Spread Spurious Attribute: Improving Worst-group Accuracy with Spurious Attribute Estimation 

1 INTRODUCTION . Machine learning models trained on datasets containing spurious correlation ( also known as “ shortcuts ” ) often end up learning such shortcuts instead of intended solutions ( Geirhos et al. , 2020 ) . For example , consider an image classification dataset of ‘ cows ’ and ‘ camels , ’ in which most images of cows appear on grasslands and camels on deserts . When trained on such a dataset , models often learn to make predictions based on the landscape instead of the object ( Beery et al. , 2018 ) . This phenomenon can lead to very low test accuracies on groups underrepresented in the training set . Various approaches have been proposed to resolve this gap , and the idea of minimizing the worstgroup loss—e.g. , Sagawa et al . ( 2020 ) —has arisen as one of the most promising solutions . This approach forces high performances on both the majority group ( e.g. , cows standing on grasslands ) and the minority group which contradicts the spurious correlation ( e.g. , cows standing on deserts ) . Despite its effectiveness , the worst-group loss minimization approach has a drawback : The learner requires supervision on which group each training sample belongs . For example , the learner needs to know that sample belongs to both the ‘ cow ’ and the ‘ desert ’ categories to utilize such group information to perform worst-group loss minimization . Even if we put aside the issue of identifying the spuriously correlated attributes ( ‘ desert ’ and ‘ grass ’ ) in the first place , one still needs to collect additional annotation on such spurious attributes . Acquiring such fine-grained annotation is presumably more expensive to collect , as the annotator needs a clear understanding of both the target attribute ( ‘ cow ’ and ‘ camel ’ ) and the spurious attribute ( ‘ desert ’ and ‘ grass ’ ) . Acknowledging this difficulty , recent works propose worst-group loss minimization algorithms that require a smaller number of group-labeled training samples ( i.e. , training samples with spurious attribute annotations ) ( Nam et al. , 2020 ; Liu et al. , 2021 ) . At a high level , these works share a similar strategy ( Fig . 1 , Left ) : The methods first use a specialized mechanism to identify minority group samples among group-unlabeled training samples , and train a model in a way that puts more emphasis on identified-as-minority samples , e.g. , by upweighting . A small set of group-labeled samples are used to tune hyperparameters of this procedure ; as Liu et al . ( 2021 ) shows , the performance of trained models are very sensitive to these hyperparameters , indicating the high dependency of such algorithms on the availability of the group-labeled samples . Although these methods achieve higher worst-group accuracy than completely annotation-free approaches , e.g. , Sohoni et al . ( 2020 ) , they fail to perform comparably to the algorithms which use full annotations on spurious attributes , e.g. , Sagawa et al . ( 2020 ) . This performance gap gives rise to the following question : Can we closely achieve the full-annotation performance using a partially annotated dataset , if we use group-labeled samples more actively than hyperparameter-tuning ? Contribution . This paper proposes a worst-group loss minimization algorithm , coined Spread Spurious Attribute ( SSA ) . At a high level , SSA consists of two phases—pseudo-labeling and robust training—that are designed to make a full use out of the group-labeled samples ( Fig . 1 , Right ) : • Pseudo-labeling : SSA trains a spurious attribute predictor , using both group-labeled and groupunlabeled samples ( i.e. , samples lacking spurious attribute annotations ) . We find that group imbalances underlying the dataset can render pseudo-labels to be biased towards the majority group , which can be detrimental to the performance ( as in Kim et al . ( 2020 ) ) , and propose using groupwise adaptive thresholds to mitigate this problem . The predictions are used as pseudo-labels ( Lee , 2013 ) on the group-unlabeled samples . • Robust training : Based on the pseudo-labeled training set , SSA trains a model which predicts the target attribute , using the worst-group loss minimization algorithms developed for fully supervised cases . We use Group DRO ( Sagawa et al. , 2020 ) as a default choice , and re-use group-labeled samples for the hyperparameter tuning . Our experimental results suggest that SSA is a general yet effective framework for worst-group loss minimization . On various benchmark datasets , SSA consistently achieves performances comparable to fully supervised Group DRO and outperforms other baseline methods even when using only 5 % of the group-labeled samples compared to the baselines . To be more specific , SSA requires less than 1.5 % ( as little as 0.6 % ) of group-labeled samples—993 out of 182637 on CelebA , and 4123 out of 288637 on MultiNLI—to achieve a worst-group accuracy similar to that of 100 % usage . Moreover , we find that such benefits of SSA persist when combined with other robust training methods , such as Correct-N-Contrast ( CNC1 ; Zhang et al . ( 2021 ) ) , the supervised contrastive learning with contrastive batch sampling using group information . Finally , we also empirically observe that the group-wise adaptive thresholding technique—which we proposed for better pseudo-labeling—enjoy a broader usage for addressing the general problem of semi-supervised learning under class imbalance ; existing pseudo-labeling techniques ( Kim et al. , 2020 ; Wei et al. , 2021 ) require certain assumptions in datasets to work well for the task , while ours does not . 1We use the term CNC to refer to its supervised contrastive learning procedure with contrastive batch sampling only , rather than the entire process which includes spurious attribute annotation estimation via ERM . 2 RELATED WORKS . Improving worst-group accuracy with group annotations . It has been known in various literature that machine learning models often perform significantly worse on the samples from groups with a relatively small number of training samples than on samples from the majority group . The class imbalance problem ( Japkowicz , 2000 ; Johnson & Khoshgoftaar , 2019 ) is one of the representative cases of this phenomenon . Here , class labels naturally define group identities and thus do not require any additional group annotations . In this context , popular strategies to improve worst-group performances are using re-weighted loss for each group ( Huang et al. , 2016 ; Khan et al. , 2017 ) and re-sampling the given dataset to balance the group distribution of the training dataset ( Chawla et al. , 2002 ; He & Garcia , 2009 ) . This paper , in contrast , considers a setup where the group is defined as a combination of the label ( target attribute ) and the spuriously correlated attribute ; unlike the class imbalance literature , the availability of the full group identity information is not guaranteed , as spurious attributes may not have proper annotations . Under the setting where spurious attribute annotations are available on all samples , Sagawa et al . ( 2020 ) gives an online optimization algorithm that shows promising results on minimizing the worst-group loss . Improving worst-group accuracy without group annotations . To reduce additional annotation costs , recent works aim to train a robust model without requiring group annotations for all training samples . These works utilize models trained with standard procedure to identify samples that disagree with spurious correlations . Nam et al . ( 2020 ) train a model to be intentionally biased using the generalized cross entropy loss , and use it to identify-and-upweight high-loss samples for training another model . Liu et al . ( 2021 ) train a standard ERM model for a few epochs and upweight samples misclassified by this model to train the second model . Although these approaches do not use any group information for training , they still use a small number of group-labeled samples for hyperparameter tuning , which is critical to their worst-group performance . In this paper , we design a method to utilize group-labeled samples more efficiently . We note that , in the class imbalance literature , another line of works proposes to use group-labeled samples more actively ; they use labeled samples for determining sample weights for the training set through meta-learning ( Ren et al. , 2018 ) or training a model to predict sample weights ( Shu et al. , 2019 ) . 3 PROBLEM SETUP . Consider the learning a classifier in the presence of spurious correlations in the training set . Following the prior work of Sagawa et al . ( 2020 ) , we cast this problem as minimizing the worst-group loss , where the group identity is determined by the target attribute ( that we want to predict ) and the spurious attribute ( that we want to ignore ) . We assume that we do not have spurious attribute annotations of the samples in the training set ( group-unlabeled set ) , but have an access to additional set of samples with both spurioust attribute and target attribute annotations ( group-labeled set ) . More formally , we let each sample be a triplet consisting of an input x ∈ X , a target attribute y ∈ Y , and a spurious attribute a ∈ A . Our goal is to train a parameterized model fθ : X → Y that minimizes the worst-group expected loss on test samples ; for the purpose of avoiding learning spurious correlations , we define the group as an attribute pair g : = ( y , a ) ∈ Y × A = : G. In other words , we aim to minimize R ( θ ) = max g∈G E ( x , y , a ) ∼Pg [ ` ( fθ ( x ) , y ) ] , ( 1 ) for some loss function ` : Y × Y → R , where Pg denotes the group-conditioned data-generating distribution . Note that , as we focus on the group defined by the attribute pairs , Pg is deterministic on y and a , and stochastic only on x . We assume that the learner has access to two types of samples for training : The group-unlabeled set consists of n samples without spurious attribute annotations , i.e. , DU : = { ( x1 , y1 ) , . . . , ( xn , yn ) } , and the group-labeled set consists of m samples with spurious attribute annotations , i.e. , DL : = { ( x̃1 , ỹ1 , ã1 ) , . . . , ( x̃m , ỹm , ãm ) } . We assume that the group-labeled samples are much more costly to collect , and thus we have n m . 4 SPREAD SPURIOUS ATTRIBUTE . We now describe the algorithm we propose , Spread Spurious Attribute ( SSA ) . At a high level , SSA consists of two phases : pseudo-labeling and robust training . In the pseudo-labeling phase , SSA trains a model to predict the spurious attribute . In particular , we use both group-labeled and groupunlabeled samples to generate pseudo-labels on the group-unlabeled training samples ( Section 4.1 ) , with an adaptive thresholding technique for balancing the number of samples in each group ( Section 4.2 ) . Then , in the robust training phase , SSA uses generated pseudo-labels to train a model that predicts the target attribute with a small worst-group loss ( Section 4.3 ) . We use Group DRO ( Sagawa et al. , 2020 ) as our default robust training method , but SSA also performs well when combined with other existing algorithms that use full spurious label supervisions ( see Section 5.3 ) .

Summary: This paper presents a technique, spread spurious attribute, for inferring the group annotation for training samples in a dataset. The inferred group information is then used as part of a group DRO minimization scheme or some other worst case scheme. The key insight in this work is to use a small validation set (1-5 percent) of data that has annotations to learn annotations for the entire training set via pseudo-labelling. The labelling scheme presented uses different thresholds for the different spurious groups. This new dataset is then used as part of a new DRO pipeline.