Existing regression models tend to fall short in both accuracy and uncertainty estimation when the label distribution is imbalanced. In this paper, we propose a probabilistic deep learning model, dubbed variational imbalanced regression (VIR), which not only performs well in imbalanced regression but naturally produces reasonable uncertainty estimation as a byproduct. Different from typical variational autoencoders assuming I.I.D. representations (a data point's representation is not directly affected by other data points), our VIR borrows data with similar regression labels to compute the latent representation's vari-ational distribution; furthermore, different from deterministic regression models producing point estimates, VIR predicts the entire normal-inverse-gamma distributions and modulates the associated conjugate distributions to impose probabilistic reweighting on the imbalanced data, thereby providing better uncertainty estimation.

This paper focuses on supervised and unsupervised online label shift,where the class marginals $Q(y)$ variesbut the class-conditionals $Q(x|y)$ remain invariant. In the unsupervised setting, our goal is to adapt a learner, trained on some offline labeled data, to changing label distributions given unlabeled online data. In the supervised setting, we must both learn a classifier and adapt to the dynamically evolving class marginals given only labeled online data. We develop novel algorithms that reduce the adaptation problem to online regression and guarantee optimal dynamic regret without any prior knowledge of the extent of drift in the label distribution. Our solution is based on bootstrapping the estimates of *online regression oracles* that track the drifting proportions. Experiments across numerous simulated and real-world online label shift scenarios demonstrate the superior performance of our proposed approaches, often achieving 1-3% improvement in accuracy while being sample and computationally efficient.

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 can provide richer information about label polysemy than logical labels in multi-label learning. There are currently two strategies including LDL (label distribution learning) and LE (label enhancement) to predict label distributions. LDL requires experts to annotate instances with label distributions and learn a predictive mapping on such a training set. LE requires experts to annotate instances with logical labels and generates label distributions from them. However, LDL requires costly annotation, and the performance of the LE is unstable. In this paper, we study the problem of predicting label distribution from multi-label ranking which is a compromise w.r.t.

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.