# Questions tagged [variational-autoencoder]

For questions related to variational auto-encoders (VAEs). The first VAE was proposed in "Auto-Encoding Variational Bayes" (2013) by Diederik P. Kingma and Max Welling. There are several other VAEs, for example, the conditional VAE.

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### How does the VAE learn p(x,z)?

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 $\mathbf{x}$...
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### What is the most suitable measure of the distance between two VAE's latent spaces?

The problem I'm trying to solve is as follows. I have two separate domains, where inputs do not have the same dimensions. However, I want to create a common feature space between both domains using ...
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### What are the roles of the prior $\mathrm{p}(\mathbf{z})$ in a VAE?

I know the encoder is variational posterior $q_{\phi}(\mathbf{z} \mid \mathbf{x})$. I also know that the decoder represents the likelihood: $p_{\theta}(\mathbf{x} \mid \mathbf{z})$. My question is ...
63 views

### How to determine the quality of synthetic data?

I'm working on a VAE model to produce synthetic data of X-Ray diffraction spectrums. I try to figure out how I can measure the quality of the spectrums. The goal would be to produce synthetic data ...
33 views

### variational autoencoder - decoder output for images

Following the standard setup/notation for a VAE, let $z$ denote the latent variables, $q$ as the encoder, $p$ as the decoder, and $x$ as the label. Let the objective be to maximize the ELBO, where a ...
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### Building Gaussian Mixture VAE using pytorch

I am trying to implement GMM-VAE model using torch. Basically I have a problem implementing for instance equation (1c) where the posterior distribution $p(x|z,w)$ is a Gaussian with the mean and ...
27 views

### Are some low dimensional distributions known to be hard to model with VAEs?

I am trying to implement a toy VAE project. My goal is to use a VAE to model the moon dataset from scikit-learn, with an extra constant (but noisy) z-dimension. To this end I use an approximate ...
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### Tensorflow Probability Implementation of Automatic Differentiation Variational Inference with Mixtures

In this paper, the authors suggest using the following loss instead of the traditional ELBO in order to train what basically is a Variational Autoencoder with a Gaussian Mixture Model instead of a ...
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### Why is the prior on the latent variable standard gaussian in VAE?

While training a standard VAE, we assume that the prior on the latent variable Z is the standard gaussian and we use KL divergence to push the posterior as close as possible to the standard gaussian. ...
17 views

### Types of decoder parametrizations in VAE for continuous data

I'm wondering what are the different choices of parametrizations available for the decoder in a variational autoencoder. If the data is discrete, you can just output probabilities for each class, so ...
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### Why does KL divergence not satisfy the triangle inequality?

$D_{KL}=\sum_i p(x_i)log(p(x_i)/q(x_i)$ Also can't you make it satisfy the triangle inequality by taking the absolute value of the information at every point?
### In this VAE formula, why do $p$ and $q$ have the same parameters?
In $$\log p_{\theta}(x^1,...,x^N)=D_{KL}(q_{\theta}(z|x^i)||p_{\phi}(z|x^i))+\mathbb{L}(\phi,\theta;x^i),$$ why does $p(x^1,...,x^N)$ and $q(z|x^i)$ have the same parameter $\theta?$ Given that $p$ is ...