I was reading about decision trees and this is what I understood:
We build decision trees by choosing an attribute and building subtrees (which are also decision trees) as children of the node representing that attribute. This means that as we go down, in building a decision tree, the no. of training instances that we use to build a subtree decreases. This is because when we build a subtree, we only have to train it using a subset of the original data consisting of instances which satisfy the conditions on the path towards the root node of the subtree.
Now here's the question: We usually believe that if training data is not enough, the model built is incorrect. This would mean that the subtrees down in a decision tree may not be good models (as they were trained using much less data than its ancestors in the tree) and if they are not, how can they be recursively combined to give a full tree which may give a good model? Where is the fault in my reasoning?