QuantileRegressor model, hyperparameter distribution, 100 iterations, 5-fold cross-validation, and negative mean absolute error as the scoring metric.
5. Report the best cross-validation score and best set of hyperparameters found by random search.
6. Evaluate the best model on the hold-out test set and report the score.

By using RandomizedSearchCV, we can efficiently explore different hyperparameter settings and find the combination that maximizes the model’s performance. This automated approach saves time and effort compared to manual hyperparameter tuning and helps ensure we select the best configuration for our QuantileRegressor model.