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I am reading the paper SV2P - Stochastic Varaiational Video Prediction (https://arxiv.org/abs/1710.11252). In it the authors use the loss shown in the image: image form https://arxiv.org/abs/1710.11252

Why do we need expectation in the reconstruction loss? I think that the loss is similar to the one used in the VAE paper.

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It's because $z$ is a random variable, and the term is a function of $z$. So, without the expectation, the $\log$ term would be a random variable, and you can't use that as a loss; the loss needs to be a number. You can use its mean (its expectation).

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