Scikit-Learn GridSearchCV ARDRegression

Hyperparameter tuning is essential for optimizing machine learning models. In this example, we’ll demonstrate how to use scikit-learn’s GridSearchCV to perform hyperparameter tuning for ARDRegression.

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.

ARDRegression is a Bayesian regression technique that includes automatic relevance determination to manage feature relevance. The model estimates the distribution of the weights and performs feature selection during training.

The key hyperparameters for ARDRegression include the number of iterations (max_iter) for the optimization process, the hyperparameters controlling the prior distribution for the weights (alpha_1 and alpha_2), and the hyperparameters controlling the prior distribution for the noise (lambda_1 and lambda_2).

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

# 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 = {
    'max_iter': [100, 300, 500],
    '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=ARDRegression(),
                           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_
score = best_model.score(X_test, y_test)
print(f"Test set score: {score:.3f}")

Running the example gives an output like:

Best score: -0.010
Best parameters: {'alpha_1': 1e-06, 'alpha_2': 0.0001, 'lambda_1': 0.0001, 'lambda_2': 1e-05, 'max_iter': 100}
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 the parameter grid with different values for max_iter, alpha_1, alpha_2, lambda_1, and lambda_2 hyperparameters.
4. Perform grid search using GridSearchCV, specifying the ARDRegression model, parameter grid, 5-fold cross-validation, and negative mean squared error as the 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 score.

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 ARDRegression model.