Real-world sensor-based learning systems require uncertainty estimation that is both reliable and computationally efficient. Evidential Deep Learning (EDL) provides single-pass uncertainty estimation by modeling the class probabilities via Dirichlet distributions, where the Dirichlet parameters are predicted by a learned neural network mapping. However, this approach can lead to computational challenges, as Dirichlet expected objectives are more complex than standard supervised learning losses, complicating their analysis and implementation. We address this issue by approximating the objective of the first-order empirical risk minimization problem induced by EDL with a plug-in loss evaluated at the Dirichlet mean and show that, under mild assumptions, the approximation error decays with growing evidence for a broad class of loss functions, including mean-squared error and cross-entropy loss. As a special case, our analysis provides justification for the use of softmax in the context of uncertainty estimation, since under a particular evidence-to-Dirichlet mapping, our framework includes the standard softmax classifier. We validate the proposed simplified objectives on the Google Speech Commands dataset and show that they achieve predictive accuracy and selective prediction performance comparable to classical EDL, while being simpler to implement using standard deep learning losses and training pipelines. To the best of our knowledge, this empirical analysis is the first to obtain coverage-accuracy trade-offs for speech recognition tasks through EDL.

翻译：基于传感器的现实学习系统需要既可靠又计算高效的不确定性估计方法。证据深度学习（EDL）通过狄利克雷分布对类概率建模，其中狄利克雷参数由学习到的神经网络映射预测，从而提供单次前向传播的不确定性估计。然而，该方法可能带来计算挑战，因为狄利克雷期望目标函数比标准监督学习损失更复杂，增加了分析和实现的难度。我们通过将EDL诱导的一阶经验风险最小化目标函数近似为在狄利克雷均值处评估的可插拔损失函数来解决该问题，并证明在温和假设下，对于包括均方误差和交叉熵损失在内的广泛损失函数类别，近似误差随证据量的增加而衰减。作为特例，我们的分析为在不确定性估计中使用softmax提供了理论依据，因为在特定的证据-狄利克雷映射下，我们的框架包含了标准softmax分类器。我们在谷歌语音指令数据集上验证了所提出的简化目标函数，结果表明其预测准确性和选择性预测性能与经典EDL相当，同时使用标准深度学习损失和训练流水线更易实现。据我们所知，这是首次通过EDL在语音识别任务中获取覆盖率-准确率权衡曲线的实证分析。