Consistent Multilabel Ranking through Univariate Losses

TL;DR

This paper demonstrates that simple univariate surrogate losses for multilabel ranking are consistent and scalable, providing theoretical guarantees and practical algorithms, contrasting with previous pairwise loss inconsistency results.

Contribution

It proves the consistency of univariate exponential and logistic surrogate losses for multilabel ranking, offering theoretical regret bounds and scalable algorithms.

Findings

Univariate surrogate losses are consistent for rank loss minimization.

Derived regret bounds and convergence rates for the proposed losses.

Experimental results show the efficiency and scalability of the algorithms.

Abstract

We consider the problem of rank loss minimization in the setting of multilabel classification, which is usually tackled by means of convex surrogate losses defined on pairs of labels. Very recently, this approach was put into question by a negative result showing that commonly used pairwise surrogate losses, such as exponential and logistic losses, are inconsistent. In this paper, we show a positive result which is arguably surprising in light of the previous one: the simpler univariate variants of exponential and logistic surrogates (i.e., defined on single labels) are consistent for rank loss minimization. Instead of directly proving convergence, we give a much stronger result by deriving regret bounds and convergence rates. The proposed losses suggest efficient and scalable algorithms, which are tested experimentally.