Auto-encoders and sampling

1) Auto-encoders aren’t probabilistic models,  then what makes it possible to successfully sample from them? (not how can we sample,  but why can we sample)

2) Can you explain how we can sample from auto-encoders using an MCMC sampling algorithm?

3) What are the advantages and drawbacks of sampling from a shallow auto-encoder compared to an RBM or from a deep auto-encoder compared to a DBN (or DBM)?

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