Based on the discussion in Section 1.2.1.6, we are interested in knowing the $\theta$ that minimizes $NLL(\theta)=-\frac{1}{N} \sum\limits_{n=1}^{N} \log p(y_{n}|f(x_{n};\theta))$, therefore, we should calculate the conditional probability distribution of $p(y|f(x;\theta))$ rather than $p(y_{n}|x;\theta)$ in the left part of equation 1.19.
murphyk
commented
5 months ago
Based on the discussion in Section 1.2.1.6, we are interested in knowing the $
\theta$ that minimizes $NLL(\theta)=-\frac{1}{N} \sum\limits_{n=1}^{N} \log p(y_{n}|f(x_{n};\theta))$, therefore, we should calculate the conditional probability distribution of $p(y|f(x;\theta))$ rather than $p(y_{n}|x;\theta)$ in the left part of equation 1.19.