Scikit-Learn GridSearchCV Lars

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 Least Angle Regression (Lars), an algorithm suited for high-dimensional data.

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.

Least Angle Regression (Lars) is a regression algorithm similar to forward stepwise regression but uses a less greedy approach. It is particularly useful for high-dimensional data where the number of features exceeds the number of samples.

The key hyperparameters for Lars include the target number of non-zero coefficients (n_nonzero_coefs), the machine-precision regularization (eps), and whether to calculate the intercept for this model (fit_intercept).

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

# 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 parameter grid
param_grid = {
    'n_nonzero_coefs': [5, 10, 15],
    'eps': [1e-6, 1e-4, 1e-2],
    'fit_intercept': [True, False]
}

# Perform grid search
grid_search = GridSearchCV(estimator=Lars(),
                           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 score: {test_score:.3f}")

Running the example gives an output like:

Best score: -0.010
Best parameters: {'eps': 1e-06, 'fit_intercept': False, 'n_nonzero_coefs': 15}
Test set score: 1.000

The steps are as follows:

1. Generate a synthetic regression dataset using scikit-learn’s make_regression function.
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, eps, and fit_intercept.
4. Perform grid search using GridSearchCV, specifying the Lars 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 test set score.

By using GridSearchCV, we can effectively explore different hyperparameter settings and identify the configuration that minimizes the mean squared error for our Lars regression model. This automated approach simplifies the process of hyperparameter tuning and ensures optimal model performance.