Pseudo-labeling has emerged as a popular and effective approach for utilizing unlabeled data. However, in the context of semi-supervised multi-label learning (SSMLL), conventional pseudo-labeling methods encounter difficulties when dealing with instances associated with multiple labels and an unknown label count. These limitations often result in the introduction of false positive labels or the neglect of true positive ones. To overcome these challenges, this paper proposes a novel solution called Class-distribution-Aware Pseudo-labeling (CAP) that performs pseudo-labeling in a class-aware manner. The proposed approach introduces a regularized learning framework incorporating class-aware thresholds, which effectively control the assignment of positive and negative pseudo-labels for each class. Notably, even with a small proportion of labeled examples, our observations demonstrate that the estimated class distribution serves as a reliable approximation. Motivated by this finding, we develop a class-distribution-aware thresholding (CAT) strategy to ensure the alignment of pseudo-label distribution with the true distribution. Moreover, we extend CAT into a label decision method, aiming to improve the model's classification performance during the testing phase. The correctness of the estimated class distribution is theoretically verified, and a generalization error bound is provided for our proposed method. Extensive experiments on multiple benchmark datasets confirm the efficacy of CAP in addressing the challenges of SSMLL problems.

Label Distribution Learning (LDL) is a novel machine learning paradigm that addresses the problem of label ambiguity and has found widespread applications. However, obtaining complete label distributions in real-world scenarios is challenging, which has led to the emergence of Incomplete Label Distribution Learning (InLDL). Existing InLDL methods attempt to utilize low-rank label correlations to recover the complete label distribution. However, we find that real-world LDL datasets have animbalancednature; that is, the sum of the description degrees for normal labels is significantly larger than that for tail labels, which disrupts the low-rank assumption underlying the recovery of the label distribution. To solve the above problem, we propose Incomplete and Imbalance Label Distribution Learning (I2LDL), which makes the use of low-rank label correlations more reasonable for InLDL. Our method decomposes the recovered label distribution matrix into a low-rank component for frequent labels and a sparse component for tail labels, effectively capturing the structure of both head and tail labels. We further require that the entries in the observed positions of the recovered label distribution matrix be close to the observed values, and that the recovered label distribution for every instance forms a probability simplex (i.e., nonnegative entries summing to unity). Finally, the proposed model is optimized via the Alternating Direction Method of Multipliers (ADMM). We provide a theoretical analysis of its exact recovery guarantee under standard assumptions of incoherence, sparsity, and sufficient sampling. Furthermore, we establish a generalization error bound based on Rademacher complexity, offering theoretical insights into the learning performance of our method. Extensive experiments on 16 real-world datasets demonstrate the effectiveness and robustness of our framework compared to existing InLDL methods. The code is available at https://anonymous.4open.science/r/IncomLDL-tailaware-C021.

Modeling label correlations has always played a pivotal role in multi-label image classification (MLC), attracting significant attention from researchers. However, recent studies have overemphasized co-occurrence relationships among labels, which can lead to overfitting risk on this overemphasis, resulting in suboptimal models. To tackle this problem, we advocate for balancing correlative and discriminative relationships among labels to mitigate the risk of overfitting and enhance model performance. To this end, we propose the Multi-Label Visual Prompt Tuning framework, a novel and parameter-efficient method that groups classes into multiple class subsets according to label co-occurrence and mutual exclusivity relationships, and then models them respectively to balance the two relationships. In this work, since each group contains multiple classes, multiple prompt tokens are adopted within Vision Transformer (ViT) to capture the correlation or discriminative label relationship within each group, and effectively learn correlation or discriminative representations for class subsets. On the other hand, each group contains multiple group-aware visual representations that may correspond to multiple classes, and the mixture of experts (MoE) model can cleverly assign them from the group-aware to the label-aware, adaptively obtaining label-aware representation, which is more conducive to classification. Experiments on multiple benchmark datasets show that our proposed approach achieves competitive results and outperforms SOTA methods on multiple pre-trained models.

Offline reinforcement learning (RL) aims to learn an effective policy from a static dataset. To alleviate extrapolation errors, existing studies often uniformly regularize the value function or policy updates across all states. However, due to substantial variations in data quality, the fixed regularization strength often leads to a dilemma: Weak regularization strength fails to address extrapolation errors and value overestimation, while strong regularization strength shifts policy learning toward behavior cloning, impeding potential performance enabled by Bellman updates. To address this issue, we propose the selective state-adaptive regularization method for offline RL. Specifically, we introduce state-adaptive regularization coefficients to trust state-level Bellman-driven results, while selectively applying regularization on high-quality actions, aiming to avoid performance degradation caused by tight constraints on low-quality actions. By establishing a connection between the representative value regularization method, CQL, and explicit policy constraint methods, we effectively extend selective state-adaptive regularization to these two mainstream offline RL approaches. Extensive experiments demonstrate that the proposed method significantly outperforms the state-of-the-art approaches in both offline and offline-to-online settings on the D4RL benchmark. The implementation is available at https://github.com/QinwenLuo/SSAR.

Multi-label learning (MLL) has gained attention for its ability to represent real-world data. Label Distribution Learning (LDL), an extension of MLL to learning from label distributions, faces challenges in collecting accurate label distributions. To address the issue of biased annotations, based on the low-rank assumption, existing works recover true distributions from biased observations by exploring the label correlations. However, recent evidence shows that the label distribution tends to be full-rank, and naive apply of low-rank approximation on biased observation leads to inaccurate recovery and performance degradation. In this paper, we address the LDL with biased annotations problem from a novel perspective, where we first degenerate the soft label distribution into a hard multi-hot label and then recover the true label information for each instance. This idea stems from an insight that assigning hard multi-hot labels is often easier than assigning a soft label distribution, and it shows stronger immunity to noise disturbances, leading to smaller label bias. Moreover, assuming that the multi-label space for predicting label distributions is low-rank offers a more reasonable approach to capturing label correlations. Theoretical analysis and experiments confirm the effectiveness and robustness of our method on real-world datasets.

Pseudo label based semi-supervised learning (SSL) for single-label and multi-label classification tasks has been extensively studied; however, semi-supervised label distribution learning (SSLDL) remains a largely unexplored area. Existing SSL methods fail in SSLDL because the pseudo-labels they generate only ensure overall similarity to the ground truth but do not preserve the ranking relationships between true labels, as they rely solely on KL divergence as the loss function during training. These skewed pseudo-labels lead the model to learn incorrect semantic relationships, resulting in reduced performance accuracy. To address these issues, we propose a novel SSLDL method called \textit{RankMatch}. \textit{RankMatch} fully considers the ranking relationships between different labels during the training phase with labeled data to generate higher-quality pseudo-labels. Furthermore, our key observation is that a flexible utilization of pseudo-labels can enhance SSLDL performance. Specifically, focusing solely on the ranking relationships between labels while disregarding their margins helps prevent model overfitting. Theoretically, we prove that incorporating ranking correlations enhances SSLDL performance and establish generalization error bounds for \textit{RankMatch}. Finally, extensive real-world experiments validate its effectiveness.

Object–context shortcuts remain a persistent challenge in vision‑language models, undermining zero‑shot reliability when test-time scenes diverge from familiar training co-occurrences. We recast this issue as a causal inference problem and ask: Would the prediction remain if the object appeared in a different environment? To answer it at inference time, we estimate object and background expectations within CLIP’s representation space, and synthesize counterfactual embeddings by recombining object features with diverse alternative contexts sampled from external datasets, batch neighbors, or text-derived descriptions. By estimating the Total Direct Effect and simulating intervention, we further subtract background‑only activation, preserving beneficial object–context interactions while mitigating hallucinated scores. Without retraining or prompt design, our method substantially improves both worst-group and average accuracy on context-sensitive benchmarks, establishing a new zero‑shot state of the art. Beyond performance, our framework provides a lightweight representation-level counterfactual approach, offering a practical causal avenue for debiased and reliable multimodal reasoning.

Noisy label learning (NLL) in open-world scenarios poses a novel challenge due to the presence of noisy data from both known and unknown classes. Most existing methods operate under the closed-set assumption, rendering them vulnerable to open-set noise, which significantly degrades their performance. While some approaches attempt to mitigate the impact of open-set examples, they struggle to learn effective discriminative representations for them, leading to unsatisfactory recognition performance. To address these issues, we propose a unified Open Adapter (OpenAda) that identifies open-set noise from both data-centric and learning-based perspectives, and can be easily integrated into mainstream NLL methods to improve their performance and robustness. Specifically, the data-centric part leverages label clusterability to sequentially identify basic clean and basic open-set examples both with high neighbor agreement. The learning-based part integrates one-vs-all classifiers with a progressive open disambiguation strategy to learn a reliable “inlier vs. outlier” boundary for each class. This enables the model to detect challenging open-set examples that partially overlap in the representation space with closed-set ones. Extensive experiments on synthetic and real-world datasets validate the superiority of our approach. Notably, with minor modifications, DivideMix with OpenAda achieves performance improvements of 9.31% and 18.26% on the open-world CIFAR-80 dataset under 80% symmetric noise and 40% asymmetric noise. The code is available athttps://github.com/chenchenzong/OpenAda.

Learning from noisy data has attracted much attention, where most methods focus on closed-set label noise. However, a more common scenario in the real world is the presence of both open-set and closed-set noise. Existing methods typically identify and handle these two types of label noise separately by designing a specific strategy for each type. However, in many real-world scenarios, it would be challenging to identify open-set examples, especially when the dataset has been severely corrupted. Unlike the previous works, we explore how models behave when faced with open-set examples, and find that a part of open-set examples gradually get integrated into certain known classes, which is beneficial for the separation among known classes. Motivated by the phenomenon, we propose a novel two-step contrastive learning method CECL (Class Expansion Contrastive Learning) which aims to deal with both types of label noise by exploiting the useful information of open-set examples. Specifically, we incorporate some open-set examples into closed-set classes to enhance performance while treating others as delimiters to improve representative ability. Extensive experiments on synthetic and real-world datasets with diverse label noise demonstrate the effectiveness of CECL.

Learning with noisy labels can significantly hinder the generalization performance of deep neural networks (DNNs). Existing approaches address this issue through loss correction or example selection methods. However, these methods often rely on the model's predictions obtained from the softmax function, which can be over-confident and unreliable. In this study, we identify the translation invariance of the softmax function as the underlying cause of this problem and propose the \textit{Dirichlet-based Prediction Calibration} (DPC) method as a solution. Our method introduces a calibrated softmax function that breaks the translation invariance by incorporating a suitable constant in the exponent term, enabling more reliable model predictions. To ensure stable model training, we leverage a Dirichlet distribution to assign probabilities to predicted labels and introduce a novel evidence deep learning (EDL) loss. The proposed loss function encourages positive and sufficiently large logits for the given label, while penalizing negative and small logits for other labels, leading to more distinct logits and facilitating better example selection based on a large-margin criterion. Through extensive experiments on diverse benchmark datasets, we demonstrate that DPC achieves state-of-the-art performance. The code is available at https://github.com/chenchenzong/DPC.

Active learning (AL) has achieved great success by selecting the most valuable examples from unlabeled data. However, they usually deteriorate in real scenarios where open-set noise gets involved, which is studied as open-set annotation (OSA). In this paper, we owe the deterioration to the unreliable predictions arising from softmax-based translation invariance and propose a Dirichlet-based Coarse-to-Fine Example Selection (DCFS) strategy accordingly. Our method introduces simplex-based evidential deep learning (EDL) to break translation invariance and distinguish known and unknown classes by considering evidence-based data and distribution uncertainty simultaneously. Furthermore, hard known-class examples are identified by model discrepancy generated from two classifier heads, where we amplify and alleviate the model discrepancy respectively for unknown and known classes. Finally, we combine the discrepancy with uncertainties to form a two-stage strategy, selecting the most informative examples from known classes. Extensive experiments on various openness ratio datasets demonstrate that DCFS achieves state-of-art performance.

The key to multi-label image classification (MLC) is to improve model performance by leveraging label correlations. Unfortunately, it has been shown that overemphasizing co-occurrence relationships can cause the overfitting issue of the model, ultimately leading to performance degradation. In this paper, we provide a causal inference framework to show that the correlative features caused by the target object and its co-occurring objects can be regarded as a mediator, which has both positive and negative impacts on model predictions. On the positive side, the mediator enhances the recognition performance of the model by capturing co-occurrence relationships; on the negative side, it has the harmful causal effect that causes the model to make an incorrect prediction for the target object, even when only co-occurring objects are present in an image. To address this problem, we propose a counterfactual reasoning method to measure the total direct effect, achieved by enhancing the direct effect caused only by the target object. Due to the unknown location of the target object, we propose patching-based training and inference to accomplish this goal, which divides an image into multiple patches and identifies the pivot patch that contains the target object. Experimental results on multiple benchmark datasets with diverse configurations validate that the proposed method can achieve state-of-the-art performance.

The goal of semi-supervised multi-label learning (SSMLL) is to improve model performance by leveraging the information of unlabeled data. Recent studies usually adopt the pseudo-labeling strategy to tackle unlabeled data based on the assumption that labeled and unlabeled data share the same distribution. However, in realistic scenarios, unlabeled examples are often collected through cost-effective methods, inevitably introducing out-of-distribution (OOD) data, leading to a significant decline in model performance. In this paper, we propose a safe semi-supervised multi-label learning framework based on the theory of evidential deep learning (EDL), with the goal of achieving robust and effective unlabeled data exploitation. On one hand, we propose the asymmetric beta loss to not only compensate for the lack of robustness in common MLL losses, but also to solve the inherent positive-negative imbalance problem faced by the EDL losses in MLL. On the other hand, to construct a robust SSMLL framework, we adopt a dual-head structure to generate class probabilities and instance uncertainties. The former are used to generate pseudo-labels, while the latter are utilized to filter OOD examples. To avoid the need for threshold estimation, we develop a dual-measurement weighted loss function to safely perform unlabeled training. Extensive experiments on multiple benchmark datasets verify the effectiveness of the proposed method in both OOD detection and SSMLL tasks.

Offline-to-online (O2O) reinforcement learning (RL) provides an effective means of leveraging an offline pre-trained policy as initialization to improve performance rapidly with limited online interactions. Recent studies often design fine-tuning strategies for a specific offline RL method and cannot perform general O2O learning from any offline method. To deal with this problem, we disclose that there are evaluation and improvement mismatches between the offline dataset and the online environment, which hinders the direct application of pre-trained policies to online fine-tuning. In this paper, we propose to handle these two mismatches simultaneously, which aims to achieve general O2O learning from any offline method to any online method. Before online fine-tuning, we re-evaluate the pessimistic critic trained on the offline dataset in an optimistic way and then calibrate the misaligned critic with the reliable offline actor to avoid erroneous update. After obtaining an optimistic and and aligned critic, we perform constrained fine-tuning to combat distribution shift during online learning. We show empirically that the proposed method can achieve stable and efficient performance improvement on multiple simulated tasks when compared to the state-of-the-art methods.

Multi-label image classification relies on a large-scale, well-maintained dataset, which may easily be mislabeled due to various subjective reasons. Existing methods for coping with noise usually focus on improving the model robustness in the case of single-label noise. However, compared with noisy single-label learning, noisy multi-label learning is more practical and challenging. To reduce the negative impact of noisy multi-annotations, we propose a universal approach for noisy multi-label learning (UNM). In UNM, we propose the label-wise embedding network which investigates the semantic alignment between label embeddings and their corresponding output features to learn robust feature representations. Meanwhile, mining the co-occurrence of multi-labels is also added to regularize the noisy network predictions. We cyclically change the fitting status of our label-wise embedding network to distinguish the noisy samples and generate pseudo labels for them. As a result, UNM provides an effective way to exploit the label-wise features and semantic label embeddings in noisy scenarios. To verify the generalizability of our method, we also test our method on Partial Multi-label Learning (PML) and Multi-label Learning with Missing Labels (MLML). Extensive experiments on benchmark datasets including Microsoft COCO, Pascal VOC, and Visual Genome explicitly validate the proposed method.

Existing knowledge distillation methods typically work by imparting the knowledge of output logits or intermediate feature maps from the teacher network to the student network, which is very successful in multi-class single-label learning. However, these methods can hardly be extended to the multi-label learning scenario, where each instance is associated with multiple semantic labels, because the prediction probabilities do not sum to one and feature maps of the whole example may ignore minor classes in such a scenario. In this paper, we propose a novel multi-label knowledge distillation method. On one hand, it exploits the informative semantic knowledge from the logits by dividing the multi-label learning problem into a set of binary classification problems; on the other hand, it enhances the distinctiveness of the learned feature representations by leveraging the structural information of label-wise embeddings. Experimental results on multiple benchmark datasets validate that the proposed method can avoid knowledge counteraction among labels, thus achieving superior performance against diverse comparing methods. Our code is available at: https://github.com/penghui-yang/L2D.

Pseudo-labeling has emerged as a popular and effective approach for utilizing unlabeled data. However, in the context of semi-supervised multi-label learning (SSMLL), conventional pseudo-labeling methods encounter difficulties when dealing with instances associated with multiple labels and an unknown label count. These limitations often result in the introduction of false positive labels or the neglect of true positive ones. To overcome these challenges, this paper proposes a novel solution called Class-Aware Pseudo-Labeling (CAP) that performs pseudo-labeling in a class-aware manner. The proposed approach introduces a regularized learning framework incorporating class-aware thresholds, which effectively control the assignment of positive and negative pseudo-labels for each class. Notably, even with a small proportion of labeled examples, our observations demonstrate that the estimated class distribution serves as a reliable approximation. Motivated by this finding, we develop a class-distribution-aware thresholding strategy to ensure the alignment of pseudo-label distribution with the true distribution. The correctness of the estimated class distribution is theoretically verified, and a generalization error bound is provided for our proposed method. Extensive experiments on multiple benchmark datasets confirm the efficacy of CAP in addressing the challenges of SSMLL problems.

Class-conditional noise commonly exists in machine learning tasks, where the class label is corrupted with a probability depending on its ground-truth. Many research efforts have been made to improve the model robustness against the class-conditional noise. However, they typically focus on the single label case by assuming that only one label is corrupted. In real applications, an instance is usually associated with multiple labels, which could be corrupted simultaneously with their respective conditional probabilities. In this paper, we formalize this problem as a general framework of learning with Class-Conditional Multi-label Noise (CCMN for short). We establish two unbiased estimators with error bounds for solving the CCMN problems, and further prove that they are consistent with commonly used multi-label loss functions. Finally, a new method for partial multi-label learning is implemented with the unbiased estimator under the CCMN framework. Empirical studies on multiple datasets and various evaluation metrics validate the effectiveness of the proposed method.

In single positive multi-label learning (SPML), only one of multiple positive labels is observed for each instance. The previous work trains the model by simply treating unobserved labels as negative ones, and designs the regularization to constrain the number of expected positive labels. However, in many real-world scenarios, the true number of positive labels is unavailable, making such methods less applicable. In this paper, we propose to solve SPML problems by designing a Label-Aware global Consistency (LAC) regularization, which leverages the manifold structure information to enhance the recovery of potential positive labels. On one hand, we first perform pseudo-labeling for each unobserved label based on its prediction probability. The consistency regularization is then imposed on model outputs to balance the fitting of identified labels and exploring of potential positive labels. On the other hand, by enforcing label-wise embeddings to maintain global consistency, LAC loss encourages the model to learn more distinctive representations, which is beneficial for recovering the information of potential positive labels. Experiments on multiple benchmark datasets validate that the proposed method can achieve state-of-the-art performance for solving SPML tasks.

Partial multi-label learning (PML) deals with problems where each instance is assigned with a candidate label set, which contains multiple relevant labels and some noisy labels. Recent studies usually solve PML problems with the disambiguation strategy, which recovers ground-truth labels from the candidate label set by simply assuming that the noisy labels are generated randomly. In real applications, however, noisy labels are usually caused by some ambiguous contents of the example. Based on this observation, we propose a partial multi-label learning approach to simultaneously recover the ground-truth information and identify the noisy labels. The two objectives are formalized in a unified framework with trace norm and$\ell_1$norm regularizers. Under the supervision of the observed noise-corrupted label matrix, the multi-label classifier and noisy label identifier are jointly optimized by incorporating the label correlation exploitation and feature-induced noise model. Furthermore, by mapping each bag to a feature vector, we extend PML-NI mehtod into multi-instance multi-label learning by identifying noisy labels based on ambiguous instances. A theoretical analysis of generalization bound and extensive experiments on multiple data sets from various real-world tasks demonstrate the effectiveness of the proposed approach.

In partial multi-label learning (PML) problems, each instance is partially annotated with a candidate label set, which consists of multiple relevant labels and some noisy labels. To solve PML problems, existing methods typically try to recover the ground-truth information from partial annotations based on extra assumptions on the data structures. While the assumptions hardly hold in real-world applications, the trained model may not generalize well to varied PML tasks. In this paper, we propose a novel approach for partial multi-label learning with meta disambiguation (PML-MD). Instead of relying on extra assumptions, we try to disambiguate between ground-truth and noisy labels in a meta-learning fashion. On one hand, the multi-label classifier is trained by minimizing a confidence-weighted ranking loss, which distinctively utilizes the supervised information according to the label quality; on the other hand, the confidence for each candidate label is adaptively estimated with its performance on a small validation set. To speed up the optimization, these two procedures are performed alternately with an online approximation strategy. Comprehensive experiments on multiple datasets and varied evaluation metrics validate the effectiveness of the proposed method.

Precisely annotating objects with multiple labels is costly and has become a critical bottleneck in real-world multi-label classification tasks. Instead, deciding the relative order of label pairs is obviously less laborious than collecting exact labels. However, the supervised information of pairwise relevance ordering is less informative than exact labels. It is thus an important challenge to effectively learn with such weak supervision. In this paper, we formalize this problem as a novel learning framework, called multi-label learning with pairwise relevance ordering (PRO). We show that the unbiased estimator of classification risk can be derived with a cost-sensitive loss only from PRO examples. Theoretically, we provide the estimation error bound for the proposed estimator and further prove that it is consistent with respective to the commonly used ranking loss. Empirical studies on multiple datasets and metrics validate the effectiveness of the proposed method.

Partial multi-label learning (PML) deals with problems where each instance is assigned with a candidate label set, which contains multiple relevant labels and some noisy labels. Recent studies usually solve PML problems with the disambiguation strategy, which recovers ground-truth labels from the candidate label set by simply assuming that the noisy labels are generated randomly. In real applications, however, noisy labels are usually caused by some ambiguous contents of the example. Based on this observation, we propose a partial multi-label learning approach to simultaneously recover the ground-truth information and identify the noisy labels. The two objectives are formalized in a unified framework with trace norm and ℓ1 norm regularizers. Under the supervision of the observed noise-corrupted label matrix, the multi-label classifier and noisy label identifier are jointly optimized by incorporating the label correlation exploitation and feature-induced noise model. Extensive experiments on synthetic as well as real-world data sets validate the effectiveness of the proposed approach.

Partial multi-label learning (PML) deals with problems where each instance is associated with a candidate label set, which contains multiple relevant labels and some noisy labels. In many real-world scenarios, it is impractical to annotate all examples for a huge-size dataset. Instead, a more common case is that only a small set of the data are annotated with partial labels, while most data are unlabeled. In this paper, we formalize such problems as a new learning framework called Semi-Supervised Partial Multi-label Learning (SSPML). To solve the SSPML problem, a latent label variable is introduced for each example as the low-dimensional embedding of the feature space. On one hand, label variables are recovered by encouraging consistent similarity measurement between the feature space and the label space; on the other hand, the similarities are adaptively updated based on the feedback from the label space. Meanwhile, the multi-label classifier is jointly trained under the supervision of label variables. Extensive experiments on multiple datasets from various real-world tasks validate the effectiveness of the proposed approach.

Class-conditional variants of Generative adversarial networks (GANs) have recently achieved a great success due to its ability of selectively generating samples for given classes, as well as improving generation quality. However, its training requires a large set of class-labeled data, which is often expensive and difficult to collect in practice. In this paper, we propose an active sampling method to reduce the labeling cost for effectively training the class-conditional GANs. On one hand, the most useful examples are selected for external human labeling to jointly reduce the difficulty of model learning and alleviate the missing of adversarial training; on the other hand, fake examples are actively sampled for internal model retraining to enhance the adversarial training between the discriminator and generator. By incorporating the two strategies into a unified framework, we provide a cost-effective approach to train class-conditional GANs, which achieves higher generation quality with less training examples. Experiments on multiple datasets, diverse GAN configurations and various metrics demonstrate the effectiveness of our approaches.

It is expensive and difficult to precisely annotate objects with multiple labels. Instead, in many real tasks, annotators may roughly assign each object with a set of candidate labels. The candidate set contains at least one but unknown number of ground-truth labels, and is usually adulterated with some irrelevant labels. In this paper, we formalize such problems as a new learning framework called partial multi-label learning (PML). To solve the PML problem, a confidence value is maintained for each candidate label to estimate how likely it is a ground-truth label of the instance. On one hand, the relevance ordering of labels on each instance is optimized by minimizing a rank loss weighted by the confidences; on the other hand, the confidence values are optimized by further exploiting structure information in feature and label spaces.Experimental results on various datasets show that the proposed approach is effective for solving PML problems.

Feature missing is a serious problem in many applications, which may lead to low quality of training data and further significantly degrade the learning performance. While feature acquisition usually involves special devices or complex process, it is expensive to acquire all feature values for the whole dataset. On the other hand, features may be correlated with each other, and some values may be recovered from the others. It is thus important to decide which features are most informative for recovering the other features as well as improving the learning performance. In this paper, we try to train an effective classification model with least acquisition cost by jointly performing active feature querying and supervised matrix completion. When completing the feature matrix, a novel objective function is proposed to simultaneously minimize the reconstruction error on observed entries and the supervised loss on training data. When querying the feature value, the most uncertain entry is actively selected based on the variance of previous iterations. In addition, a bi-objective optimization method is presented for cost-aware active selection when features bear different acquisition costs. The effectiveness of the proposed approach is well validated by both theoretical analysis and experimental study.