The `alpha`

parameter in XGBoost controls the L1 regularization term, which can help with feature selection and prevent overfitting by encouraging sparse solutions.

Higher values of `alpha`

lead to more regularization and can shrink the coefficients of less important features to exactly zero. However, setting `alpha`

too high may lead to underfitting.

An alias for the `alpha`

parameter is `reg_alpha`

.

This example demonstrates how to tune the `alpha`

hyperparameter using grid search with cross-validation to find the optimal value that balances regularization and performance.

```
import xgboost as xgb
import numpy as np
from sklearn.datasets import make_regression
from sklearn.model_selection import GridSearchCV, KFold
from sklearn.metrics import r2_score
# Create a synthetic regression dataset
X, y = make_regression(n_samples=1000, n_features=20, n_informative=10, noise=0.1, random_state=42)
# Configure cross-validation
cv = KFold(n_splits=5, shuffle=True, random_state=42)
# Define hyperparameter grid
param_grid = {
'alpha': [0, 0.01, 0.1, 1, 10, 100]
}
# Set up XGBoost regressor
model = xgb.XGBRegressor(n_estimators=100, learning_rate=0.1, random_state=42)
# Perform grid search
grid_search = GridSearchCV(estimator=model, param_grid=param_grid, cv=cv, scoring='r2', n_jobs=-1, verbose=1)
grid_search.fit(X, y)
# Get results
print(f"Best alpha: {grid_search.best_params_['alpha']}")
print(f"Best CV R^2 score: {grid_search.best_score_:.4f}")
# Plot alpha vs. R^2 score
import matplotlib.pyplot as plt
results = grid_search.cv_results_
plt.figure(figsize=(10, 6))
plt.semilogx(param_grid['alpha'], results['mean_test_score'], marker='o', linestyle='-', color='b')
plt.fill_between(param_grid['alpha'], results['mean_test_score'] - results['std_test_score'],
results['mean_test_score'] + results['std_test_score'], alpha=0.1, color='b')
plt.title('Alpha vs. R^2 Score')
plt.xlabel('Alpha (log scale)')
plt.ylabel('CV Average R^2 Score')
plt.grid(True)
plt.show()
```

The resulting plot may look as follows:

In this example, we create a synthetic regression dataset using scikit-learn’s `make_regression`

function. We then set up a `KFold`

cross-validation object to split the data into train and test sets.

We define a hyperparameter grid `param_grid`

that specifies the range of `alpha`

values we want to test, including 0 (no regularization), and increasing orders of magnitude up to 100.

We create an instance of the `XGBRegressor`

with some basic hyperparameters set. We then perform the grid search using `GridSearchCV`

, providing the model, parameter grid, cross-validation object, scoring metric (R^2), and the number of CPU cores to use for parallel computation.

After fitting the grid search object, we can access the best `alpha`

value and the corresponding best cross-validation R^2 score.

Finally, we plot the relationship between the `alpha`

values and the cross-validation average R^2 scores using matplotlib. We use a logarithmic scale for the x-axis since the `alpha`

values span orders of magnitude. The plot includes error bars representing the standard deviation of the scores.

The optimal `alpha`

value depends on the specific dataset and problem at hand. Setting `alpha`

too high can lead to underfitting, while setting it too low may not provide enough regularization to prevent overfitting. It’s recommended to use grid search with cross-validation to find a good balance for each use case.