Note that the scoring function is shared by all the factors.
given the current decision function F m−1 , we can consider line 3 to line 9 a process of generating the pseudo Algorithm 1 S-MART: A family of structured learning algorithms with multiple additive regression trees 1: F0(x, y k ) = 0 2: for m = 1 to M do: going over all trees 3: for all examples do: going over all examples 5: for y k ∈ Ω(x) do: going over all factors 6: For all u k , obtain g ku by Equation (3)  7: end for 9: end for 10: Fm(x, y k ) = Fm−1(x, y k ) + hm(x, y k ) 12: end for training data D for modeling the regression tree.