Given a conditional prior $p_{\theta}(z|x)$ and a posterior distribution $p_{\phi}(z|x,y)$. I want to prameterize both of them using deep neural network. And the objective function of $\theta$ is $\max_{\theta} E_{p_{\phi}}\log p_{\theta}(z|x)$where $z$ is a vector of size $k$.since the objective function is equivalent to $H(p_{\phi})+KL(p_{\phi}||p_{\theta})$.Thus we can just take the KL-divergence term into account when we want to take the gradient of the objective function with respect to $\theta$. But I have no idea about what should be following. I wonder how can I use the re-parameterization trick to construct a differentiable estimator with respect to $\theta$? Thanks in advance!
How to measure the cross-entropy of prior and posterior distribution with re-parameterization trick?
machine learning;deep learning;optimization;bayesian