We propose a framework for descriptively analyzing sets of partial orders based on the concept of depth functions. Despite intensive studies of depth functions 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 analyze the distribution of different classifier performances over a sample of standard benchmark data sets. Our results promisingly demonstrate that our approach differs substantially from existing benchmarking approaches and, therefore, adds a new perspective to the vivid debate on the comparison of classifiers.

翻译：我们提出一个基于深度函数概念对偏序集进行描述性分析的框架。尽管深度函数在线性空间和度量空间中的研究已相当深入，但对偏序等非标准数据类型深度函数的探讨仍十分有限。我们将著名的单纯深度方法引入偏序集全体，提出无并泛化（ufg）深度。进一步，我们利用该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，我们分析标准基准数据集样本上不同分类器性能的分布规律。研究结果表明，我们的方法与现有基准测试方法存在本质差异，从而为分类器比较的激烈讨论提供了新的视角。