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I'm in progress working with paper "Stochastic Variational Deep Kernel Learning" NIPS 2016

and I have the problem with understanding the meaning of this normal distribution notation from part 2 Background:

in regression, one could model y(x)|f(x) ∼ N (y(x);f(x), σ2*I)

Can you please explain, what does ; mean and why y(x); is added to the notation of normal distribution in this notation and how I should understand the formula?

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It means $E(y)=f(x)$, $Var(y)=\sigma^2 \mathbf{I}$. For example a simple linear regression $y=a x +b+\epsilon,\epsilon\sim N(0,\sigma^2)$ can also be represented as $y \sim N(ax+b,\sigma^2)$

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  • $\begingroup$ thank you for the answer. However, I still don't get why the authors write N (y(x);.....). For me this adding of y(x); for Normal distribution is unclear $\endgroup$ – PasDeSence Apr 19 at 9:50
  • $\begingroup$ $N(y(x);mean,var)$ means $y(x) \sim N(mean,var)$, it's just a notation convention $\endgroup$ – Haotian Chen Apr 19 at 10:10
  • $\begingroup$ Got it! Thank you so much, @Haotian Chen $\endgroup$ – PasDeSence Apr 19 at 10:14

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