Scikit-Learn GridSearchCV BayesianRidge

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 Bayesian Ridge Regression, a robust algorithm 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.

Bayesian Ridge Regression estimates the coefficients of a linear regression model using Bayesian inference. It incorporates regularization parameters to prevent overfitting and makes predictions by averaging over all possible models.

The key hyperparameters for Bayesian Ridge Regression include the regularization parameters alpha_1, alpha_2, lambda_1, and lambda_2. These control the prior distributions over the model parameters, influencing the model complexity and performance.

from sklearn.datasets import make_regression
from sklearn.model_selection import train_test_split, GridSearchCV
from sklearn.linear_model import BayesianRidge
from sklearn.metrics import mean_squared_error

# 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_1': [1e-6, 1e-5, 1e-4],
    'alpha_2': [1e-6, 1e-5, 1e-4],
    'lambda_1': [1e-6, 1e-5, 1e-4],
    'lambda_2': [1e-6, 1e-5, 1e-4]
}

# Perform grid search
grid_search = GridSearchCV(estimator=BayesianRidge(),
                           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_
mse = mean_squared_error(y_test, best_model.predict(X_test))
print(f"Test set Mean Squared Error: {mse:.3f}")

Running the example gives an output like:

Best score: -0.010
Best parameters: {'alpha_1': 1e-06, 'alpha_2': 1e-06, 'lambda_1': 1e-06, 'lambda_2': 1e-06}
Test set Mean Squared Error: 0.010

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_1, alpha_2, lambda_1, and lambda_2 hyperparameters.
4. Perform grid search using GridSearchCV, specifying the BayesianRidge 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 mean squared error.

By using GridSearchCV, we can easily 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 Bayesian Ridge Regression model.