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。尽管线性空间和度量空间中的深度函数研究已相当深入，但对偏序等非标准数据类型深度函数的探讨却十分稀少。我们将众所周知的单纯深度适配到全体偏序集上，引入了无并通用（ufg）深度。此外，我们利用所提出的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，我们提供了两个基于标准基准数据集样本的分类器比较实例。实验结果表明，基于ufg方法的多样化分析路径具有广阔前景。同时，这些实例指出我们的方法与传统基准测试方法存在本质差异，从而为当前关于分类器比较的热烈讨论增添了新视角。