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Partial multi-label learning (PML) models the scenario where each training instance is annotated with a set of candidate labels, and only some of the labels are relevant. The PML problem is practical in real-world scenarios, as it is difficult and even impossible to obtain precisely labeled samples. Several PML solutions have been proposed to combat with the prone misled by the irrelevant labels concealed in the candidate labels, but they generally focus on the smoothness assumption in feature space or low-rank assumption in label space, while ignore the negative information between features and labels. Specifically, if two instances have largely overlapped candidate labels, irrespective of their feature similarity, their ground-truth labels should be similar; while if they are dissimilar in the feature and candidate label space, their ground-truth labels should be dissimilar with each other. To achieve a credible predictor on PML data, we propose a novel approach called PML-LFC (Partial Multi-label Learning with Label and Feature Collaboration). PML-LFC estimates the confidence values of relevant labels for each instance using the similarity from both the label and feature spaces, and trains the desired predictor with the estimated confidence values. PML-LFC achieves the predictor and the latent label matrix in a reciprocal reinforce manner by a unified model, and develops an alternative optimization procedure to optimize them. Extensive empirical study on both synthetic and real-world datasets demonstrates the superiority of PML-LFC.
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Partial-label learning (PLL) is a multi-class classification problem, where each training example is associated with a set of candidate labels. Even though many practical PLL methods have been proposed in the last two decades, there lacks a theoretical understanding of the consistency of those methods-none of the PLL methods hitherto possesses a generation process of candidate label sets, and then it is still unclear why such a method works on a specific dataset and when it may fail given a different dataset. In this paper, we propose the first generation model of candidate label sets, and develop two novel PLL methods that are guaranteed to be provably consistent, i.e., one is risk-consistent and the other is classifier-consistent. Our methods are advantageous, since they are compatible with any deep network or stochastic optimizer. Furthermore, thanks to the generation model, we would be able to answer the two questions above by testing if the generation model matches given candidate label sets. Experiments on benchmark and real-world datasets validate the effectiveness of the proposed generation model and two PLL methods.
Embedding approaches have become one of the most pervasive techniques for multi-label classification. However, the training process of embedding methods usually involves a complex quadratic or semidefinite programming problem, or the model may even involve an NP-hard problem. Thus, such methods are prohibitive on large-scale applications. More importantly, much of the literature has already shown that the binary relevance (BR) method is usually good enough for some applications. Unfortunately, BR runs slowly due to its linear dependence on the size of the input data. The goal of this paper is to provide a simple method, yet with provable guarantees, which can achieve competitive performance without a complex training process. To achieve our goal, we provide a simple stochastic sketch strategy for multi-label classification and present theoretical results from both algorithmic and statistical learning perspectives. Our comprehensive empirical studies corroborate our theoretical findings and demonstrate the superiority of the proposed methods.
We propose to formulate multi-label learning as a estimation of class distribution in a non-linear embedding space, where for each label, its positive data embeddings and negative data embeddings distribute compactly to form a positive component and negative component respectively, while the positive component and negative component are pushed away from each other. Duo to the shared embedding space for all labels, the distribution of embeddings preserves instances label membership and feature matrix, thus encodes the feature-label relation and nonlinear label dependency. Labels of a given instance are inferred in the embedding space by measuring the probabilities of its belongingness to the positive or negative components of each label. Specially, the probabilities are modeled as the distance from the given instance to representative positive or negative prototypes. Extensive experiments validate that the proposed solution can provide distinctively more accurate multi-label classification than other state-of-the-art algorithms.
Multi-label classification (MLC) studies the problem where each instance is associated with multiple relevant labels, which leads to the exponential growth of output space. MLC encourages a popular framework named label compression (LC) for capturing label dependency with dimension reduction. Nevertheless, most existing LC methods failed to consider the influence of the feature space or misguided by original problematic features, so that may result in performance degeneration. In this paper, we present a compact learning (CL) framework to embed the features and labels simultaneously and with mutual guidance. The proposal is a versatile concept, hence the embedding way is arbitrary and independent of the subsequent learning process. Following its spirit, a simple yet effective implementation called compact multi-label learning (CMLL) is proposed to learn a compact low-dimensional representation for both spaces. CMLL maximizes the dependence between the embedded spaces of the labels and features, and minimizes the loss of label space recovery concurrently. Theoretically, we provide a general analysis for different embedding methods. Practically, we conduct extensive experiments to validate the effectiveness of the proposed method.
Partial-label learning (PLL) is a typical weakly supervised learning problem, where each training instance is equipped with a set of candidate labels among which only one is the true label. Most existing methods elaborately designed learning objectives as constrained optimizations that must be solved in specific manners, making their computational complexity a bottleneck for scaling up to big data. The goal of this paper is to propose a novel framework of PLL with flexibility on the model and optimization algorithm. More specifically, we propose a novel estimator of the classification risk, theoretically analyze the classifier-consistency, and establish an estimation error bound. Then we propose a progressive identification algorithm for approximately minimizing the proposed risk estimator, where the update of the model and identification of true labels are conducted in a seamless manner. The resulting algorithm is model-independent and loss-independent, and compatible with stochastic optimization. Thorough experiments demonstrate it sets the new state of the art.
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