e is the expected value of <span class="math inline">\(\tilde{y}\)</span> given the predictors and training data, <span class="math display">\[\begin{eqnarray*}
\hat{\tilde{y}}_n
&amp; = &amp; \mathbb{E}[\tilde{y}_n \mid \tilde{x}_n, x, y]
\\[4pt]
&amp; \approx &amp; \frac{1}{M} \sum_{m = 1}^M \tilde{y}_n^{(m)}
\end{eqnarray*}\]</span> where <span class="math inline">\(\tilde{y}_n^{(m)}\)</span> is drawn from the data model <span class="math display">\[
\tilde{y}_n^{(m)}
\sim p(\tilde{y}_n \mid \tilde{x}_n,