Uncertainty estimation (UE), as an effective means of quantifying predictive uncertainty, is crucial for safe and reliable decision-making, especially in high-risk scenarios. Existing UE schemes usually assume that there are completely-labeled samples to support fully-supervised learning. In practice, however, many UE tasks often have no sufficiently-labeled data to use, such as the Multiple Instance Learning (MIL) with only weak instance annotations. To bridge this gap, this paper, for the first time, addresses the weakly-supervised issue of Multi-Instance UE (MIUE) and proposes a new baseline scheme, Multi-Instance Residual Evidential Learning (MIREL). Particularly, at the fine-grained instance UE with only weak supervision, we derive a multi-instance residual operator through the Fundamental Theorem of Symmetric Functions. On this operator derivation, we further propose MIREL to jointly model the high-order predictive distribution at bag and instance levels for MIUE. Extensive experiments empirically demonstrate that our MIREL not only could often make existing MIL networks perform better in MIUE, but also could surpass representative UE methods by large margins, especially in instance-level UE tasks.

翻译：不确定性估计（UE）作为量化预测不确定性的有效手段，对高风险场景下的安全可靠决策至关重要。现有UE方案通常假设存在完全标注的样本以支持全监督学习。然而在实践中，许多UE任务往往缺乏足够标注数据，例如仅具有弱实例标注的多实例学习（MIL）。为填补这一空白，本文首次解决了多实例UE（MIUE）中的弱监督问题，并提出了一种新的基线方案——多实例残差证据学习（MIREL）。具体而言，在仅具有弱监督的细粒度实例UE中，我们通过对称函数基本定理推导出多实例残差算子。基于该算子推导，我们进一步提出MIREL，联合建模包级和实例级的高阶预测分布以实现MIUE。大量实验表明，我们的MIREL不仅能使现有MIL网络在MIUE中表现更优，还能在实例级UE任务中显著超越代表性UE方法。