GBT Algorithm

$F_{k0}\left(x\right)=0, k=1, K$

For m = 1 to M do:

$$p_k\left(x\right)=\exp \left(F_k\left(x\right)\right)/{\displaystyle \sum }_{l=1}^K\text{exp}(F_l\left(x\right), k=1, K$$

For $k=1$ to $K$ do:

$${\tilde{y}}_{ik}=y_{ik}-p_k\left(x\right), i=1, N$$

$${\left\{R_{jkm}\right\}}_{j1}^J=j \text{terminal node} tree \left({\left\{{\tilde{y}}_{ik},x_i\right\}}_1^N\right)$$

$${\gamma }_{jkm}=\frac{K-1}{K}\frac{{{\displaystyle \sum }}_{x_iϵR_{jkm}}{\tilde{y}}_{ik}}{{{\displaystyle \sum }}_{x_iϵR_{jkm}}\left|{\tilde{y}}_{ik}\right|\left(1-\left|{\tilde{y}}_{ik}\right|\right)}, j=1, J$$

$$F_{km}\left(x\right)=F_{k, m-1}\left(x\right)+ {\displaystyle \sum }_{j=1}^J{\gamma }_{jkm}1\left(xϵR_{jkm}\right)$$

endFor

endFor

End Algorithm