We convert a tree to feature vector Then we use a procedure that chooses the DP procedure or the inner product procedure depending on maliciousness: This procedure returns the same value as the original calculation.
naively, if |V (T i )| (the number of feature subtrees such that # F i (T i ) = 0) is small enough, we can expect a speed-up because the cost of calculating the inner product is O(|V since |V (T i )| might increase as the training set becomes larger, we need a way to scale the speed-up to large data.