Comparing Machine Learning Algorithms by Union-Free Generic Depth
This work addresses the challenge of descriptive analysis for non-standard data types like partial orders in machine learning benchmarking, offering a novel framework for algorithm comparison, though it appears incremental as it adapts an existing depth concept to a new context.
The authors tackled the problem of comparing machine learning algorithms using multidimensional performance measures by introducing a depth function for partial orders, called union-free generic (ufg) depth, and demonstrated its application in classifier comparisons on benchmark datasets, showing it provides a new perspective distinct from existing methods.
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.