Scikit-Learn GridSearchCV GaussianProcessRegressor

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 GaussianProcessRegressor, a powerful 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.

GaussianProcessRegressor is a non-parametric, kernel-based model that can provide a probabilistic prediction for regression problems. It works by defining a distribution over possible functions that fit the data and making predictions based on the most probable functions.

The key hyperparameters for GaussianProcessRegressor include:

• kernel: Specifies the covariance function of the GP. Common choices include RBF, Matern, and RationalQuadratic.
• alpha: Adds a noise term to the diagonal of the kernel matrix during fitting.
• n_restarts_optimizer: The number of restarts of the optimizer for better convergence.

from sklearn.datasets import make_regression
from sklearn.model_selection import train_test_split, GridSearchCV
from sklearn.gaussian_process import GaussianProcessRegressor
from sklearn.gaussian_process.kernels import RBF, Matern, RationalQuadratic

# 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 = {
    'kernel': [RBF(), Matern(), RationalQuadratic()],
    'alpha': [1e-10, 1e-2, 1],
    'n_restarts_optimizer': [0, 1, 2]
}

# Perform grid search
grid_search = GridSearchCV(estimator=GaussianProcessRegressor(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: -133.900
Best parameters: {'alpha': 0.01, 'kernel': RBF(length_scale=1), 'n_restarts_optimizer': 0}
Test set R^2 score: 0.994

The steps are as follows:

1. Generate a synthetic regression dataset using make_regression function.
2. Split the dataset into train and test sets using train_test_split.
3. Define the parameter grid with different values for kernel, alpha, and n_restarts_optimizer hyperparameters.
4. Perform grid search using GridSearchCV, specifying the GaussianProcessRegressor 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 R^2 score.

By using GridSearchCV, we can explore different hyperparameter settings for GaussianProcessRegressor and find the combination that optimizes model performance. This approach helps in automating hyperparameter tuning and selecting the best configuration for our regression task.