XgboostR

Step-1 : Objective Function For regression tasks, the objective function of XGBoost is typically the mean squared error (MSE). The objective function to be minimized is given by:

● n is the number of training examples
● Y_i is the true target value of the i-th example
● Y_i is the predicted value of the i-th example(obtained from the sum of prediction of all trees in the ensemble).
● The regularization term helps prevent overfitting and is controlled by hyperparameters (e.g., L1 or L2 regularization terms).

Step-2 : XGBoost Algorithm Steps The steps for the XGBoost regressor are very similar to the classification version:

1. Initialize the Model: Start by initializing the model with a simple estimator, often a decision tree with only one leaf (a stump). This initial prediction will be improved in subsequent steps.
2. Compute Pseudo-Residuals: Compute the negative gradient (pseudo-residuals) of the mean squared error loss function with respect to the current predictions. The pseudo-residuals indicate how much the current model's predictions need to be adjusted to better fit the true target values.
3. Fit a New Tree: Train a new decision tree using the computed pseudo-residuals as the target values. The tree is fit to minimize the objective function, considering the current model's predictions as the base prediction. The tree is added to the ensemble.
4. Update Predictions: Update the predictions of the model by adding the predictions from the newly added tree, weighted by a learning rate (to control the step size of each tree's contribution).
5. Regularization: Apply regularization to prevent overfitting. Regularization terms are added to the objective function during training.
6. Iterate: Repeat steps 2 to 5 for a predefined number of boosting rounds (iterations), or until a stopping condition is met (e.g., the objective function improvement is below a threshold).
7. Make Predictions: Once the boosting process is complete, use the final ensemble of trees to make predictions on new data. The final predictions are obtained by summing the predictions of all the trees, weighted by their respective learning rates.

Step-3 : XGBoost Hyperparameters Similar to the classification version, XGBoost provides various hyperparameters to control the training process and model complexity for regression tasks. Some important hyperparameters include:

● learning_rate: Controls the step size at each iteration (typical values: 0.01 to 0.3).
● max_depth: Maximum depth of each decision tree (higher values may lead to overfitting).
● min_child_weight: Minimum sum of instance weight (hessian) needed in a child (node).
● subsample: Fraction of training examples used for each tree (helps reduce overfitting).
● colsample_bytree: Fraction of features (columns) used for each tree.
● gamma: Minimum loss reduction required to make a further partition on a leaf node.
● lambda: L2 regularization term.
● alpha: L1 regularization term.

Step-4 : Prediction for Regression For regression, the XGBoost regressor outputs continuous numerical values as predictions. There is no threshold involved, as in the classification case. The final prediction for each example is obtained by summing the predictions from all the trees in the ensemble, weighted by their respective learning rates.

That wraps up the detailed description of the XGBoost regressor algorithm, its steps, and relevant formulas. As with any machine learning model, appropriate hyperparameter tuning and data preprocessing are essential to achieve optimal performance.