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Rethinking Consistent Multi-Label Classification under Inexact Supervision

Wei Wang, Tianhao Ma, Ming-Kun Xie, Gang Niu, Masashi Sugiyama

TL;DR

The paper tackles multi-label classification under inexact supervision, introducing COMES, a unified framework that yields unbiased risk estimators for both first-order (Hamming) and second-order (ranking) objectives without relying on estimating the label-generation process or enforcing a uniform distribution. It provides theoretical guarantees of consistency and convergence rates, augmented by risk-correction mechanisms to improve generalization. Empirical results show that COMES-HL and COMES-RL consistently outperform state-of-the-art baselines on real-world and synthetic datasets, validating robustness to label imbalances and inexact supervision. The work advances practical weakly supervised MLC by modeling a realistic data-generation process and delivering provable, scalable learning algorithms.

Abstract

Partial multi-label learning and complementary multi-label learning are two popular weakly supervised multi-label classification paradigms that aim to alleviate the high annotation costs of collecting precisely annotated multi-label data. In partial multi-label learning, each instance is annotated with a candidate label set, among which only some labels are relevant; in complementary multi-label learning, each instance is annotated with complementary labels indicating the classes to which the instance does not belong. Existing consistent approaches for the two paradigms either require accurate estimation of the generation process of candidate or complementary labels or assume a uniform distribution to eliminate the estimation problem. However, both conditions are usually difficult to satisfy in real-world scenarios. In this paper, we propose consistent approaches that do not rely on the aforementioned conditions to handle both problems in a unified way. Specifically, we propose two unbiased risk estimators based on first- and second-order strategies. Theoretically, we prove consistency w.r.t. two widely used multi-label classification evaluation metrics and derive convergence rates for the estimation errors of the proposed risk estimators. Empirically, extensive experimental results validate the effectiveness of our proposed approaches against state-of-the-art methods.

Rethinking Consistent Multi-Label Classification under Inexact Supervision

TL;DR

The paper tackles multi-label classification under inexact supervision, introducing COMES, a unified framework that yields unbiased risk estimators for both first-order (Hamming) and second-order (ranking) objectives without relying on estimating the label-generation process or enforcing a uniform distribution. It provides theoretical guarantees of consistency and convergence rates, augmented by risk-correction mechanisms to improve generalization. Empirical results show that COMES-HL and COMES-RL consistently outperform state-of-the-art baselines on real-world and synthetic datasets, validating robustness to label imbalances and inexact supervision. The work advances practical weakly supervised MLC by modeling a realistic data-generation process and delivering provable, scalable learning algorithms.

Abstract

Partial multi-label learning and complementary multi-label learning are two popular weakly supervised multi-label classification paradigms that aim to alleviate the high annotation costs of collecting precisely annotated multi-label data. In partial multi-label learning, each instance is annotated with a candidate label set, among which only some labels are relevant; in complementary multi-label learning, each instance is annotated with complementary labels indicating the classes to which the instance does not belong. Existing consistent approaches for the two paradigms either require accurate estimation of the generation process of candidate or complementary labels or assume a uniform distribution to eliminate the estimation problem. However, both conditions are usually difficult to satisfy in real-world scenarios. In this paper, we propose consistent approaches that do not rely on the aforementioned conditions to handle both problems in a unified way. Specifically, we propose two unbiased risk estimators based on first- and second-order strategies. Theoretically, we prove consistency w.r.t. two widely used multi-label classification evaluation metrics and derive convergence rates for the estimation errors of the proposed risk estimators. Empirically, extensive experimental results validate the effectiveness of our proposed approaches against state-of-the-art methods.

Paper Structure

This paper contains 30 sections, 19 theorems, 66 equations, 3 figures, 3 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Multi-Label Classification
  4. Multi-Label Classification under Inexact Supervision
  5. Methodology
  6. Data Generation Process
  7. First-Order Strategy
  8. Second-Order Strategy
  9. Experiments
  10. Experimental Setup
  11. Experimental Results
  12. Sensitivity Analysis
  13. Conclusion
  14. More Details about the Algorithm
  15. Algorithmic Pseudo-Code
  16. ...and 15 more sections

Key Result

Lemma 1

Assume that $p(s_j=0|\bm{x},y_j=0)=p_j$, where $p_j$ is a constant. Then, we have $p(\bm{x}|s_j=0)=p(\bm{x}|y_j=0)$.

Figures (3)

  • Figure 1: A multi-label image with inexact annotations. Source: Paul Cézanne, Still Life, Jug and Fruit on a Table (1894), public domain.
  • Figure 2: Classification performance with inaccurate class priors on different datasets.
  • Figure 3: Sensitivity analysis w.r.t. $\beta$ on the mirflickr dataset.

Theorems & Definitions (34)

  • Lemma 1
  • Theorem 1
  • Theorem 2
  • Theorem 3
  • Corollary 1
  • Theorem 4
  • Theorem 5
  • Theorem 6
  • Corollary 2
  • proof
  • ...and 24 more