Learnability and the Vapnik-Chervonenkis dimension
Journal of the ACM (JACM)
Scale-sensitive dimensions, uniform convergence, and learnability
Journal of the ACM (JACM)
The Journal of Machine Learning Research
An efficient boosting algorithm for combining preferences
The Journal of Machine Learning Research
Generalization Bounds for the Area Under the ROC Curve
The Journal of Machine Learning Research
Learning to rank using gradient descent
ICML '05 Proceedings of the 22nd international conference on Machine learning
Learning to rank: from pairwise approach to listwise approach
Proceedings of the 24th international conference on Machine learning
Generalization Bounds for Ranking Algorithms via Algorithmic Stability
The Journal of Machine Learning Research
Journal of Artificial Intelligence Research
Margin-based Ranking and an Equivalence between AdaBoost and RankBoost
The Journal of Machine Learning Research
The P-Norm Push: A Simple Convex Ranking Algorithm that Concentrates at the Top of the List
The Journal of Machine Learning Research
Approximation stability and boosting
ALT'10 Proceedings of the 21st international conference on Algorithmic learning theory
Learnability, Stability and Uniform Convergence
The Journal of Machine Learning Research
A Bayesian Approximation Method for Online Ranking
The Journal of Machine Learning Research
Learnability of bipartite ranking functions
COLT'05 Proceedings of the 18th annual conference on Learning Theory
Statistical Analysis of Bayes Optimal Subset Ranking
IEEE Transactions on Information Theory
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Most studies were devoted to the design of efficient algorithms and the evaluation and application on diverse ranking problems, whereas few work has been paid to the theoretical studies on ranking learnability. In this paper, we study the relation between uniform convergence, stability and learnability of ranking. In contrast to supervised learning where the learnability is equivalent to uniform convergence, we show that the ranking uniform convergence is sufficient but not necessary for ranking learnability with AERM, and we further present a sufficient condition for ranking uniform convergence with respect to bipartite ranking loss. Considering the ranking uniform convergence being unnecessary for ranking learnability, we prove that the ranking average stability is a necessary and sufficient condition for ranking learnability.