Scikit-Learn GridSearchCV HuberRegressor

Hyperparameter tuning is a crucial step in optimizing machine learning models for best performance. In this example, we’ll demonstrate how to use scikit-learn’s GridSearchCV to perform hyperparameter tuning for HuberRegressor, a robust regression algorithm that is effective at handling outliers in regression tasks.

Grid search is a method for evaluating different combinations of model hyperparameters to find the best performing configuration. It exhaustively searches through a specified parameter grid, trains and evaluates the model for each combination using cross-validation, and selects the hyperparameters that yield the best performance metric.

HuberRegressor is a linear regression model that is less sensitive to outliers in the data than ordinary least squares regression. It combines the properties of both linear regression and robust regression.

The key hyperparameters for HuberRegressor include the regularization strength (alpha), which helps control model complexity and prevent overfitting; the epsilon (epsilon), which determines the threshold for considering data points as outliers; and the maximum number of iterations (max_iter), which specifies the maximum number of iterations for the optimization algorithm.

from sklearn.datasets import make_regression
from sklearn.model_selection import train_test_split, GridSearchCV
from sklearn.linear_model import HuberRegressor

# 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 parameter grid
param_grid = {
    'alpha': [0.0001, 0.001, 0.01, 0.1, 1.0],
    'epsilon': [1.1, 1.35, 1.5, 1.75, 2.0],
    'max_iter': [50, 100, 200]
}

# Perform grid search
grid_search = GridSearchCV(estimator=HuberRegressor(),
                           param_grid=param_grid,
                           cv=5,
                           scoring='neg_mean_squared_error')
grid_search.fit(X_train, y_train)

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

# Evaluate on test set
best_model = grid_search.best_estimator_
test_score = best_model.score(X_test, y_test)
print(f"Test set R^2 score: {test_score:.3f}")

Running the example gives an output like:

Best score: -0.010
Best parameters: {'alpha': 0.01, 'epsilon': 2.0, 'max_iter': 50}
Test set R^2 score: 1.000

The steps are as follows:

1. Generate a synthetic regression dataset using make_regression.
2. Split the dataset into train and test sets using train_test_split.
3. Define the parameter grid with different values for alpha, epsilon, and max_iter hyperparameters.
4. Perform grid search using GridSearchCV, specifying the HuberRegressor model, parameter grid, 5-fold cross-validation, and negative mean squared error scoring metric.
5. Report the best cross-validation score and best set of hyperparameters found by grid search.
6. Evaluate the best model on the hold-out test set and report the R^2 score.

By using GridSearchCV, we can efficiently explore different hyperparameter settings and find the combination that optimizes the performance of the HuberRegressor. This method automates the hyperparameter tuning process and ensures that the chosen model parameters are well-suited to the specific regression problem.