泰勒图与Wasserstein距离用于模型评估
Taylor Diagram and Wasserstein Distance for Model Evaluation
- University of Idaho（爱达荷大学）
- Colorado State University（科罗拉多州立大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出Wasserstein-Taylor图，将Wasserstein距离和分位数相关系数融入泰勒图框架，实现不同规模数据及模型与观测的分布视角比较，并证明经验分位数相关系数的收敛性。
AI中文摘要：
泰勒图用于评估和比较预测模型与观测数据，在气候和环境科学中有许多应用。三个感兴趣的统计量——中心化均方根误差、标准差和积矩相关系数——通过余弦定律相关联；泰勒图利用这一事实，可以在二维图中可视化所有三个统计量而不丢失任何信息。在这项工作中，我们提出了一种新颖的模型评估工具——Wasserstein-Taylor图——通过将最优传输中的Wasserstein距离整合到泰勒图框架中形成。该工具基于以下事实：如果将中心化均方根误差和积矩相关系数分别替换为中心化2-Wasserstein距离和分位数相关系数，余弦定律在泰勒图中仍然成立。这种Wasserstein-Taylor图的优势在于，可以利用Wasserstein距离提供的分布视角来比较不同大小的观测数据集和预测数据集，甚至可以将统计模型与仅有观测数据进行比较。我们进一步证明了经验测度上的分位数相关系数收敛到采样测度上的分位数相关系数。
英文摘要：
The Taylor diagram is used to evaluate and compare predictive models with observed data and has many applications in climate and environmental sciences. Three statistics of interest--the centered root-mean-squared error, standard deviation, and the product-moment correlation coefficient--are related by the law of cosines; Taylor diagrams leverage this fact to allow visualization of all three statistics in a two-dimensional plot without any loss of information. In this work, we present a novel model evaluation tool--the Wasserstein-Taylor diagram--formed from integrating the Wasserstein distance from optimal transport into a Taylor diagram framework. This tool is built upon the fact that the law of cosines still holds in the Taylor diagram if the centered root-mean-squared error and product-moment correlation coefficient are replaced by the centered 2-Wasserstein distance and quantile correlation coefficient, respectively. The advantage of this Wasserstein-Taylor diagram is that one can use the distribution perspective afforded by the Wasserstein distance to compare observed and predicted data sets of different sizes and even to compare statistical models with only observed data. We further show that the quantile correlation coefficient on empirical measures converges to the quantile correlation coefficient on the sampled measures.
