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.

我们提出了一个通过深度函数对部分排序集进行描述性分析的框架。具体地，我们引入了一种适用于所有部分排序的著名单形深度的改进方法，即不相交统一（ufg）深度，并利用我们的 ufg 深度对基于多维性能度量的机器学习算法进行比较。通过在标准基准数据集的样本上提供两个分类器比较的例子，我们的结果有望展示基于 ufg 方法的不同分析方法的广泛应用。此外，这些例子概述了我们的方法与现有基准方法的明显差异，从而为关于分类器比较的活跃讨论增加了新的视角。

通过无交集通用深度比较机器学习算法

Comparing Machine Learning Algorithms by Union-Free Generic Depth

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.

通过深度函数的概念，提出一个分析部分顺序集的框架，并介绍了基于联合无冗余泛型（ufg）深度的机器学习算法比较方法。结果显示，与现有的基准测试方法相比，我们的方法具有显著差异，为分类器比较提供了新的视角。