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Let's assume the probability distributions are Gaussian (or normal) distributions. In other words, in the Bayes' rule \begin{align} p(z|x)=\frac{p(x|z)p(z)}{p(x)} \tag{1}\label{1} \end{align} The posterior $p(z|x)$, the likelihood $p(x|z)$, the prior $p(z)$ and the evidence (or marginal) $p(x)$ are Gaussian distributions. You can assume this because ...


3

From this document, as you found here, $X$ is an observed variable and $Z$ is a hidden variable; $p(X)$ is the density function of $X$. The posterior distribution of the hidden variables can then be written as follows using the Bayes’ Theorem: $$p(Z|X) = \frac{p(X|Z)p(Z)}{p(X)} = \frac{p(X|Z)p(Z)}{\int_Zp(X,Z)}$$ Now base on what you post, if we denote ...


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The number of dimensions is a hyperparameter of your model, and you should do a hyperparameter search, like with any other parameters. There's also a tradeoff between dimension and training speed, so it should be small enough to be trainable in a reasonable time.


3

With Generative Adversarial Networks, all the generator cares about is fooling the discriminator. There's no requirement to be clever, or exhaustive, or make efficient use of the input space. As long as the discriminator returns "real" (vs. "fake") the generator "wins". The hope is that as the generator and discriminator are trained simultaneously, each ...


3

You can know it better, if you know the concept of entropy: Information entropy is the average rate at which information is produced by a stochastic source of data. The information content (also called the surprisal) of an event ${\displaystyle E}$ is an increasing function of the reciprocal of the ${\displaystyle p(E)}$ of the event, precisely ${\...


2

The use of KL provides a more intuitive way of what the ELBO is attempting to maximize. Basically, we want to find a posterior approximation such that $p(z\mid x) \approx q(z)\in\mathcal{Q}$ $$KL(q(z)\parallel p(z\mid x)) \rightarrow \min_{q(z)\in\mathcal{Q}}$$ As a result of this, while finding this optimal posterior approximation, we maximize the ...


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The only disadvantage and difference between these generative models and the method you describe, is the input. You describe inputting tags, where as for a GAN, or VAE, the generation segment of the model takes in some representation of a probability distribution. For a GAN, it's mostly random noise, and for a VAE it is some latent space (see nbros answer). ...


1

I will only focus on the VAE because I am more familiar with it, but the explanations may also apply to the GAN and other generative models. In the case of the VAE, you train a neural network not only to generate images but to represent them compactly in a so-called latent space, so you train the VAE to do dimensionality reduction. More precisely, the VAE ...


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