Scikit-Learn RandomizedSearchCV KernelRidge

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 KernelRidge model, commonly used for 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.

KernelRidge combines ridge regression with the kernel trick, allowing for non-linear regression by transforming input features into a higher-dimensional space. The model is trained by minimizing a regularized least squares loss function.

Key hyperparameters for KernelRidge include the regularization strength (alpha), which controls model complexity and helps prevent overfitting; the kernel type (kernel), which determines the function used to transform input features; and the kernel coefficient (gamma), which is specific to certain kernel types like rbf, poly, and sigmoid.

from sklearn.datasets import make_regression
from sklearn.model_selection import train_test_split, RandomizedSearchCV
from sklearn.kernel_ridge import KernelRidge
from scipy.stats import uniform

# Generate synthetic regression dataset
X, y = make_regression(n_samples=1000, n_features=20, 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 = KernelRidge()

# Define hyperparameter distribution
param_dist = {
    'alpha': uniform(loc=0, scale=1),
    'kernel': ['linear', 'poly', 'rbf', 'sigmoid'],
    'gamma': uniform(loc=0, scale=1)
}

# 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_
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: -0.011
Best parameters: {'alpha': 0.09310276780589921, 'gamma': 0.8972157579533268, '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 model then the hyperparameter distribution with different values for alpha, kernel, and gamma hyperparameters.
4. Perform random search using RandomizedSearchCV, specifying the KernelRidge model, hyperparameter distribution, 100 iterations, 5-fold cross-validation, and neg_mean_squared_error 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 R^2 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 KernelRidge model.