Scikit-Learn RandomizedSearchCV GaussianProcessRegressor

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 Gaussian process regressor, a powerful tool 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.

Gaussian process regression is a non-parametric, probabilistic model used for regression tasks. It provides a flexible approach to capturing complex relationships in data by modeling the distribution over possible functions that fit the data.

Key hyperparameters for Gaussian process regression include the kernel (kernel), which defines the covariance function of the process and affects the smoothness of the predictions; the noise level (alpha), which controls the regularization and helps manage noise in the data; and the optimizer (optimizer), which is the method used to find the best hyperparameters for the kernel.

from sklearn.datasets import make_regression
from sklearn.model_selection import train_test_split, RandomizedSearchCV
from sklearn.gaussian_process import GaussianProcessRegressor
from sklearn.gaussian_process.kernels import RBF, Matern
from scipy.stats import expon

# Generate synthetic regression dataset
X, y = make_regression(n_samples=100, 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 the model
model = GaussianProcessRegressor(random_state=42)

# Define hyperparameter distribution
param_dist = {
    'kernel': [RBF(), Matern()],
    'alpha': expon(scale=1.0),
    'optimizer': ['fmin_l_bfgs_b', None]
}

# Perform random search
random_search = RandomizedSearchCV(estimator=model,
                                   param_distributions=param_dist,
                                   n_iter=50,
                                   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_
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: -3034.143
Best parameters: {'alpha': 0.07747586881130901, 'kernel': RBF(length_scale=1), 'optimizer': 'fmin_l_bfgs_b'}
Test set score: 0.904

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 model then the hyperparameter distribution with different values for kernel, alpha, and optimizer hyperparameters.
4. Perform random search using RandomizedSearchCV, specifying the GaussianProcessRegressor model, hyperparameter distribution, 50 iterations, 5-fold cross-validation, and negative 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 score.

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 Gaussian process regression model.