Improvements! And another figure.

content/method/method.tex

@@ -251,6 +251,23 @@ of the two populations, turning a TPR@FPR objective into a FPR@TPR one. Because
 two objectives are therefore interchangeable at the implementation level, all derivations
 and implementation details below are given for \eqref{eq:roll-tpr-at-fpr} only;
 \eqref{eq:roll-fpr-at-tpr} follows by the same transformation applied to the inputs.
+\Cref{fig:roll-principle} provides a geometric view of \eqref{eq:roll-tpr-at-fpr}.
+
+\begin{figure}[H]
+  \centering
+  \includegraphics[width=0.85\textwidth]{content/method/figures/roll_principle.png}
+  \caption{Geometric picture of the ROLL TPR@FPR objective. \textit{Upper}: score PDFs
+    for the negative (blue, $y=0$) and positive (orange, $y=1$) classes. The operating
+    threshold $\tau$ (dashed) is placed at the $(1-\alpha)$-quantile of the negative
+    class, so that exactly $\alpha$ fraction of negative scores exceed it ($\operatorname{FPR}=\alpha$).
+    The shaded area under the positive-class PDF to the left of $\tau$ is
+    $\hat{F}_1(\tau)$ --- the ROLL loss we minimize. Tick marks along the bottom represent
+    observed positive-class scores. \textit{Lower}: corresponding CDFs $\hat{F}_0$ (blue)
+    and $\hat{F}_1$ (orange). Reading horizontally at height $1-\alpha$ on $\hat{F}_0$
+    gives $\tau$; reading $\hat{F}_1(\tau)$ off $\hat{F}_1$ at the same $\tau$ gives the
+    loss; the distance from $\hat{F}_1(\tau)$ to $1$ is the resulting TPR.}
+  \label{fig:roll-principle}
+\end{figure}
 
 We now derive the gradient of \eqref{eq:roll-tpr-at-fpr} with respect to $f_\theta(\mathbf{x}_i)$.