Scikit-Learn GridSearchCV LinearRegression

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 linear regression, a fundamental 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.

Linear regression models the relationship between input features and the target variable by fitting a linear equation to the observed data. The model is trained by minimizing the mean squared error between the predicted and actual values.

The key hyperparameters for linear regression include fit_intercept, which decides whether to calculate the intercept for the model, and positive, which determines whether the model coefficients will be forced to be positive or not.

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

# 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 (for LinearRegression, hyperparameters are limited)
param_grid = {
    'fit_intercept': [True, False],
    'positive': [True, False]
}

# Perform grid search
grid_search = GridSearchCV(estimator=LinearRegression(),
                           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 score: {test_score:.3f}")

Running the example gives an output like:

Best score: -0.010
Best parameters: {'fit_intercept': True, 'positive': False}
Test set 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 possible values for fit_intercept and normalize hyperparameters.
4. Perform grid search using GridSearchCV, specifying the LinearRegression model, parameter grid, 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 grid search.
6. Evaluate the best model on the hold-out test set and report the score.

By using GridSearchCV, we efficiently identify the best hyperparameter settings for LinearRegression, optimizing model performance with minimal manual effort.