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：我们提出一个框架，用于基于深度函数对偏序集进行描述性分析。尽管深度函数在线性空间和度量空间中已得到广泛研究，但对于偏序等非标准数据类型，其讨论仍十分有限。我们将著名的单纯深度方法适配到所有偏序集上，引入无并集泛化深度（union-free generic depth, ufg深度）。此外，我们利用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，我们提供了两个基于标准基准数据集样本的分类器比较实例。研究结果初步表明，基于ufg方法可开展多种不同的分析途径。同时，这些实例指出，我们的方法与现有基准测试方法存在本质差异，从而为分类器比较这一激烈讨论增添了全新视角。