Scikit-Learn RandomizedSearchCV QuadraticDiscriminantAnalysis

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 QuadraticDiscriminantAnalysis model, commonly used for classification 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.

Quadratic Discriminant Analysis is a generative model for classification that models the distribution of each class and uses Bayes’ theorem to find the best class for given data. It assumes that each class follows a Gaussian distribution with a different covariance matrix.

Key hyperparameters for Quadratic Discriminant Analysis include the regularization parameter (reg_param), which helps prevent overfitting by shrinking the covariance estimates towards the identity matrix, and the tolerance (tol), which is the threshold for stopping the iterative process when fitting the model.

from sklearn.datasets import make_classification
from sklearn.model_selection import train_test_split, RandomizedSearchCV
from sklearn.discriminant_analysis import QuadraticDiscriminantAnalysis
from scipy.stats import uniform

# Generate synthetic classification dataset
X, y = make_classification(n_samples=1000, n_features=10, n_informative=5, n_redundant=5, 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 = QuadraticDiscriminantAnalysis()

# Define hyperparameter distribution
param_dist = {
    'reg_param': uniform(loc=0, scale=1),
    'tol': uniform(loc=1e-5, scale=1e-4)
}

# Perform random search
random_search = RandomizedSearchCV(estimator=model,
                                   param_distributions=param_dist,
                                   n_iter=100,
                                   cv=5,
                                   scoring='accuracy',
                                   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_
accuracy = best_model.score(X_test, y_test)
print(f"Test set accuracy: {accuracy:.3f}")

Running the example gives an output like:

Best score: 0.897
Best parameters: {'reg_param': 0.3745401188473625, 'tol': 0.00010507143064099161}
Test set accuracy: 0.885

The steps are as follows:

1. Generate a synthetic classification dataset using scikit-learn’s make_classification function.
2. Split the dataset into train and test sets using train_test_split.
3. Define the QuadraticDiscriminantAnalysis model.
4. Define the hyperparameter distribution with different values for reg_param and tol.
5. Perform random search using RandomizedSearchCV, specifying the QuadraticDiscriminantAnalysis model, hyperparameter distribution, 100 iterations, 5-fold cross-validation, and accuracy scoring metric.
6. Report the best cross-validation score and best set of hyperparameters found by random search.
7. Evaluate the best model on the hold-out test set and report the accuracy.

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 QuadraticDiscriminantAnalysis model.