Multi-label loss functions are usually non-differentiable, requiring surrogate loss functions for gradient-based optimisation. The consistency of surrogate loss functions is not proven and is exacerbated by the conflicting nature of multi-label loss functions. To directly learn from multiple related, yet potentially conflicting multi-label loss functions, we propose a Consistent Lebesgue Measure-based Multi-label Learner (CLML) and prove that CLML can achieve theoretical consistency under a Bayes risk framework. Empirical evidence supports our theory by demonstrating that: (1) CLML can consistently achieve state-of-the-art results; (2) the primary performance factor is the Lebesgue measure design, as CLML optimises a simpler feedforward model without additional label graph, perturbation-based conditioning, or semantic embeddings; and (3) an analysis of the results not only distinguishes CLML's effectiveness but also highlights inconsistencies between the surrogate and the desired loss functions.

How do we compare between hypotheses that are entirely consistent with observations? The marginal likelihood (aka Bayesian evidence), which represents the probability of generating our observations from a prior, provides a distinctive approach to this foundational question, automatically encoding Occam's razor. Although it has been observed that the marginal likelihood can overfit and is sensitive to prior assumptions, its limitations for hyperparameter learning and discrete model comparison have not been thoroughly investigated. We first revisit the appealing properties of the marginal likelihood for learning constraints and hypothesis testing. We then highlight the conceptual and practical issues in using the marginal likelihood as a proxy for generalization. Namely, we show how marginal likelihood can be negatively correlated with generalization, with implications for neural architecture search, and can lead to both underfitting and overfitting in hyperparameter learning. We also re-examine the connection between the marginal likelihood and PAC-Bayes bounds and use this connection to further elucidate the shortcomings of the marginal likelihood for model selection. We provide a partial remedy through a conditional marginal likelihood, which we show is more aligned with generalization, and practically valuable for large-scale hyperparameter learning, such as in deep kernel learning.

Contrastive learning (CL) has shown impressive advances in image representation learning in whichever supervised multi-class classification or unsupervised learning. However, these CL methods fail to be directly adapted to multi-label image classification due to the difficulty in defining the positive and negative instances to contrast a given anchor image in multi-label scenario, let the label missing one alone, implying that borrowing a commonly-used way from contrastive multi-class learning to define them will incur a lot of false negative instances unfavorable for learning. In this paper, with the introduction of a label correction mechanism to identify missing labels, we first elegantly generate positives and negatives for individual semantic labels of an anchor image, then define a unique contrastive loss for multi-label image classification with missing labels (CLML), the loss is able to accurately bring images close to their true positive images and false negative images, far away from their true negative images. Different from existing multi-label CL losses, CLML also preserves low-rank global and local label dependencies in the latent representation space where such dependencies have been shown to be helpful in dealing with missing labels. To the best of our knowledge, this is the first general multi-label CL loss in the missing-label scenario and thus can seamlessly be paired with those losses of any existing multi-label learning methods just via a single hyperparameter. The proposed strategy has been shown to improve the classification performance of the Resnet101 model by margins of 1.2%, 1.6%, and 1.3% respectively on three standard datasets, MSCOCO, VOC, and NUS-WIDE. Code is available at https://github.com/chuangua/ContrastiveLossMLML.