Many real-world classification tasks require predicting multiple labels per instance, necessitating the optimization of complex evaluation metrics such as the $F$-measure and Jaccard index. While the Empirical Utility Maximization (EUM) framework is natural for these population-level metrics, existing theoretical results are largely limited to asymptotic Bayes-consistency. In this paper, we develop principled learning algorithms for optimizing a broad class of generalized metrics within the EUM framework, grounded in the stronger notion of $H$-consistency. Our key contribution is the design of novel surrogate loss functions for multi-label learning that admit provable $H$-consistency bounds, enabling optimization with non-asymptotic guarantees tailored to the hypothesis class and finite samples. Crucially, we prove these combinatorially formulated surrogates decompose exactly, operating in strictly $O(l)$ time without approximations. Building on this foundation, we introduce MMO (Multi-Label Metric Optimization), a new family of algorithms for optimizing generalized linear-fractional metrics. We validate our approach through extensive experiments, demonstrating robust scalability and superior performance over state-of-the-art continuous baselines on large-scale datasets (MS-COCO, Reuters-21578) in high-sparsity, deep learning regimes. Our results offer both theoretical rigor and practical effectiveness for general multi-label metric optimization.

In partial multi-label learning (PML), each training example is associated with a set of candidate labels, among which only some labels are valid. As a common strategy to tackle PML problem, disambiguation aims to recover the ground-truth labeling information from such inaccurate annotations. However, existing approaches mainly rely on heuristics or ad-hoc rules to disambiguate candidate labels, which may not be universal enough in complicated real-world scenarios. To provide a principled way for disambiguation, we make a first attempt to explore the probabilistic graphical model for PML problem, where a directed graph is tailored to infer latent ground-truth labeling information from the generative process of partial multi-label data. Under the framework of stochastic gradient variational Bayes, a unified variational lower bound is derived for this graphical model, which is further relaxed probabilistically so that the desired prediction model can be induced with simultaneously identified ground-truth labeling information. Comprehensive experiments on multiple synthetic and real-world data sets show that our approach outperforms the state-of-the-art counterparts.

Multi-view learning has become a popular research topic in recent years, but research on the cross-application of classic multi-label classification and multi-view learning is still in its early stages. In this paper, we focus on the complex yet highly realistic task of incomplete multi-view weak multi-label learning and propose a masked two-channel decoupling framework based on deep neural networks to solve this problem. The core innovation of our method lies in decoupling the singlechannel view-level representation, which is common in deep multi-view learning methods, into a shared representation and a view-proprietary representation. We also design a cross-channel contrastive loss to enhance the semantic property of the two channels. Additionally, we exploit supervised information to design a labelguided graph regularization loss, helping the extracted embedding features preserve the geometric structure among samples. Inspired by the success of masking mechanisms in image and text analysis, we develop a random fragment masking strategy for vector features to improve the learning ability of encoders. Finally, it is important to emphasize that our model is fully adaptable to arbitrary view and label absences while also performing well on the ideal full data. We have conducted sufficient and convincing experiments to confirm the effectiveness and advancement of our model.

We present a detailed study of surrogate losses and algorithms for multi-label learning, supported by $H$-consistency bounds. We first show that, for the simplest form of multi-label loss (the popular Hamming loss), the well-known consistent binary relevance surrogate suffers from a sub-optimal dependency on the number of labels in terms of $H$-consistency bounds, when using smooth losses such as logistic losses. Furthermore, this loss function fails to account for label correlations. To address these drawbacks, we introduce a novel surrogate loss, *multi-label logistic loss*, that accounts for label correlations and benefits from label-independent $H$-consistency bounds. We then broaden our analysis to cover a more extensive family of multi-label losses, including all common ones and a new extension defined based on linear-fractional functions with respect to the confusion matrix.

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Pseudo-labeling has emerged as a popular and effective approach for utilizing unlabeled data.

Inlabel-noiselearning,thenoise transitionmatrix,bridgingtheclassposteriorfor noisy and clean data, has been widely exploited to learnstatistically consistent classifiers.