Uncertainty quantification (UQ) is crucial for deploying machine learning models in high-stakes applications, where overconfident predictions can lead to serious consequences. An effective UQ method must balance computational efficiency with the ability to generalize across diverse scenarios. Evidential deep learning (EDL) achieves efficiency by modeling uncertainty through the prediction of a Dirichlet distribution over class probabilities. However, the restrictive assumption of Dirichlet-distributed class probabilities limits EDL's robustness, particularly in complex or unforeseen situations. To address this, we propose \textit{flexible evidential deep learning} ($\mathcal{F}$-EDL), which extends EDL by predicting a flexible Dirichlet distribution -- a generalization of the Dirichlet distribution -- over class probabilities. This approach provides a more expressive and adaptive representation of uncertainty, significantly enhancing UQ generalization and reliability under challenging scenarios. We theoretically establish several advantages of $\mathcal{F}$-EDL and empirically demonstrate its state-of-the-art UQ performance across diverse evaluation settings, including classical, long-tailed, and noisy in-distribution scenarios.

翻译：不确定性量化对于在高风险应用中部署机器学习模型至关重要，在这些应用中，过度自信的预测可能导致严重后果。一种有效的不确定性量化方法必须在计算效率与跨多样化场景的泛化能力之间取得平衡。证据深度学习通过预测类别概率上的狄利克雷分布来建模不确定性，从而实现了效率。然而，狄利克雷分布类别概率的限制性假设限制了证据深度学习的鲁棒性，尤其是在复杂或不可预见的情况下。为解决这一问题，我们提出了 \textit{灵活证据深度学习} ($\mathcal{F}$-EDL)，该方法通过预测类别概率上的灵活狄利克雷分布——狄利克雷分布的一种推广——来扩展证据深度学习。这种方法提供了更具表达力和适应性的不确定性表示，显著增强了在挑战性场景下的不确定性量化泛化能力和可靠性。我们从理论上确立了 $\mathcal{F}$-EDL 的若干优势，并通过实验证明了其在多样化评估设置（包括经典、长尾和有噪声的分布内场景）中具有最先进的不确定性量化性能。