Scikit-Learn RandomizedSearchCV OrthogonalMatchingPursuit

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 an Orthogonal Matching Pursuit (OMP) model, which is commonly used for regression 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.

Orthogonal Matching Pursuit (OMP) is a linear regression model that selects a subset of features by solving a constrained optimization problem. It iteratively adds the feature that best reduces the error, making it useful for high-dimensional data with many features.

Key hyperparameters for OMP include the number of non-zero coefficients (n_nonzero_coefs), which controls the sparsity of the solution; fit_intercept, which determines whether to fit the intercept term; and normalize, which specifies whether to normalize the regressors before fitting.

from sklearn.datasets import make_regression
from sklearn.model_selection import train_test_split, RandomizedSearchCV
from sklearn.linear_model import OrthogonalMatchingPursuit
from scipy.stats import randint

# Generate synthetic regression dataset
X, y = make_regression(n_samples=1000, n_features=20, 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 the model
model = OrthogonalMatchingPursuit()

# Define hyperparameter distribution
param_dist = {
    'n_nonzero_coefs': randint(1, 20),
    'fit_intercept': [True, False]
}

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

Running the example gives an output like:

Best score: -0.010
Best parameters: {'fit_intercept': False, 'n_nonzero_coefs': 10}
Test set score: 1.000

The steps are as follows:

1. Generate a synthetic regression dataset using make_regression.
2. Split the dataset into train and test sets using train_test_split.
3. Define the model and the hyperparameter distribution with values for n_nonzero_coefs, fit_intercept, and normalize.
4. Perform random search using RandomizedSearchCV, specifying the OrthogonalMatchingPursuit model, hyperparameter distribution, 100 iterations, 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 random search.
6. Evaluate the best model on the hold-out test set and report the score.

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 Orthogonal Matching Pursuit model.