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maximisation needs gradient ascent; gradient descent leads to local minima |
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== Reparameterization ==
[[File:Reparameterization Trick.png|thumb|300x300px|The scheme of the reparameterization trick. The randomness variable <math>{\varepsilon}</math> is injected into the latent space <math>z</math> as external input. In this way, it is possible to backpropagate the gradient without involving stochastic variable during the update.]]
To efficiently search for <math display="block">\theta^*,\phi^* = \underset{\theta,\phi}\operatorname{arg max} \, L_{\theta,\phi}(x) </math>the typical method is [[gradient
It is straightforward to find<math display="block">\nabla_\theta \mathbb E_{z \sim q_\phi(\cdot | x)} \left[\ln \frac{p_\theta(x, z)}{q_\phi({z| x})}\right]
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