Scikit-Learn RandomizedSearchCV ARDRegression

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 an ARDRegression model, commonly used for regression tasks.

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.

ARDRegression is a linear model for Bayesian regression with automatic relevance determination. It estimates the relevance of each feature and applies different levels of regularization to them. The model is trained by minimizing the evidence approximation.

Key hyperparameters for ARDRegression include n_iter, which is the maximum number of iterations for the optimization; alpha_1 and alpha_2, which control the prior distribution of the weights; and lambda_1 and lambda_2, which control the prior distribution of the noise variance.

from sklearn.datasets import make_regression
from sklearn.model_selection import train_test_split, RandomizedSearchCV
from sklearn.linear_model import ARDRegression
from scipy.stats import uniform

# 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 = {
    'alpha_1': uniform(loc=1e-6, scale=1e-5),
    'alpha_2': uniform(loc=1e-6, scale=1e-5),
    'lambda_1': uniform(loc=1e-6, scale=1e-5),
    'lambda_2': uniform(loc=1e-6, scale=1e-5)
}

# Perform random search
random_search = RandomizedSearchCV(estimator=ARDRegression(),
                                   param_distributions=param_dist,
                                   n_iter=100,
                                   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 MSE: {mse:.3f}")

Running the example gives an output like:

Best score: 0.010
Best parameters: {'alpha_1': 8.506147516408585e-06, 'alpha_2': 9.06834739267264e-06, 'lambda_1': 1.0905051420006734e-05, 'lambda_2': 5.126176769114265e-06}
Test set MSE: 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 n_iter, alpha_1, alpha_2, lambda_1, and lambda_2 hyperparameters.
4. Perform random search using RandomizedSearchCV, specifying the ARDRegression model, hyperparameter distribution, 100 iterations, 5-fold cross-validation, and mean squared error 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 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.