Label distribution is more general than both single-label annotation and multi-label annotation. It covers a certain number of labels, representing the degree to which each label describes the instance. The learning process on the instances labeled by label distributions is called label distribution learning (LDL). Unfortunately, many training sets only contain simple logical labels rather than label distributions due to the difficulty of obtaining the label distributions directly. To solve this problem, one way is to recover the label distributions from the logical labels in the training set via leveraging the topological information of the feature space and the correlation among the labels. Such process of recovering label distributions from logical labels is defined as label enhancement (LE), which reinforces the supervision information in the training sets. This paper proposes a novel LE algorithm called Graph Laplacian Label Enhancement (GLLE). Experimental results on one artificial dataset and fourteen real-world LDL datasets show clear advantages of GLLE over several existing LE algorithms. Furthermore, experimental results on eleven multi-label learning datasets validate the advantage of GLLE over the state-of-the-art multi-label learning approaches.

Partial-label learning (PLL) utilizes instances with PLs, where a PL includes several candidate labels but only one is the true label (TL). In PLL, identification-based strategy (IBS) purifies each PL on the fly to select the (most likely) TL for training; average-based strategy (ABS) treats all candidate labels equally for training and let trained models be able to predict TL. Although PLL research has focused on IBS for better performance, ABS is also worthy of study since modern IBS behaves like ABS in the beginning of training to prepare for PL purification and TL selection. In this paper, we analyze why ABS was unsatisfactory and propose how to improve it. Theoretically, we propose two problem settings of PLL and prove that average PL losses (APLLs) with bounded multi-class losses are always robust, while APLLs with unbounded losses may be non-robust, which is the first robustness analysis for PLL. Experimentally, we have two promising findings: ABS using bounded losses can match/exceed state-of-the-art performance of IBS using unbounded losses; after using robust APLLs to warm start, IBS can further improve upon itself. Our work draws attention to ABS research, which can in turn boost IBS and push forward the whole PLL.

Partial label learning (PLL) is a form of weakly supervised learning, where each training example is linked to a set of candidate labels, among which only one label is correct. Most existing PLL approaches assume that the incorrect labels in each training example are randomly picked as the candidate labels. However, in practice, this assumption may not hold true, as the candidate labels are often instance-dependent. In this paper, we address the instance-dependent PLL problem and assume that each example is associated with a latent label distribution where the incorrect label with a high degree is more likely to be annotated as a candidate label. Motivated by this consideration, we propose two methods Valen and Milen , which train the predictive model via utilizing the latent label distributions recovered by the label enhancement process. Specifically, Valen recovers the latent label distributions via inferring the variational posterior density parameterized by an inference model with the deduced evidence lower bound. Milen recovers the latent label distribution by adopting the variational approximation to bound the mutual information among the latent label distribution, observed labels and augmented instances. Experiments on benchmark and real-world datasets validate the effectiveness of the proposed methods.

Partial multi-label learning (PML) aims to learn a multilabel predictive model from the PML training examples, each of which is associated with a set of candidate labels where only a subset is valid. The common strategy to induce a predictive model is identifying the valid labels in each candidate label set. Nonetheless, this strategy ignores considering the essential label distribution corresponding to each instance as label distributions are not explicitly available in the training dataset. In this article, a novel partial multilabel learning method is proposed to recover the latent label distribution and progressively enhance it for predictive model induction. Specifically, the label distribution is recovered by considering the observation model for logical labels and the sharing topological structure from feature space to label distribution space. Besides, the latent label distribution is progressively enhanced by recovering latent labeling information and supervising predictive model training alternatively to make the label distribution appropriate for the induced predictive model. Experimental results on PML datasets clearly validate the effectiveness of the proposed method for solving partial multilabel learning problems. In addition, further experiments show the high quality of the recovered label distributions and the effectiveness of adopting label distributions for partial multilabel learning.

Multi-label learning focuses on the ambiguity at the label side, i.e., one instance is associated with multiple class labels, where the logical labels are always adopted to partition class labels into relevant labels and irrelevant labels rigidly. However, the relevance or irrelevance of each label corresponding to one instance is essentially relative in real-world tasks and the label distribution is more fine-grained than the logical labels by denoting one instance with a certain number of the description degrees of all class labels. As the label distribution is not explicitly available in most training sets, a process named label enhancement emerges to recover the label distributions in training datasets. By inducing the generative model of the label distribution and adopting the variational inference technique, the approximate posterior density of the label distributions should maximize the variational lower bound. Following the above consideration, LEVI is proposed to recover the label distributions from the training examples. In addition, the multi-label predictive model is induced for multi-label learning by leveraging the recovered label distributions along with a specialized objective function. The recovery experiments on fourteen label distribution datasets and the predictive experiments on fourteen multi-label learning datasets validate the advantage of our approach over the state-of-the-art approaches.

Multi-label text classification (MLTC) refers to the problem of tagging a given document with the most relevant subset of labels. One of the biggest challenges for MLTC is the existence of class imbalance. Most advanced MLTC models suffer from this issue, which limits the performance of the models. In this paper, we propose a model-agnostic framework named variational continuous label distribution learning (VCLDL) to address this problem. VCLDL theoretically builds a corresponding relationship between the feature space and the label space to mine the information hidden in the observable logical labels. Specifically, VCLDL regards label distribution as a continuous density function in latent space and forms a flexible variational approach to approximate the density function of the labels with the collaboration of the feature space. Combined with VCLDL, MLTC models can pay more attention to the distribution of the whole label set, rather than specific labels with maximum response values, thus the class imbalance problem can be well overcome. Experimental results on multiple benchmark datasets demonstrate that VCLDL can bring significant performance improvements over the existing MLTC models.