gradient boosting resulting algorithm is called gradient boosting the general gradient boosting algorithm is summarized in algorithm the main idea is to mimic gradient descent algorithm in the following sense at each stage of the boosting procedurewe calculate negative gradient on training points xn (lines - thenwe fit simple model (such as shallow decision treeto approximate the gradient (line for any feature finallysimilar to the gradient descent methodwe make -sized step in the direction of the negative gradient (line algorithm gradient boosting inputtraining set {(xi yi )}ni= the number of boosting rounds ba differentiable loss function loss( , )and gradient step-size parameter outputgradient boosted prediction function set ( for to do for to do evaluate the negative gradient of the loss at (xi yi via ri( loss (yi zz =gb- (xi approximate the negative gradient by solving  (bri (xi hb argmin = hh ( set gb (xgb- (xg hb (xreturn gb example (gradient boosting for regression treelet us continue with the basic bagging and random forest examples for regression tree (examples and )where we compared the standard decision tree estimator with the corresponding bagging and random forest estimators nowwe use the gradient boosting estimator from algorithm as implemented in sklearn we use and perform boosting rounds as prediction function hb for we use small regression trees of depth at most note that such individual trees do not usually give good performancethat isthey are weak prediction functions we can see that the resulting boosting prediction function gives the score equal to which is better than scores of simple decision tree ( )the bagged tree ( )and the random forest ( gradientboostingregression py import numpy as np from sklearn datasets import make_friedman from sklearn tree import decisiontreeregressor from sklearn model_selection import train_test_split from sklearn metrics import _score