对距离度量的信息量进行排序
Ranking the information content of distance measures
摘要：
真实世界的数据通常包含大量的特征，这些特征在性质、相关性和度量单位上往往是异构的。当评估数据点之间的相似性时，可以使用这些特征的子集来构建各种距离度量。在许多统计学习方法中，使用最少的特征但仍然保留关于系统的足够信息是至关重要的，特别是当数据稀疏时。我们引入了一个统计测试，可以评估使用两种不同的距离测量时保留的相对信息，并确定它们是否是等效的，独立的，或者如果一个比另一个更翔实。这反过来又允许从候选池中找到信息量最大的距离度量。该方法被应用于寻找与控制新冠肺炎疫情最相关的政策变量，并找到原子结构的紧凑但信息丰富的表示，但其潜在应用范围广泛，涉及许多科学分支。
英文摘要：
Real-world data typically contain a large number of features that are often heterogeneous in nature, relevance, and also units of measure. When assessing the similarity between data points, one can build various distance measures using subsets of these features. Using the fewest features but still retaining sufficient information about the system is crucial in many statistical learning approaches, particularly when data are sparse. We introduce a statistical test that can assess the relative information retained when using two different distance measures, and determine if they are equivalent, independent, or if one is more informative than the other. This in turn allows finding the most informative distance measure out of a pool of candidates. The approach is applied to find the most relevant policy variables for controlling the Covid-19 epidemic and to find compact yet informative representations of atomic structures, but its potential applications are wide ranging in many branches of science.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
