SlowGuess/NeurIPS_2023_OCR huggingface dataset:
Using such expression, we can estimate the AUC and train model to directly optimize the AUC. It loses the focus on a specific trade-off between precision and recall, but instead optimizes overall performance. We trained a RealNVP model on a 2D 8 Gaussians example, similar to Section 6. We observe in Figure 27(d) that while the model trained to minimize the AUC performs poorly in terms of  $\lambda = 0.1$  and  $\lambda = 1$ . However, we can clearly see that the AUC is greater and the model performs better in  $\lambda = 1$  than the model trained for  $\lambda = 1$  itself. We can also observe in Figure 27(d), the resulting model.
Figure E.25: Illustration of the change of variable to compute the AUC. Instead of parametrising the frontier  $\partial \mathrm{PRD}(P,\hat{P})$  with  $\lambda \in \mathbb{R}\cup [0,\infty ]$ , we take  $\theta \in [0,\frac{\pi}{2} ]$  with  $\lambda = \tan \theta$ .
Figure E.26: PR-Curves corresponding to the models represented in Figure E.
(d) AUC