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Scikit-Learn GridSearchCV OrthogonalMatchingPursuit

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 Orthogonal Matching Pursuit (OMP), a regression technique that selects a subset of features to fit a linear model.

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.

Orthogonal Matching Pursuit is a regression algorithm that iteratively selects the most significant features to include in the model, resulting in a sparse solution. This can be particularly useful when dealing with high-dimensional data where only a few features are truly relevant.

The key hyperparameters for Orthogonal Matching Pursuit include n_nonzero_coefs, which specifies the number of non-zero coefficients in the solution, and tol, which is the tolerance for the stopping criteria.

from sklearn.datasets import make_regression
from sklearn.model_selection import train_test_split, GridSearchCV
from sklearn.linear_model import OrthogonalMatchingPursuit

# Generate synthetic regression dataset
X, y = make_regression(n_samples=1000, n_features=10, n_informative=5, 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 parameter grid
param_grid = {
    'n_nonzero_coefs': [5, 10, 15],
    'tol': [1e-3, 1e-4, 1e-5]
}

# Perform grid search
grid_search = GridSearchCV(estimator=OrthogonalMatchingPursuit(),
                           param_grid=param_grid,
                           cv=5,
                           scoring='neg_mean_squared_error')
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_
test_score = best_model.score(X_test, y_test)
print(f"Test set R^2 score: {test_score:.3f}")

Running the example gives an output like:

Best parameters: {'n_nonzero_coefs': 5, 'tol': 0.001}
Test set R^2 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 parameter grid with different values for n_nonzero_coefs and tol hyperparameters.
  4. Perform grid search using GridSearchCV, specifying the OrthogonalMatchingPursuit model, parameter grid, 5-fold cross-validation, and negative mean squared error 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 R^2 score.

By using GridSearchCV, we can efficiently explore different hyperparameter settings for Orthogonal Matching Pursuit and find the combination that maximizes the model’s performance. This automated approach saves time and ensures optimal configuration for the OMP model.



See Also