In this work, we demonstrate how to reliably estimate epistemic uncertainty while maintaining the flexibility needed to capture complicated aleatoric distributions. To this end, we propose an ensemble of Normalizing Flows (NF), which are state-of-the-art in modeling aleatoric uncertainty. The ensembles are created via sets of fixed dropout masks, making them less expensive than creating separate NF models. We demonstrate how to leverage the unique structure of NFs, base distributions, to estimate aleatoric uncertainty without relying on samples, provide a comprehensive set of baselines, and derive unbiased estimates for differential entropy. The methods were applied to a variety of experiments, commonly used to benchmark aleatoric and epistemic uncertainty estimation: 1D sinusoidal data, 2D windy grid-world ($\it{Wet Chicken}$), $\it{Pendulum}$, and $\it{Hopper}$. In these experiments, we setup an active learning framework and evaluate each model's capability at measuring aleatoric and epistemic uncertainty. The results show the advantages of using NF ensembles in capturing complicated aleatoric while maintaining accurate epistemic uncertainty estimates.

翻译：本文展示了如何在保持捕获复杂偶然分布所需灵活性的同时，可靠地估计认知不确定性。为此，我们提出了一种正则化流集成方法，该方法在建模偶然不确定性方面处于领先水平。集成通过一组固定丢弃掩码创建，相比独立创建多个NF模型成本更低。我们演示了如何利用NF独特的结构（基分布）在不依赖样本的情况下估计偶然不确定性，提供了全面的基准方法，并推导出微分熵的无偏估计。该方法应用于一系列常用于评估偶然与认知不确定性估计的实验：一维正弦数据、二维有风网格世界（$\it{Wet Chicken}$）、$\it{Pendulum}$ 和 $\it{Hopper}$。在这些实验中，我们构建了主动学习框架，并评估了各模型在测量偶然和认知不确定性方面的能力。结果表明，NF集成在捕获复杂偶然分布的同时，能保持准确的认知不确定性估计优势。