How the ranking of feature importance is generated in Random Forests? I'm searching for a less formal explanation, that is, an intuitive way to explain it, for instance in a nutshell.
There are at least three ways in which one can formally compute the relevance of each feature in a dataset once the forest has been built. However, rationale behind all of the procedures that I am aware of, is almost the same in all three cases.
When you are building a tree, you have some candidate features for the best split in a given node you want to split. If a feature is very important intuition tells us that it should produce a very good split, i.e., reduce the variability measure significantly.
Thus, the relevance of a feature can be defined as a sum of variability measure reductions over the nodes where feature appears.