Scikit-Learn RandomizedSearchCV BayesianRidge

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 BayesianRidge 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.

BayesianRidge is a linear regression model that estimates the posterior distribution of the model parameters. This approach allows for better handling of multicollinearity and incorporates regularization directly into the estimation process.

Key hyperparameters for BayesianRidge include alpha_1 and alpha_2, which are shape and inverse scale parameters for the Gamma distribution prior over the alpha parameter, and lambda_1 and lambda_2, which are shape and inverse scale parameters for the Gamma distribution prior over the lambda parameter.

from sklearn.datasets import make_regression
from sklearn.model_selection import train_test_split, RandomizedSearchCV
from sklearn.linear_model import BayesianRidge
from scipy.stats import loguniform

# 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 hyperparameter distribution
param_dist = {
    'alpha_1': loguniform(1e-6, 1e-1),
    'alpha_2': loguniform(1e-6, 1e-1),
    'lambda_1': loguniform(1e-6, 1e-1),
    'lambda_2': loguniform(1e-6, 1e-1)
}

# Perform random search
random_search = RandomizedSearchCV(estimator=BayesianRidge(),
                                   param_distributions=param_dist,
                                   n_iter=100,
                                   cv=5,
                                   scoring='r2',
                                   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: 1.000
Best parameters: {'alpha_1': 6.026889128682509e-06, 'alpha_2': 6.025215736203862e-06, 'lambda_1': 1.9517224641449486e-06, 'lambda_2': 0.021423021757741054}
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 a hyperparameter distribution with different values for alpha_1, alpha_2, lambda_1, and lambda_2 hyperparameters using log-uniform distributions.
4. Perform random search using RandomizedSearchCV, specifying the BayesianRidge model, hyperparameter distribution, 100 iterations, 5-fold cross-validation, and R-squared 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 test set 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 BayesianRidge model.