用于标量场数据鲁棒不确定性可视化的分布无关等轮廓置信边界
Distribution-Agnostic Isocontour Confidence Bounds for Robust Uncertainty Visualization of Scalar Field Data
- Oak Ridge National Laboratory（橡树岭国家实验室）
- U. of I. Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
针对标量场不确定性可视化的缺陷，提出分布无关的 Hoeffding 置信带方法，其在合成与真实数据集上表现出准确捕捉真实值且计算高效的优势。
AI中文摘要：
不确定性可视化已被证明对于传达从标量场提取特征的可靠性至关重要。由等轮廓表示的特征中，平均等轮廓缺乏空间不确定性的指示，而 spaghetti 等轮廓图可能会变得杂乱且难以解释。现有方法依赖特定分布假设（如高斯分布和非参数自助法）来提供紧凑、无杂乱的空间置信边界，但对于样本数量有限的集合，这些方法可能会低估不确定性。我们提出一种鲁棒的、分布无关的 Hoeffding 置信带，作为一种新颖的补充（而非竞争）技术，以缓解基于分布假设可能产生的误导性不确定性边界。该方法使用 Hoeffding 不等式构造逐顶点的置信边界，并将其传播以生成等轮廓置信带。在合成和真实集合数据集上的结果表明，Hoeffding 置信带虽然宽松，但能准确捕捉高斯法和自助法替代方法可能遗漏的潜在真实值，同时保持计算效率。
英文摘要：
Uncertainty visualization has been shown to be pivotal for conveying the reliability of features extracted from scalar fields. Features represented by individual isocontours and mean isocontours lack an indication of spatial uncertainty, whereas spaghetti isocontour plots can become cluttered and difficult to interpret. Existing methods relying on specific distribution assumptions, such as Gaussian and nonparametric bootstrap, provide compact, clutter-free spatial confidence bounds but may underestimate uncertainty for ensembles with a limited number of samples. We introduce a robust, distribution-agnostic Hoeffding confidence band as a novel complementary (and not competitive) technique to mitigate potentially misleading uncertainty bounds that may arise from distribution-based assumptions. The approach constructs vertex-wise confidence bounds using Hoeffding's inequality and propagates them to generate isocontour confidence bands. Results on synthetic and real ensemble datasets show that the Hoeffding confidence bands are loose but accurately capture underlying true values that may be missed by the Gaussian and bootstrap alternatives, while remaining computationally efficient.
