If the label distribution across the clients is skewed and the class conditionals have the same support, then the class probabilities {pi(y |x) |i [m]} are non-identical, i.e., for all i 6= uand i,u [m], there exists x, y such that pi(y | x) 6= pu(y | x). We prove the result by contradiction.

Label distribution learning is a powerful learning paradigm to deal with label polysemy and has been widely applied in many practical tasks. A significant obstacle to the effective utilization of label distribution is the substantial expenses of accurate quantifying the label distributions. To tackle this challenge, label enhancement methods automatically infer label distributions from more easily accessible multi-label data based on binary annotations. However, the binary annotation of multi-label data requires experts to accurately assess whether each label can describe the instance, which may diminish the annotating efficiency and heighten the risk of erroneous annotation since the relationship between the label and the instance is unclear in many practical scenarios. Therefore, we propose to predict label distribution from ternary labels, allowing experts to annotate labels in a three-way annotation scheme.

Long-tailed semi-supervised learning poses a significant challenge in training models with limited labeled data exhibiting a long-tailed label distribution. Current state-of-the-art LTSSL approaches heavily rely on high-quality pseudo-labels for large-scale unlabeled data. However, these methods often neglect the impact of representations learned by the neural network and struggle with real-world unlabeled data, which typically follows a different distribution than labeled data. This paper introduces a novel probabilistic framework that unifies various recent proposals in long-tail learning. Our framework derives the class-balanced contrastive loss through Gaussian kernel density estimation. We introduce a continuous contrastive learning method, CCL, extending our framework to unlabeled data using and pseudo-labels. By progressively estimating the underlying label distribution and optimizing its alignment with model predictions, we tackle the diverse distribution of unlabeled data in real-world scenarios. Extensive experiments across multiple datasets with varying unlabeled data distributions demonstrate that CCL consistently outperforms prior state-of-the-art methods, achieving over 4% improvement on the ImageNet-127 dataset. The supplementary material includes the source code for reproducibility.

Popular zero-shot models suffer due to artifacts inherited from pretraining. One particularly detrimental issue, caused by unbalanced web-scale pretraining data, is mismatched label distribution. Existing approaches that seek to repair the label distribution are not suitable in zero-shot settings, as they have mismatching requirements, such as needing access to labeled downstream task data or knowledge of the true label balance in the pretraining distribution. We sidestep these challenges and introduce a simple and lightweight approach to adjust pretrained model predictions via optimal transport. Our technique requires only an estimate of the label distribution of a downstream task. Theoretically, we characterize the improvement produced by our procedure under certain mild conditions and provide bounds on the error caused by misspecification.

Label Distribution Learning (LDL) has been extensively studied in IID data applications such as computer vision, thanks to its more generic setting over single-label and multi-label classification. This paper advances LDL into graph domains and aims to tackle a novel and fundamentalheterogeneous graph label distribution learning (HGDL) problem.We argue that the graph heterogeneity reflected on node types, node attributes, and neighborhood structures can impose significant challenges for generalizing LDL onto graphs. To address the challenges, we propose a new learning framework with two key components: 1) proactive graph topology homogenization, and 2) topology and content consistency-aware graph transformer. Specifically, the former learns optimal information aggregation between meta-paths, so that the nodeheterogeneity can be proactively addressed prior to the succeeding embedding learning; the latter leverages an attention mechanism to learn consistency between meta-path and node attributes, allowing network topology and nodal attributes to be equally emphasized during the label distribution learning. By using KL-divergence and additional constraints, \method~delivers an end-to-end solution for learning and predicting label distribution for nodes.

Label distribution learning (LDL) is a general learning framework, which assigns to an instance a distribution over a set of labels rather than a single label or multiple labels. Current LDL methods have either restricted assumptions on the expression form of the label distribution or limitations in representation learning, e.g., to learn deep features in an end-to-end manner. This paper presents label distribution learning forests (LDLFs) - a novel label distribution learning algorithm based on differentiable decision trees, which have several advantages: 1) Decision trees have the potential to model any general form of label distributions by a mixture of leaf node predictions.