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Good article, but I had to get rid of a bunch of unnecessary fluff in the Architecture section which obscured the point (diff : https://en.wikipedia.org/w/index.php?title=Variational_autoencoder&type=revision&diff=1040705234&oldid=1039806485 ). 26 August 2021
I disagree, the article really needs attention, it is very hard to understand the "Formulation" part now. I propose the following changes for the first paragraphs, but subsequent ones need revision as well:
From a formal perspective, given an input <s>dataset</s> vector <math>\mathbf{x}</math> <s>characterized by</s> '''from''' an unknown probability <s>function</s> '''distribution''' <math>P(\mathbf{x})</math> <s>and a multivariate latent encoding vector <math>\mathbf{z}</math> </s>, the objective is to model <s>the data</s> <math>P(\mathbf{x})</math> as a '''parametric''' distribution with density <math>p_\theta(\mathbf{x})</math>, where <math>\theta</math> is a vector of parameters to be learned. <s>defined as the set of the network parameters.</s>
For the parametric model we assume that each <math>\mathbf{x}</math> is associated with (arises from) a latent encoding vector <math>\mathbf{z}</math>, and we write <math>p_\theta(\mathbf{x}, \mathbf{z})</math> to denote their joint density.
<s>It is possible to formalize this distribution as</s> We can then write
: <math>p_\theta(\mathbf{x}) = \int_{\mathbf{z}}p_\theta(\mathbf{x,z}) \, d\mathbf{z} </math>
<s>where <math>p_\theta</math> is the [[Model evidence|evidence]] of the model's data with [[Marginalization (probability)|marginalization]] performed over unobserved variables and thus <math>p_\theta(\mathbf{x,z})</math> represents the [[joint distribution]] between input data and its latent representation according to the network parameters <math>\theta</math>.</s>
[[Special:Contributions/193.219.95.139|193.219.95.139]] ([[User talk:193.219.95.139|talk]]) 10:18, 2 October 2021 (UTC)
== Observations and suggestions for improvements ==
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