Biorder families, valued relations and preference modelling
Journal of Mathematical Psychology
An existence theorem for fuzzy utility functions: a new elementary proof
Fuzzy Sets and Systems
Journal of Mathematical Psychology
Robust Classification for Imprecise Environments
Machine Learning
General transitivity conditions for fuzzy reciprocal preference matrices
Fuzzy Sets and Systems - Special issue: Preference modelling and applications
The Journal of Machine Learning Research
In Defense of One-Vs-All Classification
The Journal of Machine Learning Research
Probability Estimates for Multi-class Classification by Pairwise Coupling
The Journal of Machine Learning Research
Generalization Bounds for the Area Under the ROC Curve
The Journal of Machine Learning Research
Cycle-transitive comparison of independent random variables
Journal of Multivariate Analysis
An introduction to ROC analysis
Pattern Recognition Letters - Special issue: ROC analysis in pattern recognition
A compendium of fuzzy weak orders: Representations and constructions
Fuzzy Sets and Systems
On the transitivity of the comonotonic and countermonotonic comparison of random variables
Journal of Multivariate Analysis
ROC analysis in ordinal regression learning
Pattern Recognition Letters
On the cycle-transitive comparison of artificially coupled random variables
International Journal of Approximate Reasoning
The Journal of Machine Learning Research
Binary Decomposition Methods for Multipartite Ranking
ECML PKDD '09 Proceedings of the European Conference on Machine Learning and Knowledge Discovery in Databases: Part I
Transitivity frameworks for reciprocal relations: cycle-transitivity versus FG-transitivity
Fuzzy Sets and Systems
Regression for ordinal variables without underlying continuous variables
Information Sciences: an International Journal
On the cycle-transitivity of the mutual rank probability relation of a poset
Fuzzy Sets and Systems
A transitivity analysis of bipartite rankings in pairwise multi-class classification
Information Sciences: an International Journal
Computational Statistics & Data Analysis
A comparison of methods for multiclass support vector machines
IEEE Transactions on Neural Networks
Hi-index | 0.00 |
In domains like decision theory and social choice theory it is known for a long time that stochastic transitivity properties yield necessary and sufficient conditions for the ranking or utility representability of reciprocal preference relations. In this article we extend these results for reciprocal preference relations originating from the pairwise comparison of random vectors in a machine learning context. More specifically, the expected ranking accuracy (ERA) is such a reciprocal relation that occurs in multi-class classification problems, when ranking or utility functions are fitted to the data in a pairwise manner. We establish necessary and sufficient conditions for which these pairwise bipartite ranking functions can be simplified to a single ranking function such that the pairwise expected ranking accuracies of both models coincide. Similarly as for more common reciprocal preference relations, cycle transitivity plays a crucial role in this new setting. We first consider the finite sample case, for which expected ranking accuracy can be estimated by means of the area under the ROC curve (AUC), and subsequently, we further generalize these results to the underlying distributions. It turns out that the ranking representability of pairwisely compared random vectors can be expressed elegantly in a distribution-independent way by means of a specific type of cycle transitivity, defined by a conjunctor that is closely related to the algebraic product.