Label correlation is helpful to alleviate the overwhelming output space of label distribution learning (LDL). However, existing studies either only consider one of global and local label correlations or exploit label correlation by some prior knowledge (e.g., low-rank assumption, which may not hold sometimes). To efficiently exploit both global and local label correlations in a data-driven way, we propose in this article a new LDL method called label distribution learning by exploiting label distribution manifold (LDL-LDM). Our basic idea is that the underlying manifold structure of label distribution may encode the correlations among labels. LDL-LDM works as follows. First, to exploit global label correlation, we learn the label distribution manifold and encourage the outputs of our model to lie in the same manifold. Second, we learn the label distribution manifold of different clusters of samples to consider local label correlations. Third, to handle incomplete label distribution learning (incomplete LDL), we jointly learn label distribution and label distribution manifold. Theoretical analysis demonstrates the generalization of our method. Finally, experimental results validate the effectiveness of LDL-LDM in both full and incomplete LDL cases.

Researchers have suggested leveraging label correlation to deal with the exponentially sized output space of label distribution learning (LDL). Among them, some have proposed to exploit local label correlation. They first partition the training set into different groups and then exploit local label correlation on each one. However, these works usually apply clustering algorithms, such as $K$ -means, to split the training set and obtain the clustering results independent of label correlation. The structures (e.g., low rank and manifold) learned on such clusters may not efficiently capture label correlation. To solve this problem, we put forward a novel LDL method called LDL by partitioning label distribution manifold (LDL-PLDM). First, it jointly bipartitions the training set and learns the label distribution manifold to model label correlation. Second, it recurses until the reconstruction error of learning the label distribution manifold cannot be reduced. LDL-PLDM achieves label-correlation-related partition results, on which the learned label distribution manifold can better capture label correlation. We conduct extensive experiments to justify that LDL-PLDM statistically outperforms state-of-the-art LDL methods.

As a novel learning paradigm, label distribution learning (LDL) explicitly models label ambiguity with the definition of label description degree. Although lots of work has been done to deal with real-world applications, theoretical results on LDL remain unexplored. In this paper, we rethink LDL from theoretical aspects, towards analyzing learnability of LDL. Firstly, risk bounds for three representative LDL algorithms (AA-kNN, AA-BP and SA-ME) are provided. For AA-kNN, Lipschitzness of the label distribution function is assumed to bound the risk, and for AA-BP and SA-ME, rademacher complexity is utilized to give data-dependent risk bounds. Secondly, a generalized plug-in decision theorem is proposed to understand the relation between LDL and classification, uncovering that approximation to the conditional probability distribution function in absolute loss guarantees approaching to the optimal classifier, and also data-dependent error probability bounds are presented for the corresponding LDL algorithms to perform classification. As far as we know, this is perhaps the first research on theory of LDL.

Robust few-shot learning (RFSL), which aims to address noisy labels in few-shot learning, has recently gained considerable attention. Existing RFSL methods are based on the assumption that the noise comes from known classes (in-domain), which is inconsistent with many real-world scenarios where the noise does not belong to any known classes (out-of-domain). We refer to this more complex scenario as open-world few-shot learning (OFSL), where in-domain and out-of-domain noise simultaneously exists in few-shot datasets. To address the challenging problem, we propose a unified framework to implement comprehensive calibration from instance to metric. Specifically, we design a dual-networks structure composed of a contrastive network and a meta network to respectively extract feature-related intra-class information and enlarged inter-class variations. For instance-wise calibration, we present a novel prototype modification strategy to aggregate prototypes with intra-class and inter-class instance reweighting. For metric-wise calibration, we present a novel metric to implicitly scale the per-class prediction by fusing two spatial metrics respectively constructed by the two networks. In this way, the impact of noise in OFSL can be effectively mitigated from both feature space and label space. Extensive experiments on various OFSL settings demonstrate the robustness and superiority of our method. Our source codes is available at https://github.com/anyuexuan/IDEAL .