XGBoost
{\displaystyle {\hat {\phi }}_{m}={\underset {\phi \in \mathbf {\Phi } }{\arg \min }}\sum _{i=1}^{N}{\frac {1}{2}}{\hat {h}}_{m}(x_{i})\left[-{\frac {{\hat {g}}_{m}(x_{i})}{{\hat {h}}_{m}(x_{i})}}-\phi (x_{i})\right]^{2}.} f ^ m ( x ) = α φ ^ m ( x ) . {\displaystyle {\hat {f}}_{m}(x)=\alpha {\hat {\phi }}_{m}(x).} Update the model: f ^ ( m ) ( x ) = f ^ ( m − 1 ) ( x ) + f ^ m ( x ) . {\displaystyle {\hat {f}}_{(m)}(x)={\hat {f}}_{(m-1)}(x)+{\hat {f}}_{m}(x).}
Output f ^ ( x ) = f ^ ( M ) ( x ) = ∑ m = 0 M f ^ m ( x ) . {\displaystyle {\hat {f}}(x)={\hat {f}}_{(M)}(x)=\sum _{m=0}^{M}{\hat {f}}_{m}(x).}