# In XGBoost, how is a leaf index corresponding to the particular leaf node in actual base learner trees?

I've trained a XGBoost model for regression, where the max depth is 2.

# Create the ensemble
ensemble_size = 200
ensemble = xgb.XGBRegressor(n_estimators=ensemble_size, n_jobs=4, max_depth=2, learning_rate=0.1,
objective='reg:squarederror')

ensemble.fit(train_x, train_y)


I've plotted the first tree in the ensemble:

# Plot single tree
plot_tree(ensemble, rankdir='LR')


Now I retrieve the leaf indices of the first training sample in the XGBoost ensemble model:

ensemble.apply(train_x[:1]) # leaf indices in all 200 base learner trees


array([[6, 6, 4, 6, 4, 6, 5, 5, 4, 5, 4, 3, 5, 4, 5, 3, 6, 3, 5, 5, 3, 3, 3, 5, 4, 4, 3, 4, 3, 6, 6, 6, 4, 6, 6, 3, 5, 3, 5, 4, 6, 4, 4, 6, 3, 3, 6, 3, 6, 3, 4, 3, 6, 6, 3, 6, 5, 3, 6, 6, 3, 4, 6, 5, 3, 3, 3, 6, 3, 4, 3, 6, 3, 6, 3, 3, 3, 4, 6, 3, 4, 4, 6, 3, 3, 6, 3, 6, 6, 3, 3, 4, 4, 4, 3, 3, 6, 6, 3, 3, 6, 3, 3, 3, 6, 6, 6, 4, 4, 3, 5, 3, 3, 3, 4, 5, 3, 3, 6, 3, 3, 6, 3, 4, 5, 3, 6, 3, 5, 3, 4, 4, 3, 3, 4, 6, 6, 6, 6, 3, 4, 4, 3, 5, 6, 6, 3, 5, 3, 3, 6, 6, 3, 3, 6, 3, 3, 4, 4, 3, 4, 3, 5, 3, 3, 3, 3, 3, 4, 4, 6, 3, 6, 4, 4, 5, 6, 3, 4, 5, 6, 3, 4, 3, 4, 5, 6, 6, 5, 4, 3, 3, 6, 6, 3, 6, 5, 4, 3, 3]], dtype=int32)

Here is my question:

• Since there are four leaf nodes in the first tree, how come there is index 6 for the first training sample?

• In the official doc for apply(), it says "Leaves are numbered within [0; 2**(self.max_depth+1)), possibly with gaps in the numbering." So if max_depth is 2, the leaves are numbered between 0 and 7. Since there are only four leaves in a binary tree of depth 2, shouldn't the leaves numbered within [0, 4)? What is the reason behind the design $$[0; 2^{(self.max\_depth+1)})$$?

I think what you are seeing is the fact that all nodes in the tree are indexed because a priori the model doesn't know where splits will happen (i.e. any node could be a leaf). My guess is that the nodes follow an ordering similar to:

In your case all of the leaf nodes are at the max depth of the tree, so nodes 3-6 show up in your list. By contrast, if your data was all the same value I would expect all labels to be node 0 (because the split criteria was not met). And then you could have intermediate situations where after 1 split there is a node which does not meet the split criteria (in this case you could see either node 1 or 2 show up in your list).

Hope this helps!