Adversarial Paritial Multi-label Learning

1 INTRODUCTION . In partial multi-label learning ( PML ) , each training instance is assigned multiple candidate labels which are only partially relevant ; that is , some assigned labels are irrelevant noise . As it is typically difficult and costly to precisely annotate instances for multi-label data ( Xie & Huang , 2018 ) , the task of PML naturally arises in many real-world scenarios with crowdsource annotations . Figure 1 presents an example of training images for object recognition under the PML setting , where the union of candidate labels provided by crowdsource annotators is overcomplete and contains both ground truth labels ( in black color ) and irrelevant noise labels ( in red color ) . PML is much more challenging than standard multi-label learning as the true labels are hidden among irrelevant labels and the number of true labels is unknown . The goal of PML is to learn a good multi-label prediction model from such a partial label training set , and hence reduce the annotation cost . An intuitive strategy of PML is to treat all candidate labels as relevant ground truth , thus any off-theshelf multi-label classification methods can be adapted to induce an expected multi-label predictor ( Zhang & Zhou , 2014 ) . This strategy , though simple , can not work well since taking the noisy labels as part of the true labels will mislead the multi-label training and induce inferior prediction models . The PML work in ( Xie & Huang , 2018 ) assumes that each candidate label has a confidence score of being a true label , and learns the confidence scores and classifier in an alternative manner by minimizing a confidence weighted ranking loss between the candidate and non-candidate labels . Although this work yields some reasonable results , the estimation of label confidence scores is error-prone , especially when noisy labels dominate , which can seriously impair the classifier ’ s performance . Another recent work in ( Fang & Zhang , 2019 ) also exploits label confidence values of candidate labels for PML . It estimates the confidence values using iterative label propagation and chooses the candidate labels with high confidence values as credible labels , which are then used to induce a multi-label prediction model . This work however suffers from the cumulative errors induced in propagation , which can impact the estimation of the credible labels and consequently impair the prediction model . In this paper , we propose a novel adversarial learning model , PML-GAN , under a generalized encoder-decoder framework to tackle the partial multi-label learning problem . The PML-GAN model comprises four component networks : a disambiguation network that predicts the probability of each candidate label being an additive noise for a training instance ; a prediction network that predicts the disambiguated true labels of each instance from its input features ; a generation network that generates samples in the feature space given latent vectors in the label space ; and a discrimination network that separates the generated samples from the real data . The prediction network and disambiguation network together form an encoder that maps data samples in the input feature space to the disambiguated label vectors , while the generation network and discrimination network forms a generative adversarial network ( GAN ) ( Goodfellow et al. , 2014 ) as an inverse decoding mapping from vectors in the multi-label space to samples in the input feature space . The learning of the overall model corresponds to a minimax adversarial game , which enhances the correspondence of input features with the output labels , and consequently boosts multi-label prediction performance . To the best of our knowledge , this is the first work that exploits GANs for PML . We conduct extensive experiments on multi-label datasets under partial multi-label learning setting . The empirical results show the proposed PML-GAN yields the state-of-the-art PML performance . 2 RELATED WORK . Multi-label learning is a prevalent classification problem in many real world domains , where each instance can be assigned into multiple classes simultaneously . Many multi-label learning methods developed in the literature exploit label correlations at different degrees to produce multi-label classifiers ( Zhang & Zhou , 2014 ) , including the first order methods ( Zhang et al. , 2018 ) , second order methods ( Li et al. , 2014 ) , and high-order methods ( Burkhardt & Kramer , 2018 ) . Nevertheless , standard multi-label learning methods all assume each training instance is annotated with a complete set of ground truth labels , which can be impractical in many domains , where the annotations are obtained through crowdsourcing . With the union of annotations produced by multiple noisy labelers under the crowdsourcing setting , the partial multi-label learning ( PML ) problem arises naturally in real world scenarios , where the set of labels assigned to each training instance not only contain the ground truth labels , but also some additional irrelevant labels . PML is more challenging than standard multi-label learning . The previous PML work in ( Xie & Huang , 2018 ) proposes two methods , PML-FP and PML-LC , to estimate the label confidence values and optimize the relevance ordering of labels on each training instance by exploring the structural information in both feature and label spaces . However , due to the inherent property of alternative optimization , in these methods , the estimation error of labeling confidence values can negatively impact the coupled multi-label predictor . The work in ( Sun et al. , 2019 ) denoises the observed label matrix based on low-rank and sparse matrix decomposition . In another recent work ( Fang & Zhang , 2019 ) , the authors propose to address PML problem using a two-stage strategy . It first estimates the label confidence value of each candidate label with iterative label propagation , and then performs multi-label learning over selected credible labels based on the confidence values by using pairwise label ranking ( PARTICLE-VLS ) or maximum a posteriori reasoning ( PARTICLE-MAP ) . However , their credible label estimation can be impaired by the cumulative error induced in the propagation process , which can consequently degrade the multi-label learning performance , especially when there are many noisy labels . Studies on weak learning and partial label learning have some connections with PML , but address different problems . Weak label learning tackles the problem of multi-label learning with incomplete labels ( Sun et al. , 2010 ; Wei et al. , 2018 ) , where some ground truth labels are missed out from the annotations . Partial label learning ( PLL ) tackles multi-class classification under the setting where for each training instance there is one ground-truth label among the given candidate label set ( Cour et al. , 2011 ; Liu & Dietterich , 2012 ; Zhang & Yu , 2015 ; Yu & Zhang , 2016 ; Chen et al. , 2018 ) . PLL methods can not be directly applied on the more challenging PML problems , as under PML one has unknown numbers of ground truth labels among the candidate label set for each training instance . Generative adversarial networks ( GANs ) ( Goodfellow et al. , 2014 ) , which perform minimax adversarial training over a generation network and a discrimination network , are one of the most popular generative models since its introduction . During the past years , a vast range of GAN-based adversarial learning methods have been developed to address different tasks , including semi-supervised learning ( Kumar et al. , 2017 ; Lecouat et al. , 2018 ) , unsupervised learning ( Jakab et al. , 2018 ) , and learning with noisy labels ( Thekumparampil et al. , 2018 ) . The proposed work in this paper however is the first one that exploits GAN models for PML . 3 PROPOSED APPROACH . In this section , we present the proposed adversarial partial multi-label learning model , PML-GAN , under the following setting . Assume we have a training set S = ( X , Y ) = { ( xi , yi ) } Ni=1 , where xi ∈ Rd denotes the input feature vector for the i-th instance , and yi ∈ { 0 , 1 } L is the corresponding annotated label indicator vector . The multiple 1 values in each yi indicate either the ground truth labels or the additional mis-annotated labels . We aim to learn a good multi-label prediction model from this partially labeled training set . The proposed PML-GAN model is illustrated in Figure 2 , which comprises four component networks , disambiguation network D̃ , prediction network F , generation network G and discrimination network D. The four components coordinate with and enhance each other under an encoder-decoder learning framework , which forms inverse mappings between the instance vectors in the input feature space and the label vectors in the output class label space . Below we present these model components , the learning objective and training algorithm in details . 3.1 PREDICTION WITH DISAMBIGUATED LABELS . Comparing to standard multi-label learning , the main difficulty of PML is that the annotated labels { yi } in the training data contain additive noisy labels . The main challenge lies in identifying the ground truth labels z∗i from each annotated candidate label vectors yi ; that is dropping the additional 1s from each candidate label vector yi . We propose to tackle this challenge by using a disambiguation network D̃ : Ωx → Ω∆ ( Ω· denotes the corresponding domain space ) , which predicts the irrelevant labels for a given instance . Hence the true label vector z∗i can be recovered as z ∗ i = ReLU ( yi −∆i ) , where ReLU ( · ) = max ( · , 0 ) denotes the commonly used rectified linear unit activation function for deep neural networks . Then we can learn a prediction network F : Ωx → Ωz , i.e. , a multi-label classifier , to predict the disambiguated ground truth labels for each instance . Although the label indicator vectors in the training data are provided as discrete values , it is difficult for either the disambiguation network or the prediction network to directly produce discrete output values . Instead , by using a sigmoid activation function on the last layer of each network , D̃ ( x ) and F ( x ) can predict the probability of each class label being the additive irrelevant label and the ground truth label respectively . With the disambiguation network and prediction network , we can perform partial multi-label learning by minimizing the classification loss on training data S : min F , D̃ Lc ( X , Y ; F , D̃ ) = ∑ ( xi , yi ) ∼S ` c ( F ( xi ) , zi ) ( 1 ) s.t . zi = ReLU ( yi −∆i ) , ∆i = D̃ ( xi ) , ∀ ( xi , yi ) ∼ S where zi denotes the disambiguated label confidence vector with continuous values in [ 0 , 1 ] , which can be viewed as a relaxation of a true label indicator vector , while ` c ( · , · ) denotes the cross-entropy loss between the predicted probability of each label and its confidence of being a ground-truth label . 3.2 INVERSE MAPPING WITH GANS . The prediction network and disambiguation network together form an encoder that maps data samples in the input feature space to the disambiguated label vectors . To enhance the label disambiguation and hence improve multi-label classification , we propose to conduct an inverse decoding mapping from label vectors ẑ ∈ { 0 , 1 } L to samples in the input feature space . In particular , we propose to deploy a generative adversarial network ( GAN ) model to generate samples in the input feature space given label vectors in the label space . The GAN model comprises a generation network G and a discrimination network D. Given a label vector ẑ sampled from a prior binomial distribution P ( ẑ ) , one can generate a sample x̂ using the generation network , x = G ( ẑ ) . A two-class discriminator D is used to discriminate the generated samples from the real samples in S. The training of the GAN model is a minimax optimization problem over an adversarial loss function : min G max D Ladv ( G , D , S ) = Exi∼S [ logD ( xi ) ] + Eẑ∼P ( ẑ ) [ log ( 1−D ( G ( ẑ ) ) ) ] ( 2 ) where the discriminator D tries to maximally distinguish the generated samples G ( ẑ ) from the real data samples in S , and the generator G tries to generate samples that are similar to the real data as much as possible such that the discriminator can not tell the difference . In theory , the samples generated by the adversarially trained generator G can have an identical distribution with the real data S ( Goodfellow et al. , 2014 ) . But this does not guarantee the generated samples can match the real training samples . To ensure the generator G can provide an inverse mapping function relative to the predictor F , we further propose to decode the disambiguated training label vectors into the training samples S with G by deploying a generation loss : Lg ( G , S ) = ∑ ( xi , yi ) ∼S ` g ( G ( zi ) , xi ) , where zi = ReLU ( yi − D̃ ( xi ) ) ( 3 ) where ` g ( · , · ) measures the generation loss on each training instance and can be a least squares function . This generation loss can enhance the label disambiguation and improve multi-label learning .

Summary: This paper proposed a new method for partial multi-label learning, based on the idea of generative adversarial networks. The partial multi-label learning is the problem that one instance is associated with several ground truth labels simultaneously, but we are given a superset of the ground truth labels for training. To solve the problem, the paper proposes a learning model composing of four deep neural networks, two of them for prediction the ground truth labels (the prediction network, and the disambiguation network), one of them to generate instances based on the disambiguated labels, and one discriminative network to discriminated generated instance versus true instances. The four network are concatenated, and the paper proposed to optimize the sum of generation loss, the classification loss, and the adversarial loss. Theoretical results like the theories in the original GAN paper are also given. Finally, the paper does thorough empirical studies compared the proposed method with four other baselines and three variants on fourteen datasets with various settings.