Contrastive Label Disambiguation for Partial Label Learning

1 INTRODUCTION . The training of modern deep neural networks typically requires massive labeled data , which imposes formidable obstacles in data collection . Of a particular challenge , data annotation in the real-world can naturally be subject to inherent label ambiguity and noise . For example , as shown in Figure 1 , identifying an Alaskan Malamute from a Siberian Husky can be difficult for a human annotator . The issue of labeling ambiguity is prevalent yet often overlooked in many applications , such as web mining ( Luo & Orabona , 2010 ) and automatic image annotation ( Chen et al. , 2018 ) . This gives rise to the importance of partial label learning ( PLL ) ( Hüllermeier & Beringer , 2006 ; Cour et al. , 2011 ) , where each training example is equipped with a set of candidate labels instead of the exact groundtruth label . This stands in contrast to its supervised counterpart where one label must be chosen as the “ gold ” . Arguably , the PLL problem is deemed more common and practical in various situations due to its relatively lower cost to annotations . Despite the promise , a core challenge in PLL is label disambiguation , i.e. , identifying the groundtruth label from the candidate label set . Existing methods typically require a good feature representation ( Liu & Dietterich , 2012 ; Zhang et al. , 2016 ; Lyu et al. , 2021 ) , and operate under the assumption that data points closer in the feature space are more likely to share the same ground-truth label . However , the reliance on representations has led to a non-trivial dilemma—the inherent label uncertainty can undesirably manifest in the representation learning process—the quality of which may in turn prevent effective label disambiguation . To date , few efforts have been made to resolve this . This paper bridges the gap by reconciling the intrinsic tension between the two highly dependant problems—representation learning and label disambiguation—in one coherent and synergistic framework . Our framework , Partial label learning with COntrastive label disambiguation ( dubbed PiCO ) , produces closely aligned representations for examples from the same classes and facilitates label disambiguation . Specifically , PiCO encapsulates two key components . First , we leverage contrastive learning ( CL ) ( Khosla et al. , 2020 ) to partial label learning , which is unexplored in previous PLL literature . To mitigate the key challenge of constructing positive pairs , we employ the classifier ’ s output and generate pseudo positive pairs for contrastive comparison ( Section 3.1 ) . Second , based on the learned embeddings , we propose a novel prototype-based label disambiguation strategy ( Section 3.2 ) . Key to our method , we gradually update the pseudo target for classification , based on the closest class prototype . By alternating the two steps above , PiCO converges to a solution with a highly distinguishable representation for accurate classification . Empirically , PiCO establishes state-of-the-art performance on three benchmark datasets , outperforming the baselines by a significant margin ( Section 4 ) and obtains results that are competitive with fully supervised learning . Theoretically , we demonstrate that our contrastive representation learning and prototype-based label disambiguation are mutually beneficial , and can be rigorously interpreted from an ExpectationMaximization ( EM ) algorithm perspective ( Section 5 ) . First , the refined pseudo labeling improves contrastive learning by selecting pseudo positive examples accurately . This can be analogous to the E-step , where we utilize the classifier ’ s output to assign each data example to one label-specific cluster . Second , better contrastive performance in turn improves the quality of representations and thus the effectiveness of label disambiguation . This can be reasoned from an M-step perspective , where the contrastive loss partially maximizes the likelihood by clustering similar data examples . Finally , the training data will be mapped to a mixture of von Mises-Fisher distributions on the unit hypersphere , which facilitates label disambiguation by using the component-specific label . Our main contributions are summarized as follows : 1 ( Methodology ) . To the best of our knowledge , our paper pioneers the exploration of contrastive learning for partial label learning and proposes a novel framework termed PiCO . As an integral part of our algorithm , we also introduce a new prototype-based label disambiguation mechanism , leverages the contrastively learned embeddings . 2 ( Experiments ) . Empirically , our proposed PiCO framework establishes the state-of-the-art performance on three PLL tasks . Moreover , we make the first attempt to conduct experiments on fine-grained classification datasets , where we show classification performance improvement by up to 9.61 % compared with the best baseline on the CUB-200 dataset . 3 ( Theory ) . We theoretically interpret our framework from the expectation-maximization perspective . Our derivation is also generalizable to other CL methods and shows the alignment property in CL ( Wang & Isola , 2020 ) mathematically equals the M-step in center-based clustering algorithms . 2 BACKGROUND The problem of partial label learning ( PLL ) is defined using the following setup . Let X be the input space , and Y = { 1 , 2 , ... , C } be the output label space . We consider a training dataset D = { ( xi , Yi ) } ni=1 , where each tuple comprises of an image xi ∈ X and a candidate label set Yi ⊂ Y . Identical to the supervised learning setup , the goal of PLL is to obtain a functional mapping that predicts the one true label associated with the input . Yet differently , the PLL setup bears significantly more uncertainty in the label space . A basic assumption of PLL is that the groundtruth label yi is concealed in its candidate set , i.e. , yi ∈ Yi , and is invisible to the learner . For this reason , the learning process can suffer from inherent ambiguity , compared with the supervised learning task with explicit ground-truth . The key challenge of PLL is to identify the ground-truth label from the candidate label set . During training , we assign each image xi a normalized vector si ∈ [ 0 , 1 ] C as the pseudo target , whose entries denote the probability of labels being the ground-truth . The total probability mass of 1 is allocated among candidate labels in Yi . Note that si will be updated during the training procedure . Ideally , si should put more probability mass on the ( unknown ) ground-truth label yi over the course of training . We train a classifier f : X → [ 0 , 1 ] C using cross-entropy loss , with si being the target prediction . The per-sample loss is given by : Lcls ( f ; xi , Yi ) = ∑C j=1 −si , j log ( f j ( xi ) ) s.t . ∑ j∈Yi si , j = 1 and si , j = 0 , ∀j /∈ Yi , ( 1 ) where j denotes the indices of labels . si , j denotes the j-th pseudo target of xi . Here f is the softmax output of the networks and we denote f j as its j-th entry . In the remainder of this paper , we omit the sample index i when the context is clear . We proceed by describing our proposed framework . 3 METHOD . In this section , we describe our novel Partial label learning with COntrastive label disambiguation ( PiCO ) framework in detail . In a nutshell , PiCO comprises two key components tackling the representation quality ( Section 3.1 ) and label ambiguity respectively ( Section 3.2 ) . The two components systematically work as a whole and reciprocate each other . We further rigorously provide a theoretical interpretation of PiCO from an EM perspective in Section 5 . 3.1 CONTRASTIVE REPRESENTATION LEARNING FOR PLL . The uncertainty in the label space posits a unique obstacle for learning effective representations . In PiCO , we couple the classification loss in Eq . ( 1 ) with a contrastive term that facilitates a clustering effect in the embedding space . While contrastive learning has been extensively studied in recent literature , it remains untapped in the domain of PLL . The main challenge lies in the construction of positive sample set . In conventional supervised CL frameworks , the positive sample pairs can be easily drawn according to the ground-truth labels ( Khosla et al. , 2020 ) . However , this is not straightforward in the setting of PLL . Training Objective . To begin with , we describe the standard contrastive loss term . We adopt the most popular setups by closely following MoCo ( He et al. , 2020 ) and SupCon ( Khosla et al. , 2020 ) . Given each sample ( x , Y ) , we generate two views—a query view and a key view—by way of randomized data augmentation Aug ( x ) . The two images are then fed into a query network g ( · ) and a key network g′ ( · ) , yielding a pair of L2-normalized embeddings q = g ( Augq ( x ) ) and k = g′ ( Augk ( x ) ) . In implementations , the query network shares the same convolutional blocks as the classifier , followed by a prediction head ( see Figure 2 ) . Following MoCo , the key network uses a momentum update with the query network . We additionally maintain a queue storing the most current key embeddings k , and we update the queue chronologically . To this end , we have the following contrastive embedding pool : A = Bq ∪Bk ∪ queue , ( 2 ) where Bq and Bk are vectorial embeddings corresponding to the query and key views of the current mini-batch . Given an example x , the per-sample contrastive loss is defined by contrasting its query embedding with the remainder of the pool A , Lcont ( g ; x , τ , A ) = − 1 |P ( x ) | ∑ k+∈P ( x ) log exp ( q > k+/τ ) ∑ k′∈A ( x ) exp ( q > k′/τ ) , ( 3 ) where P ( x ) is the positive set and A ( x ) = { A\ { q } } . τ ≥ 0 is the temperature . Positive Set Selection . As mentioned earlier , the crucial challenge is how to construct the positive set P ( x ) . We propose utilizing the predicted label ỹ = arg maxj∈Y f j ( Augq ( x ) ) from the classifier . Note that we restrict the predicted label to be in the candidate set Y . The positive examples are then selected as follows , P ( x ) = { k′|k′ ∈ A ( x ) , ỹ′ = ỹ } . ( 4 ) where ỹ′ is the predicted label for the corresponding training example of k′ . For computational efficiency , we also maintain a label queue to store past predictions . In other words , we define the positive set of x to be those examples carrying the same approximated label prediction ỹ . Despite its simplicity , we show that our selection strategy can be theoretically justified ( Section 5 ) and also lead to superior empirical results ( Section 4 ) . Note that more sophisticated selection strategies can be explored , for which we discuss in Appendix B.4 . Putting it all together , we jointly train the classifier as well as the contrastive network . The overall loss function is : L = Lcls + λLcont . ( 5 ) Still , our goal of learning high-quality representation by CL relies on accurate classifier prediction for positive set selection , which remains unsolved in the presence of label ambiguity . To this end , we further propose a novel label disambiguation mechanism based on contrastive embeddings and show that these two components are mutually beneficial .

Summary: This work approaches the partial label learning problem where each training example is annotated with multiple candidate labels, in contrast to the conventional supervised learning setup that the ground-truth label is provided. The proposed framework comprises two key components: (1) a contrastive learning module that uses the classifier output to select positive pairs and (2) a label disambiguation method that uses the contrastive prototypes to update the pseudo targets in a moving-average style. The experimental results look quite strong, where the performance of PiCO nearly approaches the fully-supervised results.