Solved – Does decision tree need to use the same feature to split in the same layer

Question

I know in decision tree, we select features which maximize information gain (IG) to split data. My question is that, does such selections need to be the same in the same layer?

Suppose data has features X: sunny = {True, False}, windy = {True, False}, holiday = {True, False} and Y: play = {True, False}.

From root, assume sunny gives maximum IG, such that True and False groups are split in the first child layer. Next, should we consider IG using windy (assume windy gives maximum IG) on both groups to split, or we can allow True group to use windy whereas False group to use holiday to split? The later cases means that we can just consider to maximize IG on local branch.

Answer 1

The second option.

There's no reason to constrain a tree to split on the same variable at all nodes at a given level.