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Can Class-Priors Help Single-Positive Multi-Label Learning?

Biao Liu, Ning Xu, Jie Wang, Xin Geng

TL;DR

This work tackles single-positive multi-label learning by relaxing the common equal-class-prior assumption. It introduces Crisp, a framework that (i) estimates per-class priors from a black-box classifier via a threshold-based mechanism that converges to the true priors, and (ii) derives an unbiased, priors-guided risk estimator with learning guarantees that approximate the fully supervised optimum. The approach yields theoretical convergence bounds and demonstrates superior performance across ten benchmark datasets, with robust priors prediction and favorable training efficiency. Overall, Crisp provides a principled, practical solution for SPMLL that mitigates bias from imbalanced class priors and improves multi-label prediction quality.

Abstract

Single-positive multi-label learning (SPMLL) is a typical weakly supervised multi-label learning problem, where each training example is annotated with only one positive label. Existing SPMLL methods typically assign pseudo-labels to unannotated labels with the assumption that prior probabilities of all classes are identical. However, the class-prior of each category may differ significantly in real-world scenarios, which makes the predictive model not perform as well as expected due to the unrealistic assumption on real-world application. To alleviate this issue, a novel framework named {\proposed}, i.e., Class-pRiors Induced Single-Positive multi-label learning, is proposed. Specifically, a class-priors estimator is introduced, which could estimate the class-priors that are theoretically guaranteed to converge to the ground-truth class-priors. In addition, based on the estimated class-priors, an unbiased risk estimator for classification is derived, and the corresponding risk minimizer could be guaranteed to approximately converge to the optimal risk minimizer on fully supervised data. Experimental results on ten MLL benchmark datasets demonstrate the effectiveness and superiority of our method over existing SPMLL approaches.

Can Class-Priors Help Single-Positive Multi-Label Learning?

TL;DR

This work tackles single-positive multi-label learning by relaxing the common equal-class-prior assumption. It introduces Crisp, a framework that (i) estimates per-class priors from a black-box classifier via a threshold-based mechanism that converges to the true priors, and (ii) derives an unbiased, priors-guided risk estimator with learning guarantees that approximate the fully supervised optimum. The approach yields theoretical convergence bounds and demonstrates superior performance across ten benchmark datasets, with robust priors prediction and favorable training efficiency. Overall, Crisp provides a principled, practical solution for SPMLL that mitigates bias from imbalanced class priors and improves multi-label prediction quality.

Abstract

Single-positive multi-label learning (SPMLL) is a typical weakly supervised multi-label learning problem, where each training example is annotated with only one positive label. Existing SPMLL methods typically assign pseudo-labels to unannotated labels with the assumption that prior probabilities of all classes are identical. However, the class-prior of each category may differ significantly in real-world scenarios, which makes the predictive model not perform as well as expected due to the unrealistic assumption on real-world application. To alleviate this issue, a novel framework named {\proposed}, i.e., Class-pRiors Induced Single-Positive multi-label learning, is proposed. Specifically, a class-priors estimator is introduced, which could estimate the class-priors that are theoretically guaranteed to converge to the ground-truth class-priors. In addition, based on the estimated class-priors, an unbiased risk estimator for classification is derived, and the corresponding risk minimizer could be guaranteed to approximately converge to the optimal risk minimizer on fully supervised data. Experimental results on ten MLL benchmark datasets demonstrate the effectiveness and superiority of our method over existing SPMLL approaches.
Paper Structure (28 sections, 5 theorems, 47 equations, 4 figures, 13 tables, 1 algorithm)

This paper contains 28 sections, 5 theorems, 47 equations, 4 figures, 13 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Preliminaries
  4. The Proposed Method
  5. The Crisp Algorithm
  6. Estimation Error Bound
  7. Experiments
  8. Experimental Configurations
  9. Experimental Results
  10. Further Analysis
  11. Class-Prior Prediction
  12. Sensitivity Analysis
  13. Ablation Study
  14. Time Cost of Class-Priors Estimation
  15. Conclusion
  16. ...and 13 more sections

Key Result

Theorem 4.1

Define $z^\star = \arg\min_{z\in[0,1]} q_j^n(z) / q_j^p(z)$, for every $0<\delta<1$, define $\hat{z} = \arg\min_{z\in [0,1]} \left( \frac{\hat{q}_j(z)}{\hat{q}_j^p(z)} + \frac{1+\tau}{\hat{q}_j^p(z)}\left( \sqrt{\frac{\log(4/\delta)}{2n}} + \sqrt{\frac{\log(4/\delta)}{2n_j^p}} \right) \right)$. Assu

Figures (4)

  • Figure 1: Predicted class-prior of Ancole2021multi, An-lscole2021multi, Wancole2021multi, Eprcole2021multi, Rolecole2021multi, Emcole2021multi, Em-Aplzhou2022acknowledging, Smilexu2022one, Mimeliu2023revisiting, Llkim2022large and Crisp on the $3$-rd (left), $10$-th (middle), and $12$-th labels (right) of the dataset Yeast.
  • Figure 2: (a) Parameter sensitivity analysis of $\delta$ ($\tau$ is fixed as $0.01$, $\lambda$ is fixed as $1$); (b) The initial data point represents the performance of the proposed Crisp (with class-priors estimator). The others are the performance with a fixed value for all class-priors gradually increasing from $0.001$ to $0.3$.
  • Figure 3: Convergence of $\hat{\pi}$ on four MLIC datasets.
  • Figure 4: (a) Parameter sensitivity analysis of $\tau$ ($\delta$ is fixed as $0.01$, $\lambda$ is fixed as $1$); (b) Parameter sensitivity analysis of $\lambda$ ($\tau$ and $\delta$ are fixed as $0.01$).

Theorems & Definitions (8)

  • Theorem 4.1
  • Theorem 4.2
  • proof
  • Lemma A.1
  • proof
  • Lemma A.2
  • Theorem A.3
  • proof