Scikit-Learn GridSearchCV Ridge

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 Ridge regression, an effective algorithm for linear regression tasks with regularization.

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.

Ridge regression is a linear model that includes L2 regularization to prevent overfitting by shrinking the coefficients. The model is trained by minimizing the residual sum of squares plus a penalty proportional to the sum of the squared coefficients.

The key hyperparameters for Ridge regression include the regularization strength (alpha), which controls the degree of shrinkage applied to the coefficients, and the solver algorithm, which determines the optimization method used to find the model coefficients.

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

# 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, 1.0, 10.0, 100.0],
    'solver': ['auto', 'svd', 'cholesky', 'lsqr', 'sparse_cg', 'sag', 'saga']
}

# Perform grid search
grid_search = GridSearchCV(estimator=Ridge(random_state=42),
                           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, 'solver': 'sparse_cg'}
Test set R^2 score: 1.000

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 and solver hyperparameters.
4. Perform grid search using GridSearchCV, specifying the Ridge 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 R^2 score.

By using GridSearchCV, we can efficiently find the optimal hyperparameter settings for the Ridge regression model, ensuring the best performance on our data. This systematic approach to hyperparameter tuning simplifies the process and improves model accuracy.