Multi-label complementary label learning (MLCLL) is a weakly supervised paradigm that addresses multi-label learning (MLL) tasks using complementary labels (i.e., irrelevant labels) instead of relevant labels. Existing methods typically adopt an unbiased risk estimator (URE) under the assumption that complementary labels follow a uniform distribution. However, this assumption fails in real-world scenarios due to instance-specific annotation biases, making URE-based methods ineffective under such conditions. Furthermore, existing methods underutilize label correlations inherent in MLL. To address these limitations, we propose ComRank, a ranking loss framework for MLCLL, which encourages complementary labels to be ranked lower than non-complementary ones, thereby modeling pairwise label relationships. Theoretically, our surrogate loss ensures Bayes consistency under both uniform and biased cases. Experiments demonstrate the effectiveness of our method in MLCLL tasks. The code is available at https://github.com/JellyJamZhu/ComRank.

In multi-labeled complementary label learning (MLCLL), a complementary label (CL) represents an irrelevant label for an instance. Utilizing CLs instead of relevant labels as annotations simplifies the annotation process in multi-label learning (MLL) tasks, underscoring the practicality of the MLCLL problem. However, existing MLCLL approaches mainly focus on scenarios where an instance is associated with a single CL. This restricts their applicability in situations where annotators provide multiple CLs per instance. To address this limitation, we propose a novel paradigm called multi-label learning with multiple complementary labels (ML-MCL), which allows each instance to be associated with multiple CLs simultaneously. Through analyzing the generation process of multiple CLs, we construct the relationship between relevant labels and CLs. This assists in deriving a tailored risk-consistent estimator to solve MLCLL with multiple CLs. Theoretically, we establish an estimation error bound for this estimator, with a convergence rate of $\mathcal {O}(1/\sqrt{n})$O(1/n). Furthermore, we observed that unbounded gradients can be produced in the derived estimator when optimizing with certain loss functions, which may lead to unstable optimization. To mitigate this issue, we enhance the estimator with a confidence truncation loss, stabilizing the optimization process. Experimental results confirm the effectiveness of our approach, showing improved learning stability and performance in MLCLL tasks involving multiple CLs.