Scikit-Learn RandomizedSearchCV LinearRegression

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 linear regression model, commonly used for predicting continuous target variables.

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.

Linear regression is a linear model used for predicting a continuous target variable. It estimates the relationship between the input features and the target by minimizing the mean squared error (MSE).

Key hyperparameters for linear regression include fit_intercept, which determines if the intercept should be calculated.

from sklearn.datasets import make_regression
from sklearn.model_selection import train_test_split, RandomizedSearchCV
from sklearn.linear_model import LinearRegression
from scipy.stats import randint

# 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 = {
    'fit_intercept': [True, False],
}

# Perform random search
random_search = RandomizedSearchCV(estimator=LinearRegression(),
                                   param_distributions=param_dist,
                                   n_iter=10,
                                   cv=5,
                                   scoring='neg_mean_squared_error',
                                   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_
mse = -best_model.score(X_test, y_test)
print(f"Test set mean squared error: {mse:.3f}")

Running the example gives an output like:

Best score: 0.010
Best parameters: {'fit_intercept': True}
Test set mean squared error: -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 fit_intercept.
4. Perform random search using RandomizedSearchCV, specifying the LinearRegression model, hyperparameter distribution, 10 iterations, 5-fold cross-validation, and MSE 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 mean squared error.

By using RandomizedSearchCV, we can efficiently explore different hyperparameter settings and find the combination that minimizes the model’s mean squared error. This automated approach saves time and effort compared to manual hyperparameter tuning and helps ensure we select the best configuration for our linear regression model.