# Comparing Machine Learning Algorithms by Union-Free Generic Depth

arXiv: https://arxiv.org/abs/2312.12839 · HTML: https://mlsanity.com/paper/2312.12839/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 64 references that are in the map.
- First posted on arXiv 20 Dec 2023.

## Builds on (most cited first, 2 of 2)

- [Statistical Depth Functions for Ranking Distributions: Definitions, Statistical Learning and Applications](https://mlsanity.com/paper/2201.08105/) (2022)
- [Learning partially ranked data based on graph regularization](https://mlsanity.com/paper/1902.10963/) (2019)

## Built on by (most cited first, 4 of 4)

- [Statistical Multicriteria Benchmarking via the GSD-Front](https://mlsanity.com/paper/2406.03924/) (2024)
- [Towards Better Open-Ended Text Generation: A Multicriteria Evaluation Framework](https://mlsanity.com/paper/2410.18653/) (2024)
- [Statistical Multicriteria Evaluation of LLM-Generated Text](https://mlsanity.com/paper/2506.18082/) (2025)
- [Beyond Arrow: From Impossibility to Possibilities in Multi-Criteria Benchmarking](https://mlsanity.com/paper/2602.07593/) (2026)

## Abstract (arXiv)

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.