$w$}}_{j_1} > 0 \right) 
\cdot P\left( {\mbox{\boldmath $X$}}_i^T {\mbox{\boldmath $w$}}_{j_1} > 0 \right) \nonumber\\
& & + P \left( {\mbox{\boldmath $X$}}_i^T {\mbox{\boldmath $w$}}_{j_1} > 0, \left[ \varphi( U_1^{(1)} ) \cdots \varphi(U_{d_1}^{(1)} ) \right] 
{\mbox{\boldmath $w$}}_{j_2} > 0, \right. \nonumber\\ 
& & \left. \cdots, \left[ \varphi( U_1^{(H-1)} ) \cdots \varphi(U_{d_{H-1}}^{(H-1)}) \right] 
{\mbox{\boldmath $w$}}_{j_H} > 0 \ \  \Big\vert \ {\mbox{\boldmath $X$}}_i^T {\mbox{\boldmath $w$}}_{j_1} \leq 0 \right) 
\cdot P\left( {\mbox{\boldmath $X$}}_i^T {\mbox{\boldmath $w$}}_{j_1} \leq 0 \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*{2cm} \left. \Big\vert \ {\mbox{\boldmath $X$}}_i^T {\mbox{\boldmath $w$}}_{j_1} > 0 \right) 
\cdot P\left( {\mbox{\boldmath $X$}}_i^T {\mbox{\boldmath $w$}}_{j_1} > 0 \right). $$ Here, the first term of the right-hand-side of Eq. (\[eqn4-4\]) 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)} ) ]^T \in {\mbox{\boldmath $R$}}^{d_1}$ such that $U_{j_1}^{(1)} = {\mbox{\boldmath $X$}}_i^T {\mbox{\boldmath $w$}}_{j_1} > 0$ is active. Also, for any $1 \leq s \leq d_1$, by denoting ${\mbox{\boldmath $X$}}_i = (x_1 \cdots x_{d_0})^T$ and ${\mbox{\boldmath $w$}}_s = 