Scikit-Learn GridSearchCV QuadraticDiscriminantAnalysis

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 QuadraticDiscriminantAnalysis, an algorithm that models each class with a Gaussian distribution and fits a quadratic decision boundary.

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.

QuadraticDiscriminantAnalysis (QDA) assumes that each class has a different covariance matrix and is well-suited for data with complex class boundaries. The key hyperparameters for QDA include reg_param, which regularizes the covariance estimate, and store_covariance, a boolean that indicates if the individual class covariance matrices should be stored.

from sklearn.datasets import make_classification
from sklearn.model_selection import train_test_split, GridSearchCV
from sklearn.discriminant_analysis import QuadraticDiscriminantAnalysis

# Generate synthetic binary classification dataset
X, y = make_classification(n_samples=1000, n_features=20, n_informative=10, n_redundant=10, 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 = {
    'reg_param': [0.0, 0.1, 0.5, 1.0],
    'store_covariance': [True, False]
}

# Perform grid search
grid_search = GridSearchCV(estimator=QuadraticDiscriminantAnalysis(),
                           param_grid=param_grid,
                           cv=5,
                           scoring='accuracy')
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_
accuracy = best_model.score(X_test, y_test)
print(f"Test set accuracy: {accuracy:.3f}")

Running the example gives an output like:

Best score: 0.931
Best parameters: {'reg_param': 0.1, 'store_covariance': True}
Test set accuracy: 0.935

The steps are as follows:

1. Generate a synthetic binary classification dataset using make_classification.
2. Split the dataset into train and test sets using train_test_split.
3. Define the parameter grid with different values for reg_param and store_covariance hyperparameters.
4. Perform grid search using GridSearchCV, specifying the QuadraticDiscriminantAnalysis model, parameter grid, 5-fold cross-validation, and accuracy 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 accuracy.

By using GridSearchCV, we can efficiently explore different hyperparameter settings and find the optimal configuration for our QuadraticDiscriminantAnalysis model, ensuring improved performance and accuracy on classification tasks.