I am trying to use CARTs (Classification and Regression Trees) for AdaBoost as weak learner. My question concerns the update of the weights after fitting the best weak learner.
A single CART node consists of a simple threshold (and of course the selected feature descriptor) which separates the data set for the left successor and/or right successor node.
Let us assume that I want to update the weight of a single data point $x_i$ by using a single CART with depth 3.
root / \ n1(-1) p1(+1) / \ / \ n2(-1) p2 (+1) n3(-1) p3(+1)
Must I use all traversed nodes for the update of the weight or do I only need the final output of the tree for the update? I saw the first approach in the GML AdaBoost MATLAB Toolbox.
I hope I could describe my problem sufficiently.