{\mbox{\boldmath $w$}}_{j_2} > 0, \cdots, \left[ \varphi( U_1^{(H-1)} ) \cdots \varphi(U_{d_{H-1}}^{(H-1)}) \right] 
{\mbox{\boldmath $w$}}_{j_H} > 0 \ \ \right. \nonumber\\
& & \hspace*{2cm} \left. 
\Big\vert \ {\mbox{\boldmath $X$}}_i^T {\mbox{\boldmath $w$}}_{j_1} > 0, w_{j_1 j_0} = \lambda_1, 
\cdots, w_{j_H j_{H-1} } = \lambda_H \right) \cdot \nonumber\\
& & \hspace*{2cm} P\left( {\mbox{\boldmath $X$}}_i^T {\mbox{\boldmath $w$}}_{j_1} > 0 \ \Big\vert \ w_{j_1 j_0} = \lambda_1, 
\cdots, w_{j_H j_{H-1} } = \lambda_H \right) \nonumber\\
&=& P \left( \left[ \varphi( U_1^{(1)} ) \cdots \varphi(U_{d_1}^{(1)} ) \right] 
{\mbox{\boldmath $w$}}_{j_2} > 0, \cdots, \left[ \varphi( U_1^{(H-1)} ) \cdots \varphi(U_{d_{H-1}}^{(H-1)}) \right] 
{\mbox{\boldmath $w$}}_{j_H} > 0 \right. \nonumber\\
& & \hspace*{0.5cm} \left. \Big\vert \ {\mbox{\boldmath $X$}}_i^T {\mbox{\boldmath $w$}}_{j_1} > 0, 
\ w_{j_1 j_0} = \lambda_1, \cdots, w_{j_H j_{H-1} } = \lambda_H \right)  \cdot P\left( {\mbox{\boldmath $X$}}_i^T {\mbox{\boldmath $w$}}_{j_1} > 0 \ \Big\vert \ w_{j_1 j_0} = \lambda_1 \right). \\
& & (\mbox{$w_{j_2 j_1} = \lambda_2, \cdots, w_{j_H j_{H-1}} = \lambda_H$ are removed 
because they are independent of ${\mbox{\boldmath $w$}}_{j_1}$ } ) \nonumber\end{aligned}$$ Here, the first term of the right-hand-side of Eq. (\[eqn4-8\]) represents the probability that the path passing through the $H-1$ hidden neurons $j_2, \cdots, j_H$ for the input training pattern $[ \varphi( U_1^{(1)} ) \cdots \varphi(U_{d_1}^{(1)} ) 