\begin{equation}
\begin{aligned}
\mathcal{L}^{\mathrm{r}}_{\mathrm{ELBO}} := & \underbrace{\mathbb{E}_{q_{\phi_{\mathrm{r}}}(\boldsymbol{z}_{\mathrm{r}} \mid \boldsymbol{x}_{\mathrm{r}})}\Big[\log p_{\theta_{\mathrm{r}}}(\boldsymbol{x}_{\mathrm{r}} \mid \boldsymbol{z}_{\mathrm{r}})}_{\mathcal{L}_{\mathrm{R}}^{\mathrm{r}}}\Big] \\
 & - \beta \underbrace{D_{K L}\big(q_\phi(\boldsymbol{z}_{\mathrm{r}} \mid \boldsymbol{x}_{\mathrm{r}}) || p(\boldsymbol{z})}_{\mathcal{L}_{\mathrm{I}}^{\mathrm{r}}}\big).
\end{aligned}
\label{eq:raw_eblo}
\end{equation}
