Depth Functions for Partial Orders with a Descriptive Analysis of Machine Learning Algorithms
This work addresses the problem of descriptive analysis for partial orders, which is incremental as it adapts an existing concept to a new data type.
The authors tackled the lack of depth functions for non-standard data types like partial orders by introducing the union-free generic (ufg) depth, and applied it to compare machine learning algorithms on benchmark datasets, showing that their approach differs substantially from existing methods.
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.