Label Distribution Learning (LDL) is an effective machine learning paradigm for addressing label ambiguity, where each sample is annotated with a distribution that conveys rich semantic information. However, during the actual annotation process of label distributions, annotators often exhibit divergent labeling preferences for the same sample. Most existing LDL methods overlook this heterogeneity, assuming that the observed label distribution originates from a single labeling pattern. Such an assumption limits their capacity to manage inter-annotator disagreement and constrains the generalization of the resulting models. To address this issue, we propose, for the first time, a Dirichlet process mixture model (DPMM)-based framework for LDL. This framework leverages nonparametric Bayesian methods to adaptively uncover diverse latent labeling patterns from the data and to accurately model annotator heterogeneity. Specifically, the ground-truth label distribution of each sample is modeled as a weighted mixture of multiple latent components, where a feature-conditioned gating mechanism adaptively controls the contribution of each component. Experimental results demonstrate that the proposed model consistently achieves competitive performance on several widely-used benchmark datasets.

Label polysemy, where an instance can be associated with multiple labels, is common in real-world tasks. LDL (label distribution learning) is an effective learning paradigm for handling label polysemy, where each instance is associated with a label distribution. Although numerous LDL algorithms have been proposed and achieved satisfactory performance on most existing datasets, they are typically trained directly on the collected label distributions which often lack quality guarantees in real-world tasks due to annotator subjectivity and algorithm assumptions. Consequently, direct learning from such uncertain label distributions can lead to unpredictable generalization performance. To address this problem, we propose an adaptive-grained label distribution learning framework whose main idea is to extract relatively reliable supervision information from unreliable label distributions, and thus the label distribution learning task can be decomposed into three subtasks: coarsening label distributions, learning coarse-grained labels and refining coarse-grained labels. In this framework, we design an adaptive label coarsening algorithm to extract an optimal coarsen-grained labels and a label refining function to enhance the coarse-grained label into the final label distributions. Finally, we conduct extensive experiments on real-world datasets to demonstrate the advantages of our proposal.

Label distribution learning (LDL) is a powerful learning paradigm that emulates label polysemy by assigning label distributions over the label space. However, existing LDL evaluation metrics struggle to capture meaningful performance differences due to their insensitivity to subtle distributional changes, and existing LDL learning objectives often exhibit biases by disproportionately emphasizing a small subset of samples with extreme predictions. As a result, the LDL metrics lose their discriminability, and the LDL objectives are also at risk of overfitting. In this paper, we propose DeltaLDL, a percentage of predictions that are approximately correct within the context of LDL, as a solution to the above problems. DeltaLDL can serve as a novel evaluation metric, which is parameter-free and reflects more on real performance improvements. DeltaLDL can also serve as a novel learning objective, which is differentiable and encourages most samples to be predicted as approximately correct, thereby mitigating overfitting. Our theoretical analysis and empirical results demonstrate the effectiveness of the proposed solution.

Label distribution learning (LDL) is a novel machine learning paradigm that can handle label ambiguity. This paper focuses on the interpretability issue of label distribution learning. Existing local interpretability models are mainly designed for single-label learning problems and are difficult to directly interpret label distribution learning models. In response to this situation, we propose an improved local interpretable model-agnostic explanations algorithm that can effectively interpret any black-box model in label distribution learning. To address the label dependency problem, we introduce the feature attribution distribution matrix and derive the solution formula for explanations under the label distribution form. Meanwhile, to enhance the transparency and trustworthiness of the explanation algorithm, we provide an analytical solution and derive the boundary conditions for explanation convergence and stability. In addition, we design a feature selection scoring function and a fidelity metric for the explanation task of label distribution learning. A series of numerical experiments and human experiments were conducted to validate the performance of the proposed algorithm in practical applications. The experimental results demonstrate that the proposed algorithm achieves high fidelity, consistency, and trustworthiness in explaining LDL models.

Label Distribution Learning (LDL) has emerged as a powerful framework for estimating complete conditional label distributions, providing crucial reliability for risk-sensitive decision-making tasks. While existing LDL algorithms exhibit competent performance under the conventional LDL performance evaluation methods, two key limitations remain: (1) current algorithms systematically underperform on the samples with low-entropy label distributions, which can be particularly valuable for decision making, and (2) the conventional performance evaluation methods are inherently biased due to the numerical imbalance of samples. In this paper, through empirical and theoretical analyses, we find that excessive cohesion between anchor vectors contributes significantly to the observed entropy bias phenomenon in LDL algorithms. Accordingly, we propose an inter-anchor angular regularization term that mitigates cohesion among anchor vectors by penalizing over-small angles. Besides, to alleviate the numerical imbalance of high-entropy samples in test set, we propose an entropy-calibrated aggregation strategy that obtains the overall model performance by evaluating performance on the low-entropy and high-entropy subsets of the overall test set separately. Finally, we conduct extensive experiments on various real-world datasets to demonstrate the effectiveness of our proposal.

Label distribution in recent years has been applied in a diverse array of complex decision-making tasks. To address the availability of label distributions, label enhancement has been established as an effective learning paradigm that aims to automatically infer label distributions from readily available multi-label data, e.g., logical labels. Recently, numerous works have demonstrated that the label ranking is significantly beneficial to label enhancement. However, these works still exhibit deficiencies in representing the probabilistic relationships between label distribution and label rankings, or fail to accommodate scenarios where multiple labels are equally important for a given instance. Therefore, we propose PROM, a pairwise ranking model with orderliness and monotonicity, to explain the probabilistic relationship between label distributions and label rankings. Specifically, we propose the monotonicity and orderliness assumptions for the probabilities of different ranking relationships and derive the mass functions for PROM, which are theoretically ensured to preserve the monotonicity and orderliness. Further, we propose a generative label enhancement algorithm based on PROM, which directly learns a label distribution predictor from the readily available multi-label data. Finally, extensive experiments demonstrate the efficacy of our proposed model.

Label distribution learning (LDL) is an effective learning paradigm for handling label ambiguity. When applying LDL, it typically requires datasets annotated with label distributions. However, obtaining supervised data for LDL is a challenging task. Due to the randomness of label annotation, the annotator can produce inaccurate annotation results for the instance, affecting the accuracy and generalization ability of the LDL model. To address this problem, we propose a generative approach to calibrate the inaccurate annotation for LDL using variational inference techniques. Specifically, we assume that instances with similar features share latent similar label distributions. The feature vectors and label distributions are generated by Gaussian mixture and Dirichlet mixture, respectively. The relationship between them is established through a shared categorical variable, which effectively utilizes the label distribution of instances with similar features, and achieves a more accurate label distribution through the generative approach. Furthermore, we use a confusion matrix to model the factors that contribute to the inaccuracy during the annotation process, which captures the relationship between label distributions and inaccurate label distributions. Finally, the label distribution is used to calibrate the available information in the noisy dataset to obtain the ground-truth label distribution.

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. They can annotate the label as "$0$" indicating "uncertain relevant" if it is difficult to definitively determine whether the label can describe the instance, in addition to the binary annotation of "$1$" indicating "definitely relevant" and "$-1$" indicating "definitely irrelevant". Both the theoretical and methodological studies are conducted for the proposed learning paradigm. In the theoretical part, we conduct a quantitative comparison of approximation error between ternary and binary labels to elucidate the superiority of ternary labels over binary labels. In the methodological part, we propose a Categorical distribution with monotonicity and orderliness to model the mapping from label description degrees to ternary labels, which can serve as a loss function or as a probability distribution, allowing most existing label enhancement methods to be adapted to our task. Finally, we experimentally demonstrate the effectiveness of our proposal.

Label distribution learning (LDL) is a novel machine-learning paradigm generalized from multilabel learning (MLL). LDL attaches a label distribution to each instance, giving the description degree of different labels. In many real-world applications, key labels, that is, labels with relatively higher description degrees, are preferable to be better predicted. Unfortunately, existing LDL metrics measure the distance or similarity between label distributions from a global perspective, failing to give sufficient attention to key labels. Therefore, we design a novel LDL metric, the description-degree percentile average (DPA), which simultaneously integrates both the exact ranking value and the description degree of each label. The DPA can enhance accuracy in predicting key labels. Furthermore, noting the shape characteristics of the label distributions, we minimize the variance distance between the predicted and the ground-truth label distributions, to better maintain the distinguishability of labels. Finally, we propose an adaptive weighted ranking-oriented LDL algorithm, which is more suitable for realistic LDL problems that require higher accuracy in predicting key labels. We conduct extensive comparison experiments on various types of LDL datasets. Experimental results on both traditional and newly introduced metrics demonstrate the effectiveness of our proposal.

Label distribution learning (LDL) is an effective learning paradigm for dealing with label ambiguity. When applying LDL, the datasets annotated with label distributions (i.e., the real-valued vectors like the probability distribution) are typically required. Unfortunately, most existing datasets only contain the logical labels, and manual annotating with label distributions is costly. To address this problem, we treat the label distribution as a latent vector and infer its posterior by variational Bayes. Specifically, we propose a generative label enhancement model to encode the process of generating feature vectors and logical label vectors from label distributions in a principled way. In terms of features, we assume that the feature vector is generated by a Gaussian mixture dominated by the label distribution, which captures the one-to-many relationship from the label distribution to the feature vector and thus reduces the feature generation error. In terms of logical labels, we design a probability distribution to generate the logical label vector from a label distribution, which captures partial label ranking in the logical label vector and thus provides a more accurate guidance for inferring the label distribution. Besides, to approximate the posterior of the label distribution, we design a inference model, and derive the variational learning objective. Finally, extensive experiments on real-world datasets validate our proposal.

Label distribution is an effective label form to portray label polysemy (i.e., the cases that an instance can be described by multiple labels simultaneously). However, the expensive annotating cost of label distributions limits its application to a wider range of practical tasks. Therefore, LE (label enhancement) techniques are extensively studied to solve this problem. Existing LE algorithms mostly estimate label distributions by the instance relation or the label relation. However, they suffer from biased instance relations, limited model capabilities, or suboptimal local label correlations. Therefore, in this paper, we propose a deep generative model called JRC to simultaneously learn and cluster the joint implicit representations of both features and labels, which can be used to improve any existing LE algorithm involving the instance relation or local label correlations. Besides, we develop a novel label distribution recovery module, and then integrate it with JRC model, thus constituting a novel generative label enhancement model that utilizes the learned joint implicit representations and instance clusters in a principled way. Finally, extensive experiments validate our proposal.

Label distribution offers more information about label polysemy than logical label. There are presently two approaches to obtaining label distributions: LDL (label distribution learning) and LE (label enhancement). In LDL, experts must annotate training instances with label distributions, and a predictive function is trained on this training set to obtain label distributions. In LE, experts must annotate instances with logical labels, and label distributions are recovered from them. However, LDL is limited by expensive annotations, and LE has no performance guarantee. Therefore, we investigate how to predict label distribution from TMLR (tie-allowed multi-label ranking) which is a compromise on annotation cost but has good performance guarantees. On the one hand, we theoretically dissect the relationship between TMLR and label distribution. We define EAE (expected approximation error) to quantify the quality of an annotation, provide EAE bounds for TMLR, and derive the optimal range of label distributions corresponding to a given TMLR annotation. On the other hand, we propose a framework for predicting label distribution from TMLR via conditional Dirichlet mixtures. This framework blends the procedures of recovering and learning label distributions end-to-end and allows us to effortlessly encode our knowledge by a semi-adaptive scoring function. Extensive experiments validate our proposal.

Label distribution learning (LDL) is a novel machine learning paradigm that gives a description degree of each label to a particular instance. But many existing datasets contain only simple logical labels, since it is difficult and time-consuming to directly obtain the label distribution. So label enhancement (LE) is proposed to convert multi-label datasets consisting of logical labels into label distribution datasets. In recently, many LE algorithms have been proposed and most of them concentrate on the fitting degree, but ignore the ordering relation between positive and negative labels. Therefore, in this paper, we propose an LE algorithm based on maintaining positive and negative label relation, which contains a novel ranking loss that can generate different penalties according to different ranking errors. Our algorithm achieves a good balance between the degree of fitting and the ordering relation. The experimental results on several real-world datasets validate the effectiveness of our method.

Label distribution learning (LDL) is a novel machine learning paradigm that can be seen as an extension of multi-label learning (MLL). Compared with MLL, the advantages of LDL are reflected in the following perspectives: (1) the label distribution gives the relevance description of each label to unknown instances in quantitative terms; (2) the distribution implicitly gives the relevance intensities relation of different labels to a particular instance in qualitative terms, i.e., the label ranking relation. All existing LDL models aim to fit the ground-truth label distribution by quantitatively minimizing the distance between distributions or maximizing the similarity between distributions, which only uses the first advantage of the label distribution but ignores the label ranking relation, which may lose some useful semantic information implied in the label distribution, thus reducing the performance of LDL. Therefore, we propose a novel algorithm to solve this problem by introducing the ranking loss function to LDL. In addition, in order to evaluate the LDL algorithms more comprehensively and verify that the ranking loss is beneficial for keeping the label ranking relation, we also introduce two popular ranking evaluation metrics for LDL. The experimental results on 13 real-world datasets validate the effectiveness of our method.

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. annotation cost but has good guarantees for performance. On the one hand, we theoretically investigate the relation between multi-label ranking and label distribution. We define the notion of EAE (expected approximation error) to quantify the quality of an annotation, give the bounds of EAE for multi-label ranking, and derive the optimal range of label distribution corresponding to a particular multi-label ranking. On the other hand, we propose a framework of label distribution predicting from multi-label ranking via conditional Dirichlet mixtures. This framework integrates the processes of recovering and learning label distributions end-to-end and allows us to easily encode our knowledge about current tasks by a scoring function. Finally, we implement extensive experiments to validate our proposal.