Communication Dans Un Congrès Année : 2025

Active Bipartite Ranking with Smooth Posterior Distributions

Résumé

In this article, bipartite ranking, a statistical learning problem involved in many applications and widely studied in the passive context, is approached in a much more general active setting than the discrete one previously considered in the literature. While the latter assumes that the conditional distribution is piece wise constant, the framework we develop permits in contrast to deal with continuous conditional distributions, provided that they fulfill a Hölder smoothness constraint. We first show that a naive approach based on discretisation at a uniform level, fixed a priori and consisting in applying next the active strategy designed for the discrete setting generally fails. Instead, we propose a novel algorithm, referred to as smooth-rank and designed for the continuous setting, which aims to minimise the distance between the ROC curve of the estimated ranking rule and the optimal one w.r.t. the sup norm. We show that, for a fixed confidence level ε > 0 and probability δ ∈ (0, 1), smooth-rank is PAC(ε, δ). In addition, we provide a problem dependent upper bound on the expected sampling time of smooth-rank and establish a problem dependent lower bound on the expected sampling time of any PAC(ε, δ) algorithm. Beyond the theoretical analysis carried out, numerical results are presented, providing solid empirical evidence of the performance of the algorithm proposed, which compares favorably with alternative approaches.

Fichier principal
Vignette du fichier
AISTATS2025_continuous_ranking-1.pdf (798.26 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Licence

Dates et versions

hal-04975150 , version 1 (04-03-2025)
hal-04975150 , version 2 (25-02-2026)

Licence

Identifiants

  • HAL Id : hal-04975150 , version 2

Citer

James Cheshire, Stephan Clémençon. Active Bipartite Ranking with Smooth Posterior Distributions. Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, May 2025, Mai Khao, Thailand. ⟨hal-04975150v2⟩
157 Consultations
190 Téléchargements

Partager

  • More