Scikit-Learn GridSearchCV LinearDiscriminantAnalysis

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 LinearDiscriminantAnalysis, a popular algorithm for classification 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.

LinearDiscriminantAnalysis is a classification algorithm that finds a linear combination of features that separates two or more classes. It is particularly useful for reducing dimensionality before classification.

The key hyperparameters for LinearDiscriminantAnalysis include the solver, which determines the method to use for the analysis, and the shrinkage parameter, which is used for regularization to prevent overfitting.

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

# Generate synthetic binary 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 parameter grid
param_grid = {
    'solver': ['svd', 'lsqr', 'eigen'],
    'shrinkage': [None, 'auto', 0.1, 0.5, 1.0]
}

# Perform grid search
grid_search = GridSearchCV(estimator=LinearDiscriminantAnalysis(),
                           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: 0.834
Best parameters: {'shrinkage': 'auto', 'solver': 'lsqr'}
Test set accuracy: 0.805

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 solver and shrinkage hyperparameters.
4. Perform grid search using GridSearchCV, specifying the LinearDiscriminantAnalysis 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 combination that maximizes the model’s performance, ensuring an optimized LinearDiscriminantAnalysis model.