The Evidential Regression Network (ERN) represents a novel approach that integrates deep learning with Dempster-Shafer's theory to predict a target and quantify the associated uncertainty. Guided by the underlying theory, specific activation functions must be employed to enforce non-negative values, which is a constraint that compromises model performance by limiting its ability to learn from all samples. This paper provides a theoretical analysis of this limitation and introduces an improvement to overcome it. Initially, we define the region where the models can't effectively learn from the samples. Following this, we thoroughly analyze the ERN and investigate this constraint. Leveraging the insights from our analysis, we address the limitation by introducing a novel regularization term that empowers the ERN to learn from the whole training set. Our extensive experiments substantiate our theoretical findings and demonstrate the effectiveness of the proposed solution.

翻译：证据回归网络（ERN）是一种将深度学习与Dempster-Shafer理论相结合的新型方法，用于预测目标并量化相关的不确定性。在理论指导下，必须采用特定的激活函数来确保非负值，这一约束通过限制模型从所有样本中学习的能力，折损了模型性能。本文对该局限性进行了理论分析，并提出了一种改进方法以克服该问题。首先，我们定义了模型无法有效从样本中学习的区域。随后，我们深入分析了ERN并研究了这一约束。基于分析结果，我们引入了一种新颖的正则化项，使ERN能够从整个训练集中学习，从而解决了该局限性。广泛的实验验证了我们的理论发现，并证明了所提方法的有效性。