clearlyit is hard to visualize and understand the prediction process based on trees howeverfigure shows that the features and were correctly identified as being important boosting boosting is powerful idea that aims to improve the accuracy of any learning algorithmespecially when involving weak learners -simple prediction functions that exhibit performance slightly better than random guessing shallow decision trees typically yield weak learners originallyboosting was developed for binary classification tasksbut it can be readily extended to handle general classification and regression problems the boosting approach has some similarity with the bagging method in the sense that boosting uses an ensemble of prediction functions despite this similaritythere exists fundamental difference between these methods specificallywhile bagging involves the fitting of prediction functions to bootstrapped datathe predicting functions in boosting are learned sequentially that iseach learner uses information from previous learners the idea is to start with simple model (weak learnerg for the data {(xi yi )}ni= and then to improve or "boostthis learner to learner : herethe function is found by minimizing the training loss for over all functions in some class of functions for exampleh could be the set of prediction functions that can be obtained via decision tree of maximal depth given loss function lossthe function is thus obtained as the solution to the optimization problem loss (yi (xi (xi ) argmin = hh ( this process can be repeated for to obtain and so onyielding the boosted prediction function gb (xg (xhb ( ( = instead of using the updating step gb gb- hb one prefers to use the smooth updating step gb gb- hb for some suitably chosen step-size parameter as we shall see shortlythis helps reduce overfitting boosting can be used for regression and classification problems we start with simple regression settingusing the squared-error lossthusloss( , ( ) in this caseit is common to start with (xn- ni= yi and each hb for isnchosenoas learner for the data set tb of residuals corresponding to gb- that istb :xi (bi = with (bi :yi gb- (xi ( this leads to the following boosting procedure for regression with squared-error loss weak learners