There is gradient boosting and random forest with 1000 trees. What will happen to the quality of each model if the first built tree is removed?

In the case of random forest, each tree is built independently, and the final prediction is an average (regression) or voting (classification) over all trees. Removing the first tree slightly decreases the model's quality, but not significantly, as the remaining 999 trees continue to work and compensate for the loss.

In the case of gradient boosting, trees are built sequentially, with each subsequent tree trained on the errors of the previous ones. The first tree provides the initial approximation. Removing the first tree would disrupt the entire sequence, and the model's quality would significantly deteriorate, as subsequent trees would not be able to correctly compensate for the error without the initial approximation.

Summary:

• Random forest: slight decrease in quality, the model remains functional.
• Gradient boosting: significant deterioration in quality, the model loses its meaning without the first tree.