The `"reg:pseudohubererror"`

objective in XGBoost is used for regression tasks when the target variable is continuous.

It is a variant of the Huber loss function that combines squared error for small differences and absolute error for large differences, making it more robust to outliers compared to the squared error loss.

```
from sklearn.datasets import make_regression
from sklearn.model_selection import train_test_split
from xgboost import XGBRegressor
from sklearn.metrics import mean_absolute_error
# Generate a synthetic dataset for regression with outliers
X, y = make_regression(n_samples=1000, n_features=10, noise=0.1, random_state=42)
y[::100] += 10 # Add outliers to the target variable
# Split the data into training and testing sets
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)
# Initialize an XGBRegressor with the "reg:pseudohubererror" objective
model = XGBRegressor(objective="reg:pseudohubererror", n_estimators=100, learning_rate=0.1)
# Fit the model on the training data
model.fit(X_train, y_train)
# Make predictions on the test set
y_pred = model.predict(X_test)
# Calculate the mean absolute error of the predictions
mae = mean_absolute_error(y_test, y_pred)
print(f"Mean Absolute Error: {mae:.4f}")
```

The `"reg:pseudohubererror"`

objective is particularly useful when the dataset contains outliers that may unduly influence a squared error objective. It is less sensitive to outliers because it uses absolute error for large differences, which reduces the impact of extreme values.

However, it is important to note that the pseudo Huber error is less interpretable than the squared error. If interpretability is a key concern, the `"reg:squarederror"`

objective may be preferred.

When deciding whether to use the `"reg:pseudohubererror"`

objective, consider the following:

- Assess if the dataset contains outliers that could significantly impact a squared error objective.
- Determine if the interpretability of the squared error is a priority for the given problem.
- Compare the performance of
`"reg:pseudohubererror"`

with other regression objectives, such as`"reg:squarederror"`

or`"reg:absoluteerror"`

, to select the most appropriate one for the task at hand.

By understanding the characteristics and use cases of the `"reg:pseudohubererror"`

objective, data scientists and machine learning engineers can effectively apply it to regression problems where robustness to outliers is a key consideration.