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1 vote
1 answer
359 views

Do we use two distinct layers to compute the mean and variance of a Gaussian encoder/decoder in the VAE?

I am looking at appendix C of the VAE paper: It says: C.1 Bernoulli MLP as decoder In this case let $p_{\boldsymbol{\theta}}(\mathbf{x} \mid \mathbf{z})$ be a multivariate Bernoulli whose ...
a12345's user avatar
  • 243
2 votes
3 answers
224 views

Are the authors of the VAE paper writing the PDFs as a function of the random variables?

Usually, I see the conventions: discrete random variable is denoted as $X$, the pmf is written as $P(X=x)$ or $p(X=x)$ or $p_{X}(x)$ or $p(x)$, where $x$ is an instance of $X$ a continuous random ...
a12345's user avatar
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1 vote
1 answer
660 views

How is the VAE related to the Autoencoding Variational Bayes (AEVB) algorithm?

I am familiar with the variational autoencoder, but not totally clear on what exactly the AEVB is. In the original VAE paper (by Kingma and Welling), he uses both the terms variational autoencoder and ...
a12345's user avatar
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4 votes
1 answer
1k views

How does the VAE learn a joint distribution?

I found the following paragraph from An Introduction to Variational Autoencoders sounds relevant, but I am not fully understanding it. A VAE learns stochastic mappings between an observed $\mathbf{x}$...
a12345's user avatar
  • 243
2 votes
2 answers
511 views

In variational autoencoders, what does p(x|z) mean?

If $x \sim \mathcal{N}(\mu,\,\sigma^{2})$, then it is a continuous variable, and therefore $P(x) = 0$ for any x. One can only consider things like $P(x<X)$ to get a probability greater than 0. So ...
IttayD's user avatar
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2 votes
1 answer
69 views

What is the "contradictory loss" in the "Old Photo Restoration via Deep Latent Space Translation" paper?

In page 4 of the paper Old Photo Restoration via Deep Latent Space Translation, it says the encoder $E_{R,X}$ of $VAE_1$ tries to fool the discriminator with a contradictory loss to ensure that $R$ ...
Robert's user avatar
  • 21
1 vote
1 answer
73 views

What is the main contribution of the paper Disentangling by Factorising?

Considering the paper Disentangling by Factorising, in addition to introducing a new model for Disentangled Representation Learning, FactorVAE (see figure), what is the main theoretical contribution ...
Nicola Bernini's user avatar