AMissing Details453 A.1 Motivations for working with model latent space454 In Section 3, we introduced the confusion density matrix that allows us to categorize suspicious455 examples at testing time. Crucially, this density matrix relies on kernel density estimations in the456 latent space H associated to the model f through Assumption 1. Why are we performing a kernel457 density estimation in latent space rather than in input space X? The answer is fairly straightforward:458 we want our density estimation to be coupled to the model and its predictions.459 Let us now make this point more rigorous.

Uncertainty Quantification (UQ) is essential for creating trustworthy machine learning models. Recent years have seen a steep rise in UQ methods that can flag suspicious examples, however, it is often unclear what exactly these methods identify. In this work, we propose a framework for categorizing uncertain examples flagged by UQ methods in classification tasks. We introduce the confusion density matrix--a kernel-based approximation of the misclassification density--and use this to categorize suspicious examples identified by a given uncertainty method into three classes: out-of-distribution (OOD) examples, boundary (Bnd) examples, and examples in regions of high in-distribution misclassification (IDM). Through extensive experiments, we show that our framework provides a new and distinct perspective for assessing differences between uncertainty quantification methods, thereby forming a valuable assessment benchmark.

Let us now make this point more rigorous. In our experiments, we use empirical quantiles as thresholds. This is the case for all the kernels that rely on a distance (e.g. the Radial Basis Function Kernel, the Matern Knowing the category that a suspicious example belongs to, can we improve its prediction? B&I class are always the lowest among all classes. Table 4: DAUC is not the only choice in identifying OOD examples.

Uncertainty Quantification (UQ) is essential for creating trustworthy machine learning models. Recent years have seen a steep rise in UQ methods that can flag suspicious examples, however, it is often unclear what exactly these methods identify. In this work, we propose a framework for categorizing uncertain examples flagged by UQ methods in classification tasks. We introduce the confusion density matrix -- a kernel-based approximation of the misclassification density -- and use this to categorize suspicious examples identified by a given uncertainty method into three classes: out-of-distribution (OOD) examples, boundary (Bnd) examples, and examples in regions of high in-distribution misclassification (IDM). Through extensive experiments, we show that our framework provides a new and distinct perspective for assessing differences between uncertainty quantification methods, thereby forming a valuable assessment benchmark.