# Don't understand one particular normal distribution notation from opaper Stochastic Variational Deep Kernel Learning, help needed

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?

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 $$y \sim N(ax+b,\sigma^2)$$
• $N(y(x);mean,var)$ means $y(x) \sim N(mean,var)$, it's just a notation convention – Haotian Chen Apr 19 at 10:10