The `max_depth`

parameter in XGBoost controls the maximum depth of the decision trees used in the model.

It is a key hyperparameter that influences the model’s complexity and performance.

Smaller values of `max_depth`

create shallower trees, which can help prevent overfitting, while larger values allow the model to capture more complex relationships but may lead to overfitting if set too high.

This example demonstrates how to tune the `max_depth`

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

```
import xgboost as xgb
import numpy as np
from sklearn.datasets import make_classification
from sklearn.model_selection import GridSearchCV, StratifiedKFold
from sklearn.metrics import accuracy_score
# Create a synthetic dataset
X, y = make_classification(n_samples=1000, n_classes=2, n_features=20, n_informative=10, random_state=42)
# Configure cross-validation
cv = StratifiedKFold(n_splits=5, shuffle=True, random_state=42)
# Define hyperparameter grid
param_grid = {
'max_depth': [2, 3, 4, 5, 6, 7, 8, 9, 10]
}
# Set up XGBoost classifier
model = xgb.XGBClassifier(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='accuracy', n_jobs=-1, verbose=1)
grid_search.fit(X, y)
# Get results
print(f"Best max_depth: {grid_search.best_params_['max_depth']}")
print(f"Best CV accuracy: {grid_search.best_score_:.4f}")
# Plot max_depth vs. accuracy
import matplotlib.pyplot as plt
results = grid_search.cv_results_
plt.figure(figsize=(10, 6))
plt.plot(param_grid['max_depth'], results['mean_test_score'], marker='o', linestyle='-', color='b')
plt.fill_between(param_grid['max_depth'], results['mean_test_score'] - results['std_test_score'],
results['mean_test_score'] + results['std_test_score'], alpha=0.1, color='b')
plt.title('Max Depth vs. Accuracy')
plt.xlabel('Max Depth')
plt.ylabel('CV Average Accuracy')
plt.grid(True)
plt.show()
```

The resulting plot may look as follows:

In this example, we create a synthetic binary classification dataset using scikit-learn’s `make_classification`

function. We then set up a `StratifiedKFold`

cross-validation object to ensure that the class distribution is preserved in each fold.

We define a hyperparameter grid `param_grid`

that specifies the range of `max_depth`

values we want to test. In this case, we consider values from 2 to 10.

We create an instance of the `XGBClassifier`

with some basic hyperparameters set, such as `n_estimators`

and `learning_rate`

. We then perform the grid search using `GridSearchCV`

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

After fitting the grid search object with `grid_search.fit(X, y)`

, we can access the best `max_depth`

value and the corresponding best cross-validation accuracy using `grid_search.best_params_`

and `grid_search.best_score_`

, respectively.

Finally, we plot the relationship between the `max_depth`

values and the cross-validation average accuracy scores using matplotlib. We retrieve the results from `grid_search.cv_results_`

and plot the mean accuracy scores along with the standard deviation as error bars. This visualization helps us understand how the choice of `max_depth`

affects the model’s performance and guides us in selecting an appropriate value.

By tuning the `max_depth`

hyperparameter using grid search with cross-validation, we can find the optimal value that balances the model’s complexity and performance. This helps prevent overfitting and ensures that the model generalizes well to unseen data.