Q1 [10 pts] Tree-based methods (a) [6] For tree-based ensemble method, bagging, random forest and boosting, what is the main difference in these ideas for classification problems? (b) [2] Suppose, you are working on a binary classification problem with 3 input features, and you chosen to apply a random forest algorithm on this data, you choose mtry = 2 and atree = 3, and the accuracy of each tree is 70% as indicated in below table. Random forest aggregates the results of individual trees based on majority voting, what will be the accuracy you could get for this data? obs Actual Y Tl T2 T3 Output 09 19 # 10 (c) [2 pts] Suppose you have given the following result table for training and validation error with boosting method, what is the optimal depth in such case? Scenario Depth Training error validation error 100 110 105 49 19 P 50 100 105 Scenario Depth Training error validation error 10 3 30 150 160 training error validation error 120 error 2 4 6 8 10 Depth