We propose a framework for descriptively analyzing sets of partial orders based on the concept of depth functions. Despite intensive studies in linear and metric spaces, there is very little discussion on depth functions for non-standard data types such as partial orders. We introduce an adaptation of the well-known simplicial depth to the set of all partial orders, the union-free generic (ufg) depth. Moreover, we utilize our ufg depth for a comparison of machine learning algorithms based on multidimensional performance measures. Concretely, we provide two examples of classifier comparisons on samples of standard benchmark data sets. Our results demonstrate promisingly the wide variety of different analysis approaches based on ufg methods. Furthermore, the examples outline that our approach differs substantially from existing benchmarking approaches, and thus adds a new perspective to the vivid debate on classifier comparison.

翻译：我们提出一个基于深度函数对偏序集进行描述性分析的框架。尽管在线性空间和度量空间中已有深入研究，但针对偏序等非标准数据类型深度函数的讨论仍十分有限。我们将著名的单纯深度概念推广至全体偏序集，引入无联合泛化深度。进一步利用所提出的ufg深度，基于多维性能指标对机器学习算法进行比较。具体而言，我们给出两个基于标准基准数据集样本的分类器比较实例。实验结果充分展示了基于ufg方法的各种不同分析路径的多样性。此外，这些实例表明我们的方法显著区别于现有的基准测试方法，从而为分类器比较这一激烈辩论增添了新的视角。