A Multiclass Classification Approach to Label Ranking

Stéphan Clémencon, Robin Vogel

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract / Description of output

In multiclass classification, the goal is to learn how to predict a random label Y, valued in Y = {1,;...,;K} with K ≥ 3, based upon observing a r.v. X, taking its values in ℝq with q ≥ 1 say, by means of a classification rule g : ℝqY with minimum probability of error ℙ{Yeqg(X)}. However, in a wide variety of situations, the task targeted may be more ambitious, consisting in sorting all the possible label values y that may be assigned to X by decreasing order of the posterior probability ηy(X) = ℙ{Y = y | X }. This article is devoted to the analysis of this statistical learning problem, halfway between multiclass classification and posterior probability estimation (regression) and referred to as label ranking here. We highlight the fact that it can be viewed as a specific variant of ranking median regression (RMR), where, rather than observing a random permutation Σ assigned to the input vector X and drawn from a Bradley-Terry-Luce-Plackett model with conditional preference vector (η1(X),;...; ηK(X)), the sole information available for training a label ranking rule is the label Y ranked on top, namely Σ-1(1). Inspired by recent results in RMR, we prove that under appropriate noise conditions, the One-Versus-One (OVO) approach to multiclassification yields, as a by-product, an optimal ranking of the labels with overwhelming probability. Beyond theoretical guarantees, the relevance of the approach to label ranking promoted in this article is supported by experimental results.

Original languageEnglish
Title of host publicationProceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics
EditorsSilvia Chiappa, Roberto Calandra
PublisherPMLR
Pages1421-1430
Number of pages9
Volume108
Publication statusPublished - 1 Feb 2020
Event23rd International Conference on Artificial Intelligence and Statistics - Teatro Politeama, Online, Italy
Duration: 26 Aug 202028 Aug 2020
Conference number: 23
https://www.aistats.org/

Publication series

NameProceedings of Machine Learning Research
PublisherPMLR
Volume108
ISSN (Electronic)2640-3498

Conference

Conference23rd International Conference on Artificial Intelligence and Statistics
Abbreviated titleAISTATS 2020
Country/TerritoryItaly
CityOnline
Period26/08/2028/08/20
Internet address

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