Scikit-Learn RandomizedSearchCV HuberRegressor

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 HuberRegressor model, which is robust to outliers in 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.

HuberRegressor is a linear model used for robust regression. It combines the properties of both least squares and absolute deviation loss functions to handle outliers effectively. The model is trained by minimizing the Huber loss function, which is less sensitive to outliers in the data.

Key hyperparameters for HuberRegressor include epsilon, which controls the transition point between squared loss and absolute loss, and alpha, which controls the regularization strength to help prevent overfitting.

from sklearn.datasets import make_regression
from sklearn.model_selection import train_test_split, RandomizedSearchCV
from sklearn.linear_model import HuberRegressor
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 = HuberRegressor()

# Define hyperparameter distribution
param_dist = {
    'epsilon': uniform(loc=1.0, scale=1.0),
    'alpha': uniform(loc=0.0001, scale=0.9999)
}

# Perform random search
random_search = RandomizedSearchCV(estimator=model,
                                   param_distributions=param_dist,
                                   n_iter=100,
                                   cv=5,
                                   scoring='neg_mean_squared_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_
mse = best_model.score(X_test, y_test)
print(f"Test set mean squared error: {-mse:.3f}")

Running the example gives an output like:

Best score: -0.010
Best parameters: {'alpha': 0.020682435846372867, 'epsilon': 1.9699098521619942}
Test set mean squared error: -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 HuberRegressor model.
4. Define the hyperparameter distribution with different values for epsilon and alpha.
5. Perform random search using RandomizedSearchCV, specifying the HuberRegressor model, hyperparameter distribution, 100 iterations, 5-fold cross-validation, and mean squared error as the scoring metric.
6. Report the best cross-validation score and best set of hyperparameters found by random search.
7. Evaluate the best model on the hold-out test set and report the mean squared error.

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 HuberRegressor model.