Multi-labeled complementary label learning (MLCLL) is a resource-efficient paradigm aimed at reducing labeling efforts in multi-label learning (MLL). While existing methods address the MLCLL problem using neural network-based models, they often overfit to noisy information, leading to sharp decision boundaries. This overfitting issue is further exacerbated when the label correlation, which could help denoise the supervision, is not fully explored in existing works. In this paper, we propose a novel framework called NMCB to alleviate the impact of noisy information in MLCLL, which makes a first attempt to explore mixup for MLCLL problem. Specifically, a tailored version of mixup is employed to achieve a smoother decision boundary of the trained classifier, thereby reducing the sensitivity of NMCB to noisy labels and enhancing its generalization ability. Moreover, NMCB applies a model to automatically extract label correlations from non-complementary labels transformed by mixup during the learning process. These extracted correlations serve as alignment objectives for the output distribution of instance augmentations within a consistency regularization term of NMCB, further improving the model performance. Empirical studies demonstrate the effectiveness of the proposed method.

Multiple complementary-label learning (MCLL) is a machine learning task that involves learning a classifier from instances with multiple complementary labels (MCLs). MCLs are labels that indicate the incorrect labels of an instance. Previous methods for learning with ambiguous supervised information may not be effective because MCLs only make up a small proportion of all labels. In this article, we propose MulCo, a simple yet effective framework that uses contrastive learning to enhance the representation capability in MCLL. Contrastive learning involves contrasting semantically similar and dissimilar pairs of instances, with the goal of benefiting from negatives whose ground-truth labels differ from those of anchors. However, it is possible for dissimilar pairs to have the same label due to the random sampling of negatives from inaccurately labeled data. To solve this problem, we design a sifted contrastive loss for MulCo to correct the sampling of same-label negative pairs. We also provide theoretical evidence for the feasibility of the sifted contrastive loss by establishing an upper bound on the ideal contrastive loss. Correspondingly, we develop two progressive solutions using the properties of complementary labels to approximate the ideal contrastive loss through weighting. Our empirical study demonstrates the effectiveness of the proposed method. The code of this article is available at https://github.com/gaoyi439/MulCo .

Multi-label complementary label learning (MLCLL) is a weakly supervised paradigm that addresses multi-label learning (MLL) tasks using complementary labels (i.e., irrelevant labels) instead of relevant labels. Existing methods typically adopt an unbiased risk estimator (URE) under the assumption that complementary labels follow a uniform distribution. However, this assumption fails in real-world scenarios due to instance-specific annotation biases, making URE-based methods ineffective under such conditions. Furthermore, existing methods underutilize label correlations inherent in MLL. To address these limitations, we propose ComRank, a ranking loss framework for MLCLL, which encourages complementary labels to be ranked lower than non-complementary ones, thereby modeling pairwise label relationships. Theoretically, our surrogate loss ensures Bayes consistency under both uniform and biased cases. Experiments demonstrate the effectiveness of our method in MLCLL tasks. The code is available at https://github.com/JellyJamZhu/ComRank.

In multi-labeled complementary label learning (MLCLL), a complementary label (CL) represents an irrelevant label for an instance. Utilizing CLs instead of relevant labels as annotations simplifies the annotation process in multi-label learning (MLL) tasks, underscoring the practicality of the MLCLL problem. However, existing MLCLL approaches mainly focus on scenarios where an instance is associated with a single CL. This restricts their applicability in situations where annotators provide multiple CLs per instance. To address this limitation, we propose a novel paradigm called multi-label learning with multiple complementary labels (ML-MCL), which allows each instance to be associated with multiple CLs simultaneously. Through analyzing the generation process of multiple CLs, we construct the relationship between relevant labels and CLs. This assists in deriving a tailored risk-consistent estimator to solve MLCLL with multiple CLs. Theoretically, we establish an estimation error bound for this estimator, with a convergence rate of $\mathcal {O}(1/\sqrt{n})$O(1/n). Furthermore, we observed that unbounded gradients can be produced in the derived estimator when optimizing with certain loss functions, which may lead to unstable optimization. To mitigate this issue, we enhance the estimator with a confidence truncation loss, stabilizing the optimization process. Experimental results confirm the effectiveness of our approach, showing improved learning stability and performance in MLCLL tasks involving multiple CLs.

Complementary label learning (CLL) requires annotators to give irrelevant labels instead of relevant labels for instances. Currently, CLL has shown its promising performance on multi-class data by estimating a transition matrix. However, current multi-class CLL techniques cannot work well on multi-labeled data since they assume each instance is associated with one label while each multi-labeled instance is relevant to multiple labels. Here, we show theoretically how the estimated transition matrix in multi-class CLL could be distorted in multi-labeled cases as they ignore co-existing relevant labels. Moreover, theoretical findings reveal that calculating a transition matrix from label correlations in multi-labeled CLL (ML-CLL) needs multi-labeled data, while this is unavailable for ML-CLL. To solve this issue, we propose a two-step method to estimate the transition matrix from candidate labels. Specifically, we first estimate an initial transition matrix by decomposing the multi-label problem into a series of binary classification problems, then the initial transition matrix is corrected by label correlations to enforce the addition of relationships among labels. We further show that the proposal is classifier-consistent, and additionally introduce an MSE-based regularizer to alleviate the tendency of BCE loss overfitting to noises. Experimental results have demonstrated the effectiveness of the proposed method.

Multi-label learning (MLL) usually requires assigning multiple relevant labels to each instance. While a fully supervised MLL dataset needs a large amount of labeling effort, using complementary labels can help alleviate this burden. However, current approaches to learning from complementary labels are mainly designed for multi-class learning and assume that each instance has a single relevant label. This means that these approaches cannot be easily applied to MLL when only complementary labels are provided, where the number of relevant labels is unknown and can vary across instances. In this paper, we first propose the unbiased risk estimator for the multi-labeled complementary label learning (MLCLL) problem. We also provide an estimation error bound to ensure the convergence of the empirical risk estimator. In some cases, the unbiased estimator may give unbounded gradients for certain loss functions and result in overfitting. To mitigate this problem, we improve the risk estimator by minimizing a proper loss function, which has been shown to improve gradient updates. Our experimental results demonstrate the effectiveness of the proposed approach on various datasets.

Abstract Sentence matching is widely used in various natural language tasks, such as natural language inference, paraphrase identification and question answering. For these tasks, we need to understand the logical and semantic relationship between two sentences. Most current methods use all information within a sentence to build a model and hence determine its relationship to another sentence. However, the information contained in some sentences may cause redundancy or introduce noise, impeding the performance of the model. Therefore, we propose a sentence matching method based on multi keyword-pair matching (MKPM), which uses keyword pairs in two sentences to represent the semantic relationship between them, avoiding the interference of redundancy and noise. Specifically, we first propose a sentence-pair-based attention mechanismsp-attentionto select the most important word pair from the two sentences as a keyword pair, and then propose a Bi-task architecture to model the semantic information of these keyword pairs. The Bi-task architecture is as follows: 1. In order to understand the semantic relationship at the word level between two sentences, we design a word-pair task (WP-Task), which uses these keyword pairs to complete sentence matching independently. 2. We design a sentence-pair task (SP-Task) to understand the sentence level semantic relationship between the two sentences by sentence denoising. Through the integration of the two tasks, our model can understand sentences more accurately from the two granularities of word and sentence. Experimental results show that our model can achieve state-of-the-art performance in several tasks. Our source code is publicly available1.

Complementary-label learning (CLL) deals with the weak supervision scenario where each training instance is associated with one \emph{complementary} label, which specifies the class label that the instance does \emph{not} belong to. Given the training instance ${\bm x}$, existing CLL approaches aim at modeling the \emph{generative} relationship between the complementary label $\bar y$, i.e. $P(\bar y\mid {\bm x})$, and the ground-truth label $y$, i.e. $P(y\mid {\bm x})$. Nonetheless, as the ground-truth label is not directly accessible for complementarily labeled training instance, strong generative assumptions may not hold for real-world CLL tasks. In this paper, we derive a simple and theoretically-sound \emph{discriminative} model towards $P(\bar y\mid {\bm x})$, which naturally leads to a risk estimator with estimation error bound at $\mathcal{O}(1/\sqrt{n})$ convergence rate. Accordingly, a practical CLL approach is proposed by further introducing weighted loss to the empirical risk to maximize the predictive gap between potential ground-truth label and complementary label. Extensive experiments clearly validate the effectiveness of the proposed discriminative complementary-label learning approach.

Sentiment classification is a fundamental task in many natural language processing applications. Neural networks have achieved great successes on the sentiment classification task in recent years, since recurrent neural networks and long-short-term memory networks have the ability to deal with sequences of different lengths and to capture contextual semantic information. However, the effectiveness of these methods is limited when used to extract contextual information from relatively long texts. Therefore, in our model, we apply bidirectional gated recurrent units to capture contextual information as far as possible when learning word representations, which may effectively reduce the noise compared to other methods. We also propose a novel loss function namely drop loss (DL) which makes the model focus on the hard examples - examples which are easily classified incorrectly - in order to improve the accuracy of the model. We experiment on four commonly used datasets, and the results show that the proposed method has a good performance on four datasets, and needs fewer parameters compared with recent benchmarks, such as CoVe, ULMFiT, embeddings from language models, and bidirectional encoder representations from transformers. Furthermore, we demonstrate that the classification performance of existing shallow network models can be significantly improved by using DL. In particular, the accuracy of the CNN+LSTM model improves 9% on the IMDB-10 dataset.