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

arXiv: https://arxiv.org/abs/2304.09872 · HTML: https://mlsanity.com/paper/2304.09872/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 54 references that are in the map.
- First posted on arXiv 19 Apr 2023.

## Builds on (most cited first, 7 of 7)

- [OpenML: networked science in machine learning](https://mlsanity.com/paper/1407.7722/) (2014)
- [ranger: A Fast Implementation of Random Forests for High Dimensional Data in C++ and R](https://mlsanity.com/paper/1508.04409/) (2015)
- [Should we really use post-hoc tests based on mean-ranks?](https://mlsanity.com/paper/1505.02288/) (2015)
- [Statistical Comparisons of Classifiers by Generalized Stochastic Dominance](https://mlsanity.com/paper/2209.01857/) (2022)
- [Choosing among notions of multivariate depth statistics](https://mlsanity.com/paper/2004.01927/) (2020)
- [Information efficient learning of complexly structured preferences: Elicitation procedures and their application to decision making under uncertainty](https://mlsanity.com/paper/2110.12879/) (2021)
- [Learning partially ranked data based on graph regularization](https://mlsanity.com/paper/1902.10963/) (2019)

## Built on by (most cited first, 5 of 5)

- [Robust Statistical Comparison of Random Variables with Locally Varying Scale of Measurement](https://mlsanity.com/paper/2306.12803/) (2023)
- [Explaining Bayesian Optimization by Shapley Values Facilitates Human-AI Collaboration](https://mlsanity.com/paper/2403.04629/) (2024)
- [Statistical Multicriteria Benchmarking via the GSD-Front](https://mlsanity.com/paper/2406.03924/) (2024)
- [Partial Rankings of Optimizers](https://mlsanity.com/paper/2402.16565/) (2024)
- [Machine Learning and Data Analysis Using Posets: A Survey](https://mlsanity.com/paper/2404.03082/) (2024)

## Abstract (arXiv)

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.