\begin{equation}
\begin{aligned}
p(u_1,\ldots,u_d  , v_1, \ldots, v_G | v_0 ; \boldsymbol{\theta} ) &= p(u_1,\ldots,u_d  | v_1, \ldots, v_G; \boldsymbol{\theta}) p(v_1, \ldots, v_G | v_0; \boldsymbol{\theta}),
\end{aligned}
\end{equation}
