Here's a simplified version of the Gradient Boosting Classifier algorithm in pseudocode:

Initialize the dataset (D) containing past customer information and their loan default status.

Set the number of boosting iterations (n_estimators) and learning rate (eta).

Initialize a simple model, F0(x), as a constant:
F0(x) = argmin(sum(L(y, p)))
where L is the loss function, y is the true label, and p is the prediction.

For each boosting iteration (i) from 1 to n_estimators:
a. Calculate the negative gradients (residuals) for each sample in the dataset:
r = -dL(y, F(x))/dp
where L is the loss function, y is the true label, and F(x) is the current model.

b. Fit a new weak learner (decision tree), h_i(x), to the residuals using the dataset D.

c. Compute the optimal step size (alpha) to minimize the loss function:
alpha = argmin(sum(L(y, F(x) + alpha * h_i(x))))

d. Update the model with the new weak learner and step size:
F(x) = F(x) + eta * alpha * h_i(x)

The final model, F(x), is a combination of the weak learners with their respective step sizes.

The Gradient Boosting Classifier algorithm iteratively adds new weak learners (decision trees) to the model in a way that each new tree corrects the errors made by the previous one. The learning rate (eta) controls the contribution of each tree to the final model, preventing overfitting. The algorithm stops after a predefined number of boosting iterations (n_estimators).

This pseudocode provides a high-level understanding of the algorithm. In practice, the actual implementation would involve more optimization and additional details for handling the decision trees and loss functions.
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