Recall that when training VAEs, we minimize the negative ELBO, an upper bound to$$the negative log likelihood. Show that the negative log likelihood, $$Ex$$pdata$($x$)[$log p$\backslash$theta $($x$)],$ can be written as a$$KL divergence plus an additional term that is constant with respect to $\backslash$theta $.$ We are asking if the KL divergence$$is equal to LG$,$ so after finding the expression, you will be able to deduce that. Note that the constant term$$is constant with respect to $\backslash$theta $,$ so it can be another expectation.$$Does this mean that a VAE decoder trained with ELBO and a GAN generator trained with the LG defined$$in the previous part $3$c are implicitly learning the same objective? Explain.