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What does this E symbol mean?

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It is from the GAN paper.

Tim
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Nathan
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  • Uppercase "E" is one of the very few symbols in statistics that almost always have the same meaning: [expected value](https://en.wikipedia.org/wiki/Expected_value). – Tim Aug 10 '17 at 06:51
  • @tim thanks, maybe leave that as an answer so I can accept? – Nathan Aug 10 '17 at 07:48
  • I love that we googled this exact thing, GAN paper and everything. – Script Kitty Jul 17 '18 at 22:07

1 Answers1

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In mathematics and statistics many symbols are used to denote different things, e.g. $\pi$ does not always have to be the $3.14.15...$ constant. However the uppercase "E" (written in many forms, e.g. $\mathbb{E}, E, \mathrm{E}$) is almost always used in statistics to denote the expected value. In the case of your equation

$$ \mathbb{E}_{x\sim p_\text{data}(x)}\left( \log D(x) \right) $$

means: the expected value of $\log D(x)$ given $x$ distributed as $p_\text{data}(x)$.

Tim
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