Table 1.

An overview of the Pathway-based Kernel Boosting (PKB) algorithm。

1. Initialize target function as an optimal constant:

${\displaystyle F_0\left(\mathbf{x}\right)=arg\underset{r\in R}{min}\frac{1}{n}\sum _{i=1}^{N}l(y_i,r)}$

For t from 0 to T-1 (maximum number of iterations) do:

2. calculate the first and second derivatives:

${\displaystyle h_{t,i}=-\frac{y_i}{1+e^{y_i{F}_t\left({\mathbf{x}}_i\right)}},q_{t,i}=\frac{e^{y_i{F}_t\left({\mathbf{x}}_i\right)}}{{(1+e^{y_i{F}_t\left({\mathbf{x}}_i\right)})}^2}}$

3. optimize the regularized loss function in the base learner space:

${\displaystyle \widehat{f}=arg\underset{f\in \mathcal{G}}{min}{L}_R\left(\mathbf{f}\right)}$

4. find the step length with the steepest descent:

${\displaystyle \widehat{d}=arg\underset{d\in R^{+}}{min}L(\mathbf{y},{\mathbf{F}}_t+d\widehat{f})}$

5. update the target function:

${\displaystyle F_{t+1}\left(\mathbf{x}\right)=F_t\left(\mathbf{x}\right)+\nu \widehat{d}\widehat{f}\left(\mathbf{x}\right)}$

End For

return $F_T\left(\mathbf{x}\right)$