Scikit-Learn GridSearchCV KernelRidge

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 KernelRidge, an algorithm suitable for 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.

Kernel Ridge Regression (KRR) combines Ridge Regression (linear least squares with l2-norm regularization) with the kernel trick. It is useful for non-linear regression tasks.

The key hyperparameters for Kernel Ridge Regression include the regularization strength (alpha), which controls the model complexity and helps prevent overfitting; the kernel type (kernel), which specifies the kernel function to be used (e.g., ’linear’, ‘rbf’, ‘poly’); and the kernel coefficient (gamma), which is used for ‘rbf’, ‘poly’, and ‘sigmoid’ kernels.

from sklearn.datasets import make_regression
from sklearn.model_selection import train_test_split, GridSearchCV
from sklearn.kernel_ridge import KernelRidge

# 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': [0.1, 1, 10],
    'kernel': ['linear', 'rbf', 'poly'],
    'gamma': [0.1, 1, 10]
}

# Perform grid search
grid_search = GridSearchCV(estimator=KernelRidge(),
                           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': 0.1, 'gamma': 0.1, 'kernel': 'linear'}
Test set R^2 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 parameter grid with different values for alpha, kernel, and gamma hyperparameters.
4. Perform grid search using GridSearchCV, specifying the KernelRidge 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 optimal configuration for our KernelRidge model. This approach simplifies hyperparameter tuning and ensures we select the best model parameters for our regression task.