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I know that the notation $\mathcal{N}(\mu, \sigma)$ stands for a normal distribution. But I'm reading the book "An Introduction to Variational Autoencoders" and in it, there is this notation: $$\mathcal{N}(z; 0, I)$$ What does it mean?

picture of the book: picture of the book An Introduction to Variational Autoencoders

Peyman
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1 Answers1

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It means that $z$ has a (multivariate) normal distribution with 0 mean and identity covariance matrix. This essentially means each individual element of the vector $z$ has a standard normal distribution.

David
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  • Comments are not for extended discussion; this conversation has been [moved to chat](https://chat.stackexchange.com/rooms/118283/discussion-on-answer-by-david-ireland-what-does-the-notation-mathcalnz-mu). – nbro Jan 10 '21 at 15:52