In a text i read
We shall further assume that the distribution of the target data is Gaussian. More specifically, we assume that the target variable $t_k$ is given by some deterministic function of $\mathbf{x}$ with added Gaussian noise $\varepsilon$, so that $$t_k=h_k(\mathbf{x})+\varepsilon_k.$$
Now I'm wondering if the two concepts are equivalent i.e. having a normal distribution is the same of being sum of a deterministic function and a term with normal distribution?
If you add a constant to a Gaussian-distributed variable, you get another Gaussian-distributed variable, with a different mean. A Gaussian noise is understood as a Gaussian-distributed random variable with zero mean. So the variable $t_k$ indeed follows a Gaussian distribution, with mean $h_k(\mathbb x)$.