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Is there any reason for choosing the posterior 𝑞(𝑧|𝑥) as normal distribution in variational autoencoder? or is it just for convenience?

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The "requirements" for the posterior is that

  1. You can efficiently compute the KL divergence from the posterior to the prior. Since the prior is usually chosen to be a standard normal distribution, choosing a normal posterior makes things easy

  2. You can reparameterize sampling from the posterior. For example, instead of sampling from $\mathcal{N}(\mu, \sigma^2)$, you can compute $\mu + \sigma \epsilon$, with epsilon drawn from a standard normal. This is also easily done with the normal distribution, but not with many others.

Of course people have developed techniques to use more sophisticated prior and posterior distributions with VAEs, such as mixtures of gaussians, but this requires nontrivial work.

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