We assume, there exists a C Hsuchthat ˆp(y|x) =p(y|x),i.e.,p(y|x)isrealizable; 3. We can compute an empirical risk minimizer, i.e., we can determine aCS H which minimizes(1)foragivensampleS. In the bottom row example, an experiment analogous to the top row but with a noisier version ofthe data is presented. In practice this requires the inclusion of a smallε > 0 in the denominator to circumvent numerical problems in the logarithmic loss terms. In our experiments this also results in a high aleatoric uncertaintyfarawayfrom thein-distribution asallestimated probabilities uniformly take the lower bound's valueε. InthetoproweachGaussian has its own class assigned, resulting in 9 classes and in the bottom row disconnected Gaussians were assigned to 3 classes in total.