I took a contest two days ago. one of our question is as follows:
decision tree with depth 2 is constructed for two binary feature. how many features are in hypothesis space that can be shown with the following tree ?
The answer sheet say solution as 16 but the commitment say this question is removed by reason of wrong answer. Who can add explanantion why this is removed? which part of answer is wrong?
In this case, you have represented all possible features that can be represented by decision tree. So there are overall 4 possible points in the hypothesis space.
The number of partitions that this tree carves the hypothesis space into is equal to the number of leaves (4). That is also the maximum in this case, since with two binary features the total number of unique inputs is 2^2, or 4.
16? No way. The question is dumb, honestly.
The number of features you have in Decision Tree (DT) correspond to the maximum depth of the tree, which is the maximum amount of questions you can ask the DT in order to model the feature space.
That is a logical consequence of in each node the DT discriminating the feature space according to a feature.
