Feature interaction

$interaction(f_{1}, f_{2}) = \sum_{trees} \left |\sum_{leafs: split(f_1)=split(f_2)} LeafValue { } - \sum_{leafs: split(f_1)\ne split(f_2)}LeafValue \right |$
The sum inside the modulus always contains an even number of terms. The first half of terms contains leaf values when splits by $f1$ have the same value as splits by $f2$, the second half contains leaf values when two splits have different values, and the second half is in the sum with a different sign.

The larger the difference between sums of leaf values, the bigger the interaction. This process reflects the following idea: let's fix one feature and see if the changes to the other one will result in large formula changes.

$interaction(f_{1}, f_{2}) = \sum_{trees} \left |\sum_{leafs: split(f_1)=split(f_2)} LeafValue { } - \sum_{leafs: split(f_1) \neq split(f_2)}LeafValue \right |$