\\ &=& P \left( {\mbox{\boldmath $X$}}_i^T {\mbox{\boldmath $w$}}_{j_0} > 0, \left[ \varphi( U_0^{(0)} ) \cdots \varphi(U_{d_0}^{(0)} ) \right]  {\mbox{\boldmath $w$}}_{j_0} > 0, \right. \nonumber\\  & & \left. \cdots, \left[ \varphi( U_0^{(H-0)} ) \cdots \varphi(U_{d_{H-0}}^{(H-0)}) \right]  {\mbox{\boldmath $w$}}_{j_H} > 0 \right) \ \  (\mbox{from Eq.} (\ref{eqn0-0})) \nonumber\\ &=& P \left( {\mbox{\boldmath $X$}}_i^T {\mbox{\boldmath $w$}}_{j_0} > 0, \left[ \varphi( U_0^{(0)} ) \cdots \varphi(U_{d_0}^{(0)} ) \right]  {\mbox{\boldmath $w$}}_{j_0} > 0, \right. \nonumber\\  & & \left. \cdots, \left[ \varphi( U_0^{(H-0)} ) \cdots \varphi(U_{d_{H-0}}^{(H-0)}) \right]  {\mbox{\boldmath $w$}}_{j_H} > 0 \ \ \Big\vert \ {\mbox{\boldmath $X$}}_i^T {\mbox{\boldmath $w$}}_{j_0} > 0 \right)  \cdot P\left( {\mbox{\boldmath $X$}}_i^T {\mbox{\boldmath $w$}}_{j_0} > 0 \right) 