Depth Functions for Partial Orders with a Descriptive Analysis of Machine Learning Algorithms

Blocher, Hannah ; Schollmeyer, Georg ; Jansen, Christoph und Nalenz, Malte (2023): Depth Functions for Partial Orders with a Descriptive Analysis of Machine Learning Algorithms. International Symposium on Imprecise Probability: Theories and Applications, Oviedo, Spain, 11-14 July 2023. In: Proceedings of the Thirteenth International Symposium on Imprecise Probability: Theories and Applications, pp. 59-71

Abstract

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.

• Item Type: Conference or Workshop Item (Paper)
• Faculties: Mathematics, Computer Science and Statistics > Statistics > Chairs/Working Groups > Foundations of Statistics and their Applications
• Subjects: 000 Computer science, information and general works > 004 Data processing computer science; 500 Science > 510 Mathematics
• Annotation: Proceedings of Machine Learning Research , Bd. 215
• Language: English