Scikit-Learn RandomizedSearchCV LinearDiscriminantAnalysis

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 Linear Discriminant Analysis (LDA) 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.

Linear Discriminant Analysis is a classification algorithm that finds the linear combinations of features that best separate two or more classes. It is particularly useful for dimensionality reduction while preserving class separability.

Key hyperparameters for LDA include the solver, which is the algorithm for computing the LDA; shrinkage, which determines whether to use shrinkage and the type of shrinkage; and n_components, which is the number of components for dimensionality reduction.

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

# Generate synthetic dataset for classification
X, y = make_classification(n_samples=1000, n_features=20, n_informative=10, n_redundant=5, n_classes=3, random_state=42)

# Split the dataset 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 = LinearDiscriminantAnalysis()

# Define hyperparameter distribution
param_dist = {
    'solver': ['svd', 'lsqr', 'eigen'],
    'shrinkage': ['auto', None] + list(uniform(0, 1).rvs(size=3)), # Example of using uniform distribution for shrinkage
    'n_components': randint(1, min(X.shape[1], 10))
}

# 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: 0.701
Best parameters: {'n_components': 2, 'shrinkage': None, 'solver': 'svd'}
Test set accuracy: 0.710

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 LDA model.
4. Define the hyperparameter distribution for solver, shrinkage, and n_components.
5. Perform random search using RandomizedSearchCV, specifying the LinearDiscriminantAnalysis 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 Linear Discriminant Analysis model.