Modern deep neural networks are prone to being overconfident despite their drastically improved performance. In ambiguous or even unpredictable real-world scenarios, this overconfidence can pose a major risk to the safety of applications. For regression tasks, the regression-by-classification approach has the potential to alleviate these ambiguities by instead predicting a discrete probability density over the desired output. However, a density estimator still tends to be overconfident when trained with the common NLL loss. To mitigate the overconfidence problem, we propose a loss function, hinge-Wasserstein, based on the Wasserstein Distance. This loss significantly improves the quality of both aleatoric and epistemic uncertainty, compared to previous work. We demonstrate the capabilities of the new loss on a synthetic dataset, where both types of uncertainty are controlled separately. Moreover, as a demonstration for real-world scenarios, we evaluate our approach on the benchmark dataset Horizon Lines in the Wild. On this benchmark, using the hinge-Wasserstein loss reduces the Area Under Sparsification Error (AUSE) for horizon parameters slope and offset, by 30.47% and 65.00%, respectively.

翻译：现代深度神经网络尽管性能大幅提升，但仍容易产生过度自信。在模糊甚至不可预测的现实场景中，这种过度自信可能对应用安全构成重大风险。对于回归任务，通过分类方法进行回归（regression-by-classification）具有缓解这类模糊性的潜力——该方法预测目标输出的离散概率密度而非连续值。然而，当使用常见的负对数似然（NLL）损失训练时，密度估计器仍倾向于过度自信。为缓解过度自信问题，我们提出一种基于Wasserstein距离的损失函数——Hinge-Wasserstein。与现有工作相比，该损失显著提升了偶然不确定性与认知不确定性的质量。我们在一个可分别控制两种不确定性的合成数据集上验证了新损失的性能。此外，作为现实场景的验证，我们在基准数据集Horizon Lines in the Wild上评估了我们的方法。在该基准测试中，使用Hinge-Wasserstein损失使水平线参数斜率和偏移量的稀疏化误差曲线下面积（AUSE）分别降低了30.47%和65.00%。