DOC minor clarifications in ensemble.rst
@@ -594,21 +594,20 @@ learners. Decision trees have a number of abilities that make them
valuable for boosting, namely the ability to handle data of mixed type
and the ability to model complex functions.
-Similar to other boosting algorithms GBRT builds the additive model in
-a forward stagewise fashion:
+Similar to other boosting algorithms, GBRT builds the additive model in
+a greedy fashion:
.. math::
- F_m(x) = F_{m-1}(x) + \gamma_m h_m(x)
+ F_m(x) = F_{m-1}(x) + \gamma_m h_m(x),
-At each stage the decision tree :math:`h_m(x)` is chosen to
-minimize the loss function :math:`L` given the current model
-:math:`F_{m-1}` and its fit :math:`F_{m-1}(x_i)`
+where the newly added tree :math:`h_m` tries to minimize the loss :math:`L`,
+given the previous ensemble :math:`F_{m-1}`:
.. math::
- F_m(x) = F_{m-1}(x) + \arg\min_{h} \sum_{i=1}^{n} L(y_i,
- F_{m-1}(x_i) + h(x))
+ h_m = \arg\min_{h} \sum_{i=1}^{n} L(y_i,
+ F_{m-1}(x_i) + h(x_i)).
The initial model :math:`F_{0}` is problem specific, for least-squares
regression one usually chooses the mean of the target values.
