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Boosted Tree Explanations

Contrary to a decision tree (where the leaves represent classes), a regression tree is a binary tree $T$ where the leaves represent numerical values $w_i \in \mathbb{R}$ that describe real quantities.

A boosted regression tree is an ensemble of trees {$T_1,\ldots T_n$} (alias a forest) where each $T_i$ is a regression tree such that the regression value $F(x) \in \mathbb{R}$ for an input instance $x$ is given by:

\[F(x) = \sum_{i=1}^{n} T_i(x)\]

where the weight $T_i(x) \in \mathbb{R}$ of a tree $T_i$ for an input instance $x$ is given by the label of the leaf reached from the root as follows: at each node go to the left or right child depending on whether or not the condition labeling the node is satisfied by $x$.


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