Depth functions for partial orders with a descriptive analysis of machine learning algorithms

Hannah Blocher, Georg Schollmeyer, Christoph Jansen, Malte Nalenz
Proceedings of the Thirteenth International Symposium on Imprecise Probability: Theories and Applications, PMLR 215:59-71, 2023.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v215-blocher23a, title = {Depth functions for partial orders with a descriptive analysis of machine learning algorithms}, author = {Blocher, Hannah and Schollmeyer, Georg and Jansen, Christoph and Nalenz, Malte}, booktitle = {Proceedings of the Thirteenth International Symposium on Imprecise Probability: Theories and Applications}, pages = {59--71}, year = {2023}, editor = {Miranda, Enrique and Montes, Ignacio and Quaeghebeur, Erik and Vantaggi, Barbara}, volume = {215}, series = {Proceedings of Machine Learning Research}, month = {11--14 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v215/blocher23a/blocher23a.pdf}, url = {https://proceedings.mlr.press/v215/blocher23a.html}, 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.} }
Endnote
%0 Conference Paper %T Depth functions for partial orders with a descriptive analysis of machine learning algorithms %A Hannah Blocher %A Georg Schollmeyer %A Christoph Jansen %A Malte Nalenz %B Proceedings of the Thirteenth International Symposium on Imprecise Probability: Theories and Applications %C Proceedings of Machine Learning Research %D 2023 %E Enrique Miranda %E Ignacio Montes %E Erik Quaeghebeur %E Barbara Vantaggi %F pmlr-v215-blocher23a %I PMLR %P 59--71 %U https://proceedings.mlr.press/v215/blocher23a.html %V 215 %X 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.
APA
Blocher, H., Schollmeyer, G., Jansen, C. & Nalenz, M.. (2023). Depth functions for partial orders with a descriptive analysis of machine learning algorithms. Proceedings of the Thirteenth International Symposium on Imprecise Probability: Theories and Applications, in Proceedings of Machine Learning Research 215:59-71 Available from https://proceedings.mlr.press/v215/blocher23a.html.

Related Material