# Feature importance over a subset of instance space instead of an entire instance space

I'm really curious if anyone has faced this problem before, or is it even widely studied at all.

Imagine we have a feature that isn't important (based on many widely available and textbook feature selection methods) over the entire instance space of training data. However, if we try to divide the instance space into certain subsets, can the feature become important over that subset, and are there any methods available for arbitrary datasets?

When I say 'dividing the instance space', I mean for example if I have 3 features $X_0, X_1, X_2$ with a binary label $Y$, a subset of instance space will be a region where, for example, when $X_0 >5, X_1>5$. In particular, could it be possible that $X_2$ isn't significant over the entire instance space, but is significant over the restricted space mentioned above. If it's possible (my intuition says so), are there any methods in current literature that allow me to find such a space (if it exists)?

If anyone has any links/papers/resources which can direct me to a similar study, I would gladly accept it as well.

• Just a quick update on this: a quick solution for this will be a Decision Tree. Decision Trees allow one to find feature subspaces where features become more important; we can achieve this by looking at decision splits at the lower levels of the tree. – c zl Aug 15 '18 at 7:15