Learning using  decision trees I have a quick question that I'm stumped on. This is about constructing a decision tree using information gain (entropy). Let's say we have a dataset with two input attributes such that the information gain at the root of the tree for both attributes is zero, but this tree is still a decision tree of depth two (so two questions must be asked) that is consistent with the data. 

How would this be constructed? I don't understand how I can get to a deeper depth without knowing have any information gain...
Without looking at specifics, growing a tree using information gain is a greedy procedure and won't always get you to the smallest tree consistent with the data, even if one exists.  If there are ties among attributes, you break them arbitrarily.