For Robust Worst-Group Accuracy, Ignore Group Annotations
Authors: Nathan Stromberg
Rohan Ayyagari
Monica Welfert
Sanmi Koyejo
Richard Nock
Lalitha Sankar
Venue: Accepted by TMLR ()

Abstract: Existing methods for last layer retraining that aim to optimize worst-group accuracy (WGA) rely heavily on well-annotated groups in the training data. We show, both in theory and practice, that annotation-based data augmentations using either downsampling or upweighting for WGA are susceptible to domain annotation noise. The WGA gap is exacerbated in high-noise regimes for models trained with vanilla empirical risk minimization (ERM). To this end, we introduce Regularized Annotation of Domains (RAD) to train robust last layer classifiers without needing explicit domain annotations. Our results show that RAD is competitive with other recently proposed domain annotation-free techniques. Most importantly, RAD outperforms state-of-the-art annotation-reliant methods even with only 5\% noise in the training data for several publicly available datasets.

Published in Transactions on Machine Learning Research (12/2024)
Robustness to Subpopulation Shift with Domain Label Noise via Regularized Annotation of Domains
Nathan Stromberg
nstrombe@asu.edd
Arizona State University
Rohan Ayyagari Arizona State Universiby
reyyaga2Shasu.edi edu
Monica Welfert
mwelfert@asu.edk edu
Arizona State University
Sanmi Koyejo Stanford University
sanmi@@cs.stanorr.ccom edu
Richard Nock
richarnnockkkgogle.coo
Google Research
Lalitha Sankar Arizona State University
Lsankar@asu. edu
Reviewed on OpenReview:
Abstract
Existing methods for last layer retraining that aim to optimize worst-group accuracy (WGA) rely heavily on well-annotated groups in the training data. We show, both in theory and practice, that annotation-based data augmentations using either downsampling or upweighting for WGA are susceptible to domain annotation noise. The WGA gap exacerbated high- noise regimess for models trained with vanilla empirical risk minimization (ERM). To this end, we introduce Regularized Annotation of Domains (RAD) to train robust last layer classifiers without needing explicit domain annotations. Our results show that RAD competitive with other recently proposed domain annotation-fiee techniques. Most importantly, RAD outperforms state-of-the-art annotation-reliant methods even with only 5% noise in the training data for several publicly available datasets.
1 Introduction
Last-layer retraining (LLR) has emerged as method for using embeddings from pretrained models to quickly and efficiently learn classifiers in new domains or for new tasks. Because only the lincar last layer is retrained, LLR allows transferring to new domains/ Nomains/lasks tasks with much fewer examples than required to train a deep network from scratch. One promising use of LLR is to retrain deep models with a focus on fairness or robustness, and because data is frequently made up of distinct subpopulations (oft referred to as groups which we take as a tuple of class and domain labels) (Yang al.] (023),, ensuring both fairness between subpopulations and robustness to shifts among subpopulations remains an open problem.
One way to be robust to these types of shifts and/or to be fair across groups is to optimize for the accuracy of the group that achieves the lowest accuracy, i.c., the worst-group accuracy (WGA). WGA thus presents a
'e will these terms interchangeably

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lower bound on the overall accuracy of classifier under any subpopulation shift, thereby assuring that all groups are well classified.
State-of-the-art (SOTA) methods for optimizing WGA
generally modify either the distribution of the training
data Kirichenko et al. 2023; Giannone et al. 2021: LaBonte et al. 2023) or the training loss (Arjovsky et al. 2019; Liu et al. 2021: Sagawa et al. 2020 Qiu et al. [023) to account for imbalance amongst groups and successfully learn a classifier which is fair across groups. These methods also use some form of implicit explicit regularization in the retraining step to limit overfitting to either the group imbalances the spuriously correlated features in the training data. Kirichenko et al. (223) argue that strong & regularization plus data augmentation helps to Iearn "core features," " i.c., those correlated with the label for all examples. Thus, one can instead use regularization without data augmentation to learn spurious features explicitly, in which case misclassified examples can be viewed as belonging to minority groups. This allows us to avoid the explicit use of group annotations.
We examine two representative data augmentation methods, namely downsampling (Kirichenko al. 2023 LaBonte et al., 2023 Chaudhuri et al 2023) and upweighting (Idrissi et al., 2022] Liu et al. [021 Qiu et al, 2023), which achieve SOTA WGA with simple modifications to the data and loss, respectively. In the simplest setting, cach of these methods requires access to correctly annotated groups to balance the contribution of each group to the loss. In practice, group annotations are often noisy (Wei et al. 2022). which can be caused by either domain noise, label noise, or both. Label noise generally affects classifier training and data augmentationn making analysis more challenging. We consider only domain noise so that we can compare to existing methods for enhancing WGA. Furthermore, focusing on domain noise presents a stepping stone analyzing group noise in general.
1.1 Our Contributions
We present theoretical guarantecs for the WGA under domain noisc when modeling last layer representations as symmetric mixtures. We show that both DS and UW achieve identical WGA and degrade significantly with increasing percentage of symmetric domain noise, in the limit degrading to the performance of empirical risk minimization (ERM). This is further confirmed with numerical experiments for a synthetic Gaussian mixture dataset modeling latent representations.
Our key contribution is a two-step methodology involving: (i) regularized annotation of domains (RAD) to pseudo-annotate examples by using a highly regularized model trained to learn spuriously correlated features. By lcarning the spurious correlations, RAD constructs set of examples for which such correlations do not hold; we identify these as minority examples. (ii) LLR using all available data, while upweighting (UW) examples in the pseudo-annotated minority.
This combined approach, denoted RAD-UW, captures the key observation made by many that regularized LLR methods are successful as they implicitly differentiate between "core' and "spurious" features. We test RAD-UW on several large publicly available datasets and demonstrate that achieves SOTA WGA even with noisy domain annotations. Additionally, RAD-UW incurs only a minor opportunily cost for not using domain labels even in the noise-free setting.
1.2 Related Works
Downsampling has been explored extensively in the literature and appears to be the most common method for achieving good WGA. Kirichenko et al. (2023) propose deep feature reweighting (DFR), which downsamples the majority groups to the size of the smallest group and then retrains the last layer with strong é regularization. Chaudhuui et al. (2023) explore the effect of downsampling theoretically and show that downsampling can increase WGA under certain data distribution assumptions. LaBonte et al. (2023) use a variation on downsamppling to achieve competitive WGA without domain annotations using implicitly regularized identification models.
Upweighting has been used as an alternative to downsampling as it does not require removing any data. Idrissi et al. (2022) show that upweighting relative to the proportion of groups can achieve strong WGA, and Liu et al. (2021) extend this idea (using upsampling from the same dataset, which is equivalent to
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upweighting) to the domain annotation-fre free setting using early-stopped models. Qiu et al. (2023 use the loss of the pretrained model to upweight samples that are difficult to classify, thus circumventing the need for domain annotations,
Domain annotation-fiee methods generally use a secondary model to identify minority groups. Quu et al. (2023) use the pretrained model itself but do not explicitly identify minority examples and instead upweight proportionally
the loss. Unfortunately, this ties their identification method to the choice of the loss. [Liu
et al. (2021) and Giannone al. (021 both consider fully retraining the pretrained model as opposed to only the last layer, but their method of minority identification using an early stopped model is considered in the last layer in LaBonte et al. (2023). LaBonte et al. (2023) not only consider early stopping as implicit
regularization for their identification model, but also dropout (randomly dropping weights during training).
Wei et al. (2022) show that human annotation of image class labels can be noisy with up to a 40% noise proportions, thus motivating the ncod for domain annotation-froe methods for WGA. It likely that domain annotations are noisy with similar frequency, especially since class and domain labels are frequently interchanged, like in CelebA (Liu et al. 2015). Domain noise has not been widely considered in the WGA literature, but Oh et al. (2022) consider robustness to class label noise. They utilize predictive uncertainty from a robust identification model to select an unbiased retraining set.
Our work differs from SOTA methods on several fronts. First, we present a theoretical analysis of DS and UW under noise (and structured distributions for the last layer representation), which motivates our method. Secondly, we provide intuition for our RAD-UW method and the need for explicit regularization via arguments about "spurious' and "core" features à la DFR (Kirichenko et al., 2023)_ Finally, our method requires access only to the last layer of the pretrained model and only the final weights. This is in contrast to LaBonte ct al. (2023) in which early-stopped versions of the base model are needed to gel the best performance and Liu et al. (2021) in which the entire model weights are needed. With our extensive experiments, we demonstrate that downsampling methods such as those presented in Kirichenko et al. (2023) and LaBonte et al. (0023) have a significantly higher variance than upweighting methods such as RAD-UW.
2 Problem Setup
We consider a supervised classification setting and assume that the LLR methods have access to a representation of the ambient (original high-dimensional data such as images, etc.) data, the ground-truth label, as well as the (possibly noisy) domain annotation. Taken together, the label and domain combine to define the group annotation for any sample. More formally, the training dataset is a collection of i.i.d. tuples of the random variables (Xa, Y, D) ~ PX,YD, where X, E Xa is the ambient high-dimensional sample, Y E ) is the class label, and D E D is the domain label. Here, we present the problem as generic multi-class, multi-domain learning, but for ease of analysis, we will later restrict ourselves to the binary class, binary domain setting. Since the focus here is on learning the linear last layer, we denote the latent representation that acts as an input to this last layer by X = ((X)) for an embedding function Φ Xa + X S R. such that the LLR. dataset is (X, Y, D) PXYD-
The tuples DY of class and domain labels partition the examples into g = |>> x DJ different groups with priors 7 (lv.d) = P(Y = y, D = d) for (y. d) E y x D. We denote the linear correction applied in the latent space of a pretrained model as fe : X + RDDi which is parameterized by a linear decision boundary = (w, b) E R [D| x RDI given by
fa(x) [ow> x + b).
(1)
where a: RDI + (0, 1)D' is the link function (e.g., softmax). The prediction of fa(x) is given by
V = arg f8 (x).
(2)
A general formulation for obtaining the optimal for is:
0* = arg =ag min (XY
(3)
#
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where e RDI y - -R is loss function and ) x D - R is the per-group cost which can be used to correct for imbalances in the data (Trrissi et al. 2022) or to correct for noise in the training data Patrrii et al. 2017).
We desire a model that makes fair decisions across groups, and therefore, we evaluate worst-group accuracy, T.e., the minimum accuracy among all groups, defined for a model fo as
WGA(f() = min (v.D)
(fo),
(4)
where (fo) denotes the per- ger-g accuracy for the group (y. d) E y D,
(v (So) == PXIYD(Y Y|Y = y, = d),
(5)
where Y is calculated in
2.1 Data Augmentation
Downsampling (DS) reduces the number of examples in majority groups such that minority and majority groups have the same sample size. In practice, this reduces the dataset size from n. to g Ammin where Tmmin is the number of examples in the smallest group. In the population setting (as n and ayin Tiin n)), this is equivalent to setting all group priors equal to 1/g.
Upweighting (UW) does not remove data but weights the loss more for minority examples and less for majority samples. Generally, the upweighting factor c can be a hyperparamcter, though often one uses the inverse of the prevalence of the group in practice, which estimates
cly, d) g (v.d)
(6)
This selection is motivated by the minimization problem in B where this choice of allows the optimization to happen independently of the group priors. This is explored more in Proposition 3.1
2.2 Domain Noise
We model noise in the domain label as symmetric label noise (SLN) with probability (w.p.) That is, for a sample (X, (), PXYD, we do not observe D directly but D w.p. p and w.p. p where D is drawn uniformly at random from D \ (D}. This is equivalent to flipping w.p. p in the binary domain setting.
In practice, while the training data usually regarded as noisy, is frequently necessary to have a small holdout, that is clean and fully annotated. This allows for hyperparameter selection without being affected by noisy annotations and aligns with domain annotation free settings which generally have a labeled holdout set
[Lu et al. 2021
Giannone et al. 2021 LaBonte et al. 2023).
3
Theoretical Guarantees
We first consider the general sctting (multi-class, multi-domain) and show that the models Icarned after downsampling (0%x) and upweighting (Btw) are the same in the population setting. Proposition 3.1. For any given PXYD and loss é, the objectives in (3. when modified appropriately for DS and UW, are the same. Therefore, if minimizer erists for one it also exists for the other, i.e., 0' O'
Proof. The key idea of the proof is that the upweighting factor proportional to the inverse of the priors on each group. Thus, for any fo and PXYd, the expected loss is
(xx.D(((((X)))))(((..
and can be decomposed into an expectation over groups. For such a docomposition, the priors from the expected loss cancel with the upweighting factor and we recover the downsampled problem with uniform priors.
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Class (y)
Class (y)
Dumain (d)
Domain
0.2
SRM
DS, UW
0.0
-0.2
-0.2
-0.4
-0.4
-0.3
-0.2
-0.1
0.0
0.1
0.2
-0.3
-0.2
-0.1
0.0
0.1
0.2
Figure 1: Sample drawn from distribution satisfying Assumptions 3.3 to 3.6 segments between means. Additionally the classifiers learned by SRM,, DS, and UW are shown. It is clear that DS and UW learn the separator which is unaffected by spurious correlation.
Àc and An shown line
We now consider the setting where each group, given by tuple of binary domain (D= = (S,T)) and binary class labels ()' = {0,, 1)), is symmetrically distributed with different means but equal covariance. We additionally impose a structural condition studied in Yao et al. (2022) which allows us to theoretically analyze the weights and performance of least-squares-tpee algorithms,, learning a simplified linear classifier with squared loss.
Definition 3.2. A probability distribution Q on R is symmetric around its mean je if its CDF & satisfies
1 1-4(z p)) (b-x+ Vz R.
Assumption 3.3. Conditioned on Y and D, X E X' is distributed according to Pxly,d for (v, E x D, with mcan (w = B[X|Y = D d Rm and positive semidefinite covariance E E Rmxm such that the distribution of a² XY = y, D d) is symmetric for any a E R. and its CDF Parxly,d R [0, is strictly increasing. Additionally, we place priors N I(v.d), (y.d) d) E y D, on each group and priors T(1) = P(Y v), y }, on each class.
Note that Assumption 3.3 holds for many conditional distributions on X including spherically symmetric distributions (see Fang (2018 Theorem 2.4) along with the fact that spherically symmetric distributions have symmetric marginals), Guassian distributions, and distributions with sub-independent and symmetric marginals. For ease of intuition, we focus mainly on Guassian groups. Following Chaudhuri et al. 20233 we deal only with distributions which induce strictly increasing CDFs so that there an explicit tradeoff between majority and minority group performance.
Assumption 3.4. The minority groups have equal priors, i.e., for To I 1/4,
π (0.R) = (1, To and - (1,R) n (0, = 1/2 - no.
Also, the class priors equal, i.e., n (1) 1/2.
Assumption 3.5. The difference in means between classes in a domain Ap = (1(dd)) - (.,0) is constant for deD D.
Assumption 3.5 also implies that the difference in means between domains within the same class A == (l.B)) - ( is also constant for each V. We see this by noting that each group mean makes up the vertex of a parallelogram. This is illustrated in Figure where AD and Ao are shown on data samples drawn from a distribution satisfying Assumptions 3.3 to
A Assumption 3.6. Ap and Ac orthogonal with respect to E-1 i.e. ATE-IAP

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We see example of dataset drawn from distribution satisfying Assumptions 3.3
3.6
Figure
The
data is generated mixutre of 2D Gaussians with parameters,
A (0 0.5)* T
AD (-0.25 -0.25)
.003 .003)
1
Σ
No 50%
.003 .004)
While this is simplified view of binary class, binary domain latent groups, these tractable assumplions allow us to make theoretical guarantees about the performance of downsampling and upweighting under noise. We see that the general trends observed in this simplified sctting hold in large publicly available datasots in Section 54
We now show that upweighting and downsampling achieve identical worst-group accuracy in the population setting (i.e., infinite samples) and both degrade with SLN in the domain annotation while ERM is unaffected by domain noise.
Theorem 3.7. Consider the model of latent groups satisfying Assumptions 3.3 to 3.6 under symmetric domain label noise with parameter p. Let fo(x)= = wT
and Y [ff(a)> > 1/2]. In this setting, let 8
and o denote the solution to (3 under squared loss for UW and DS, respectively. For any To E (0, 1/4], the WGA of both augmentation approaches are equal and degrade smoothly in P 1/2] to the baseline WGA of with no augmentation (with optimal parameter (gRM) That is,
3
WGA(0ERM) S WGAA0 WGA(0
with equality at p 1/2 no 1/4.
Proof Sketch. The proof of Theorem 3.7 is presented in Appendix A and involves showing that the WGA for downsampling under domain label noise is the same as that for ERM (which is noise agnostic) but with a different prior dependent on Our proof refines the analysis in Yao et al. [2022] and involves the noisy prior.
Fundamentally, this result can be seen as an effect of the domain noise on the perceived (noisy) priors To of the minority groups, which can be derived as
(p) = (1 -)=p)==-- + (1/2 - mo)
(8)
As p + 1/2 in ( the minority prior perceived by both UW and DS tends to balanced prior across groups. A UW augmentation thus would weight in inverse proportion the corresponding noisy (and not the true) prior for each group. The true prior of the minority group after DS can be derived as (sce Appendix A)
(p) DS
(1 p)ao
pno
(9)
4mD
(p)
4(1/2
Thus, with noisy domain labels, instead of the desired balancod group priors after downsampling, from ( DS results in true minority prior that decreases from 1/4 to mo. Thus, noise in domain labels drives inaction from both augmented methods as p increases.
We see the effect of noise in numerical example in Figure 2 noting that while the theorem is in the population setting, our numerical example uses finite sample methods with n = 10, 000. This shows that the performance of each method quickly degrades even in this simple setting. The ERM performance, however, remains constant because ERM does not use domain information. This motivates us to examine a robust. method that does not use domain information at all but is more effective than ERM in terms of WGA.
4 Regularized Annotation of Domains
When domain annotations are unavailable (or noisy), LaBonte et al. (2023) use implicitly regularized models trained the imbalanced retraining data to annotate the data. We take similar approach but explicitly
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Method
DS
0.9
UW
ERM
0.8
WGA
0.6
0.5
Figure 2: For latent Gaussian data, the WGA of DS and UW (seen overlapping) decreases the noise prevalence increases to 1/2. At the extreme point, the WGA of ERM is recovered.
regularize our pseudo-annotation model with an & penalty. The intuition behind using an L penalty is similar to that of DFR (Kirichenko al. 2023). Where Kirichenko ct al. (2023) argue that & penalty helps to select only "core leatures' when trained with large multiplicative factor will help to select spuriously correlated features when trained on the original imbalanced data. If we can successfully learn the spuriously correlated features, those samples which are correctly classified can be viewed as majority samples (those for which the spurious correlation holds) and those which are misclassified can be seen as minority samples.
group-balanced dataset, argue that the same penalty
We introduce RAD (Regularized Annotation of Domains) which uses a highly & regularized linear model to pseudo-annotate domain information by quantizing true domains to binary majority and minority annotations. Pseudocode for this algorithm is presented in Algorithm | We see that strongly regularized classified is first. learned, FID, which allows us to identify minority points through misclassification. We use these annotations, d, to upweight examples in the next step
RAD-UW (Algorithm 2 involves learning sequentially: (i) a pseudo-annotation RAD model (outlined Algorithm I and (ii) a regularized linear retraining model, which is trained on all examples while upweighting the pseudo-annolated minority examples output. by RAD, as the solution RAD.UW optimizing the empirical version of 3 using the logistic loss & with & regularization as:
RAD arg min
((o)) v.) + Al[wl12
(10)
6
Here again, the & regularization comes into play. While the regularization in the first step encouraged the biased model to misclassify minority points, here the same regularization encourages learning features which do well both for the majority and (upweighted) minority. This discourages learning spurious features which may be present (and helpful) in the majorities.
RAD-UW vs. M-SELF While both RAD and SELF are two-stage methods which utilize the biases of "identification" model to pseudoannotate points in minority classes, RAD explicitly trains such biased classifier using a strong & penalty whereas the classifier used by SELF is the pretrained classification head. The benefit. of retraining the classifier is that we can force the model to rely more strongly on spurious correlations. We see in practice that this leads to drastic increases in performance on some datasets. side effect of this retraining that we can more effectively correct models which were originally trained with noisy data, as the noise affects the classification head more strongly than the embeddings thenselves. We explore this is Appendix G
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Algorithm 1 Regularized Annotation of Domains (RAD)
Algorithm 2 RAD-UW
Input: data D (I.
Input: data D (z, y) Train classifier JID on D with & factor ÅID
(2r, V, d) RAD(
Train classifier freurain (z, while upweighting
for (z4, E D do
examples where d = 1 by factor c Return: 9 = fretrain (z), the estimated class label of x
if [ID( # then
d, 1+1
else d, 0 end if end for Return: v,, the pseudo-annotated data
5 Empirical Results
We present worst-group accuracies for several representative methods across four large publicly available datasets. Note that for all datasets, we use the training split to train the embedding model. Following prior work (Kirichenko et al. 2023 LaBonte et al. 2023), use half of the validation as retraining data, i.e, training data for only the last layer, and half as a clean holdout.
5.1 Datasets
CMNIST (Arjovsky al. 2019) is variant of the MNIST handwritten digit dataset in which digits 0-4 are labeled y/ = 0 and digits 5-9 are labeled y 1. Further, 90% of digits labeled are colored green and 10% are colored red. The reverse is true for those labeled = 1. Thus, we can view color as domain and we see that the color of the digit and its label are correlated.
CelebA Liu et al. 2015 is a dataset celebrity faces. For this data, we predict hair color as either blonde (y =1=1) or non-blonde (y 0) and use gender, either male (d = 1) or female (d = 0), as the domain label. There natural correlation in the dataset between hair color and gender because of the prevalence of blonde female celebritics.
Waterbirds (Sagawa et al. 2020 is a semi-synthetic dataset which places images of land birds (v = 1) sea birds (y = 0) on land (d = 1) or sea (d =d=00 0) backgrounds. There is a correlation between background and the type of bird in the training data but this correlation is removed in the validation data.
text. corpus dataset widely used natural language inference tasks. For our setup, we use MultiNLI as first introduced in (Oren al. 2019). Given two sentences, premise and hypothesis, our (ask is to predict whether the hypothesis is either entailed by, contradicted by, neutral with the premise. There is spurious correlation between there being contradiction between the hypothesis and the premise and the presence of negation word (no, never, etc.) in the hypothesis.
MultiNLI (Williams et al. 2018
CivilComennts (Borkan et al. 2019 is a text corpus dataset of public comments on news websites. Comments are labeled either as toxic (y 1) or civil (y 0) and the spurious attribute the presence (d = 1) or absence = 0) of a minority identifier (c.g. LGBTQ, race, gender). There is a strong class imbalance (most comments are civil), though the domain imbalance is modest.
5.2 Importance of & Regularization
We emphasize that a strong 4 regularizer is critical to the success of our method through the intuition of DFR, but remains be seen how this bears out in practice. To this end, we examine combinations of both l and the common & penaltics. We see in Table@thar the retraining regularizer has only a small impact on the overall performance, while the identification regularization has more impact. We note that for CelebA,
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Table
Regularizer
Datasct WGA
ID
Retrain
CMNIST
WB
CelebA
Civil Comments
l
94.06
92.52
83.51
81.57
L
l2
93.89
89.53
82.59
74.97
l2
l
94.04
92.18
68.39
51.17
l2
E
93.86
90.98
64.28
53.00
real-world image dataset of faces, 6, regularization shows dramatic gains, while the synthetic Waterbirds and CMNIST datasets are much closer.
5.3
Main Results
We present results for both group- and class- class-only-dependent methods using both downsampling and upweight- ing. Additionally, present results for vanilla LLR, which performs data loss augmentation step before retraining. Finally, present results for two-stage last layer methods, namely misclassification SELF (M-SELF) and RAD with upweighting (RAD-UW). Every retraining method solves the following empirical optimization problem:
0- = arg min
cdd, 9: (.)o((())))))) A|w|||
(11)
which can be seen as a finite sample version of 3 with an l regularization. For E, we use the logistic loss.
The group-dependent downsampling procedure we have adopted is the same as that of DFR, introduced Kirichenko et al. (2023). but the DFR methodology averages the learned model over 10 training runs. This could help reduce the variance, but we do not implement this so as to directly compare different data augmentation methods since most others do so either. More generally, we could apply model averaging to any of the data augmentation methods. We explore the effect of model averaging in Appendix
E
We use the logistic regression implementation from the scikit-learn (Pedregosa et al. 2011 package for the retraining step for all presented methods. For all final retraining steps (including LLR) an l regularization is added. The strength of the regularization À is a hyperparameter selected using the clean holdout. The upweighting factor for group aunotation-inclusivee UW methods is given by the inverse of the perceived prevalence for each group or class.
For our RAD-UW method, we tune the regularization strength Ap for the psoudo-annotation model via grid search. We additionally tune the regularization strength X of the retraining model along with the upweighting factor which is left as hyperparameter because the identification of domains by RAD is only binary and may not reflect the domains in the clean holdout data. The same upweighting factor is used for every pseudo-annotated minority sample.
Note that for all of the WGA results, we report the mean WGA over 10 independent noise seeds and training runs for each noise seed. We also present the standard deviation around this mean, which will reflect the variance over training runs with the optimal hyperparameters. For misclassiffcation SELF (M-SELF) LaBonte et al. 2023 we present both our own implementation of their algorithm and their results directly. It should be noted that they report the mean and standard deviation over only three independent runs and without noise; for the noisy setting, we observe that their method does not use domain annotations and so is unaffected by domain noise just as RAD-UW is. Our implementation utilizes the same embeddings as RAD-UW so we can ensure any differences are artifacts of the algorithms rather than the upstream model. The importance of the pretrained model is an important and underexplored factor the literature which we leave future work.

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Group Downsample
Group Downsample
M-SELF
Group Upweight
M-SELF (Our imp.)
Group Upweight
M-SELF (Our Imp.)
96
88
86
95
WGA
94
10
15
20
0
10
15
20
Noise (%)
(%)
(a) CMNIST WGA under Domain Noise
(b) CelebA WGA under Domain Noise
Figure 3: Domain-dependent methods, group downsampling and upweighting, decline in performance as the domain noise increases. Meanwhile, RAD-UW remains consistent and matches or outperforms these methods starting at 10% domain noise. The high variance of M-SELF CelebA is concerning and is likely due to the class balancing performed by M-SELF.
5.4 Worst-Group Accuracy under Noise
We now detail the results on all datasets in Figures 3a class dependent versions of downsampling and upweighting. We choose not to include them here as their performance is so poor as to distract from the results.
3b
4a
4b
and 5a See Appendix for tables including
For CMNIST, we present results in Figure 3a and Table S we see that each method that uses domain information achieves strong WGA at 0% domain annotation noise, but for increasing noise, their performance drops noticeably. Additionally the methods which rely only on class labels without inferring domain membership consistent across noise levels, but outdone by their domain-dependent counterparts even at 20% noise. Finally, RAD-UW achieves WGA comparable with the group-dependent methods, and surpasses their performance after 10% noise in domain annotation.
The results for CclebA are presented in Figure 35 and Table ! We first note that LLR achieves significantly lower WGA than any other method owing to strong spurious correlation ion even the retraining data. We also note that every domain-dependent method has much more significant decline in performance for CelebA than for CMNIST. Here, RAD-UW outperforms the domainndependent methods even at 10% SLN, Not only this, but RAD beats the performance of SELF (LaBonte et al. 2023) for this dataset with much lower variance.
For Waterbirds, we see in Figure 4a and Table 10 that noise, even significant amounts of it, has little effect on any of the methods considered. This is because the existing splits have a domain-balanced validation, which we use here for retraining. Thus domaín noise does not affect the group priors at all as argued analytically in (8) with To = 1/4. Even so, we see that RAD-UW competitive with existing methods, including the domain annotation-free methods of LaBonte al. (023).
For MultiNLI, see in Figure 4b and Table II that RAD-UW is able to match domain-dependent methods at 5% noise and outperform them at 10%, but is beaten by M-SELF's reported result. We note that we were not able lo replicate their performance with our implementation. This may be because MultiNLI has weaker spurious correlation than the other datasets we examine. Also important to note is the effect of noise on MultiNLI For 5% and 10% noise levels, we see a dramatic drop in WGA for domain-dependent methods, but this levels off as we recover the WGA of LLR. Thus even for 10% noise, LLR is competitive with top domain-dependent methods.
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Group Downsample
Group Downsample
RAD-UW
-
M-SELF
Group Upweight
M-SELF (Our Imp.)
Group Upweight
(Our Imp.)
93.5
92.5
WGA
92.0
68
91.5
10
20
0
10
15
20
(%)
(a) Waterbirds WGA under Domain Noise
(b) MultiNLI WGA under Domain Noise
Figure 4: We see that RAD-UW and M-SELF strongly outperform domain-dependent methods for most noise levels. Waterbirds is domain balanced from the beginning, so adding domain noise does not strongly bias the downsampling or upweighting classifiers.
Finally, for ComilCommnnss, we that in Figure 5a and Table 12 thatt RAD-UW drastically outperforms M-SELF and competitive with domain-dependent methods. Because CivilComments is generally domain balancod, domain noise does not have a large effect on the performance of GDS and GUW. On the other hand, the extreme class imbalance of the dataset leads to poor performance by M-SELF. The robustness of RAD-UW to extreme class imblance is an important factor in its success and likely due to the downsampling of competing methods.
An interesting observation is that for almost all datasets and noise levels, the variance of group-dependent downsampling consistently larger than upweighting at the same noise levels. This behavior is likely caused by two key issues: (i) DS reduces the dataset size, and (ii) it randomly subsamples the majority, each of which could increase the variance of the resulting classifier. DFR (Kirichenko al.) 2023) has attempted remedy this issue by averaging the linear model that is learned over 10 different random downsamplings, but this increases the complexity of learning the final model. Our results raise questions the prevalence of downsampling over the highly competitive upweighting method in the setling of WGA.
A similar comment can be made with respect to RAD-UW and M-SELF, While M-SELF has strong performance on several datasets, it consistently has higher variance than RAD-UW and struggles on datasets with large class imbalance. This likely due to the class balancing that LaBonte al. (2023) use in the retraining step. RAD-UW avoids this issue by using all of the available data and upweighting error points.
Finally, consider the opportunity cost of ignoring domain annotations in the worst case, i.c., the domain labels we have are in fact noise-free but we still ignore them. In Figure 5b see that the domain annotation- free methods cost very little in terms of lost WGA when training on cleanly annotated data. This loss is minimal in comparison to the cost of training using an aunotation-dependent method when the domain information noisy. Thus, there are concerns about domain annotation noise in the training data, is safest to use a domain annotation-free approach.
6 Discussion
We see in our experiments that these two archetypal data augmentation techniques, downsampling and upweighting, achieve very similar worst-group accuracy and degrade similarly with noise. This falls line with our thcoretical analysis, and suggests that simple symmetric mixture models for subpopulations can provide intuition for the performance of data-augmented last layer retraining methods on real datasets.
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Group Downsample
RAD-UW
M-SELF
Group Upweight
M-SELF (Our imp.)
100
Domain Noise Invariant
80
20%
60
70
WGA
65
20
0
10
15
20
CMNIST
CelebA
Waterbirds
MultiNII
Noise (%)
Dataset
(a) CivilComments WGA under Domain Noise. We see that RAD-UW strongly oulperforms M-SELF on this datasets, likely because of the extreme class im- balance present in the retraining set. This, along with the class balancing performed by M-SELF, results in a very small error set to retrain on. Domain dependent methods are not strongly affected by domain noise be- cause of the relative lack of domain imbalance.
(b) The cost of ignoring domain annotations. For each of the datasets, we compare the WGA the best domain-dependeet method at 0% and 20% domain noise with the best WGA amongst the methods which do not use domain information (labeled "Invariant"". The cost of ignoring the domain information is very small for most datasets and in Waterbirds, utilizing domain information hurts performance somewhat. Thus, the opportunity cost of not using domain information is rela- lively small, while the cost of using a domain-dependenl method with noise is quite large.
Our experiments also indicate that downsampling induces higher variance in WGA, especially in the noisy domain annotation setting. While this phenomenon is not captured in our population analysis, intuitively one should expect that having smaller dataset should increase the variance. Additionally, the models learned by group downsampling suffer from additional dependence on the data that is selected in downsampling, which in turn increases the WGA variance.
Overall, we demonstrate that achieving SOTA worst-group accuracy is strongly dependent on the quality of the domain annotations on large publicly available datasots. Our experiments consistently show that in order to be robust to noise the domain annotations, is necessary to ignore them altogether. To this end, our novel domain annotation-free method, RAD-UW, assures WGA values competitive with annotation-inclusive methods. RAD-UW does so by pseudo-annotating with a highly regularized model that allows discriminating between samples with spurious features and those without and retraining on the latter with upweighting. Our comparison of RAD-UW to two existing domain annotation-free methods and several domain annolation- dependent methods clearly highlights that it can outperform existing methods even for only 5% domain label noise.
There is a significant breadth of future work available in this area. In the domain annotation-free setting, there gap in the literature regarding identification of subpopulations beyond the binary "minority," or "majority" groups. Identifying individual groups could help to increase the performance of retrained models and give better insight into which groups are negatively affected by vanilla LLR. Additionally, tuning hyperparameters without a clean holdout set remains an open question.
Beyond this, group noise could be driven by class label noise alongside domain annotation noise. The combination of these two types of noise would necessitate a robust loss function when training both the pseudo-annotation and retraining models, or new approach entirely. We are optimistic that the approach presented here could be combined in a modular fashion with robust loss achieve robustness to more general group noise.
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Broader Impacts and Limitations
We attempt to address the issue of subgroup fairness and robustness to subpopulation shift through a pseudo annotation strategy the domain. This method could allow practitioners more easily adapt existing models while assuring fair classification across subpopulations. However, because there is a not formal guarantee of fairness, there is possible socictal consequence of practitioners assuming the retrained model is lair without verifying it. Similar lack of guarantees is downfall of most methods in the WGA literalure.
Additionally Oh et al. (2022) has demonstrated that most two-stage methods, including the full-retraining precursors to RAD and SELF, can fair dramatically with small amounts of class label noise. Addressing this issue left. as future work.
Finally we note that achieving this fairness without Comain-annotation presents an opportunity when domain labels may be private. This tradeoff between privacy and fairness is an important area of research, as discussed in King et al. (002)). Perhaps there is regime with limited private information, but enough to achieve some gains over domain-agnostic methods such as RAD and SELF.
Acknowledgements
Nathan Stromberg, Rohan Ayyagari, Monica Welfert, and Lalitha Sankar acknowledge support by NSF CIF-2007688, SCH-22050S0, PIPP-2200161, and Google Al for Social Good grant. Nathan Stromberg and Monica Welfert are grateful for support from Arizona State University's Dean's Fellowship. Sanmi Koyejo acknowledges support by NSF Career Award 2046795 and SCH-2205329, Stanford HAI, and Google Inc.
References
Arjovsky, M., BottOu, L., Gulrajani, I,, and Lopez-Paz, D. Invariant risk minimization. ar preprinl arXiv:1907.0280 2019.
Borkan, D., Dixon, L., Sorensen, J., Thain, N., and Vasserman, L. Nuanced metrics for measuring unintended bias with real data for text. classification. CoRR, abs/1903.0456) 2019. URL http::/arxiv.. /
1903.04561
Chaudhuri, K., Ahuja, K., Arjovsky, M., and Lopez-Paz, D. Why does throwing away data improve worst-group error? In Proceedings of the 40th International Conference on Machine Learning, 2023.
Fang, K. W. Symmetric multivariate and related distributions, Chapman and Hall/CRC, 2018.
Giannone, G., Havrylov, S., Massiah, J., Yilmaz, E., and Jiao, Y. Just mix once: Mixing samples with implicit group distribution. Tn NewrIPS 2021 Workshop on Distribution Shifts, 2021.
Idrissi, B. Y., Arjovsky, M., Pezeshki, M., and Lopez-Paz, D. Simple data balaneing achieves competitive gorst-group-accuracy In Proceedings of the First Conference on Causal Learning and Reasoning, 2022.
Iscen, A., Tolias, G., Avrithis, Y., and Chum, O. Label propagation for deep semi-supervised learning. In Proceedings of the IEEF/CVF conference on computer vision and pottern recognition, pp. 5070-5017 1170-5079, 2019.
Iscen, A., Valmadre, J., Arnab, A., and Schmid, C. Learning with neighbor consistency for noisy labels. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 4672-4681, 2022.
Izmailov, P., Kirichenko, P., Gruver, N., and Wilson, A. G. On feature learning in the presence of spurious corrclations. Advances in Neural Information Processing Systems, 2022.
King, J., Ho, D., Gupta, A., Wu, V., and Webley-Brown, H. The privacy- bias tradcoff: Data minimization and racial disparity assessments in u.s. government. In Proceedings of the 2023 ACM Conference on Fairness, Accountability, and Transparency, 2023.
Kirichenko, P., Izmailov, P., and Wilson, A. G. Last layer re-training is sufficient for robustness to spurious correlations. In The Fleventh International Conference Learning Representations, 2023.
13

---

Published in Transactions on Machine Learning Research (12/2024)
LaBonte, T., Muthukumar, V., and Kumar, A. Towards last-layer retraining for group robustness with fewer annotations. In Conference Neural Informalion. Processing Systems (NeurIPS), 2023.
Liu, E. Z., Haghgoo, B., Chen, A. S., Raghunathan, A., Koh, P. W., Sagawa, S., Liang, P., and Finn, C. Just train twice: Improving group robustness without training group information. In Proceedings of the 38th International Conference on Machine Learning, 2021.
Liu, Z., Luo, P., Wang, X., and Tang, X. Deep learning face attributes in the wild. In Proceedings of International Conference on Computer Vision (ICCV), 2015.
Oh, D., Lee, D., Byun, J., and Shin, B. Improving group robustness under noisy labels using predictive uncertainly. ArXio, abss2221..07225, 2022.
Oren, Y., Sagawa, S., Hashimoto, T. B., and Liang, P. Distributionally robust language modeling. In Proceedings of the 2019 Conference Empirical Methods in Natural Language Processing and the 9th International Joint Conference on Natural Language Processing
2019.
Patrini, G., Rozza, A., Krishna Menon, A., Nock, R.,, and Qu, Making deep neural networks robust label noise: A loss correction approach. In Proceedings of the IEEE conference on computer vision and pollern recognilion, 2017.
Pedregosa, F., Varoquaux, G., Gramfort, A., Michel, V., Thirion, B., Grisel, O., Blondel, M., Prettenhofer, P., Weiss, R., Dubourg, V., Vanderplas, J., Passos, A., Cournapeau, D., Brucher, M., Perrot, M., and Duchesnay, E. Scikit-learn: Machine learning in Python. Journal of Machine Learning Reseorch, 2011.
Qiu, S., Potapczynski, A., Izmailov, P., and Wilson, A. G. Simple and fast group robustness by automatic feature reweighting. In Proceedings of the 40th International Conference on Machine Learning, 2023.
Sagawa, S., Koh, P. W., Hashimoto, T. B., and Liang, P. Distributionally robust neural networks. In International Conference on Learning Representations, 2020.
Wei, J., Zhu, Z., Cheng, H., Liu, T., Niu, G., and Liu, Y. Learning with noisy labels revisited: A study using real-world human annotations. In International Conference on Learning Representations, 2022.
Williams, A., Nangia, N., and Bowman, S. broad-coverage challenge corpus for sentence understanding through inference. In Proceedings of the 2018 Conference of the North American Chapter of the Association for Computational Långuisties: Human Language Technologies, Volume (Long Papers), 2018.
Yang, Y., Zhang, H., Katabi, D., and Ghassemi, M. Change is hard: A closer look at subpopulation shift. International Conference on Machine Learning, 2023.
Yao, H., Wang, Y., Li, S., Zhang, I.., Liang, W., Zou, J., and Finn, C. Improving out-of-distribution robustness via selective augmentation. In Proceedings of the 39th International Conference on Machine Learning, 2022.
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A Proof of Theorem 3.7
Our proof can be outlined as involving five steps; these steps rely on Proposition 3.1 and include three new lemmas. We enumerate the steps below:
We first show in Lemma A.1
that ERM is agnostic to domain label noise.
2. We next show in Lemma A.2 that for clean data with any minority prior no, the WGA for ERM is given by 12
3. In Lemma A.5 we show that the model learned after downsampling with noisy domain labels is equivalent to a clean ERM model learned with prior
(1 p)mo
pmO
4mo (p)
4112 - (p)
4. We then show that the WGA of downsampling strictly decreases in p by examining the derivative.
upweighting must learn the same model downsampling We present the three lemmas below and use them to complete the proof.
Finally we note that by Proposition 3.1
Lemma A.1. ERM with no data augmentation is agnostic to the domain label noise p, i.e., the model learned by ERM in (3) in the selting of domain label noise is the same as that learned in the selling of clean domain labels (no noise).
Proof. Since ERM with no data augmentation does not use domain label information when learning a model, the model will remain unchanged under domain label noise.
In the following, let & IR + [0, 1] be the CDF of (X](X - -.X..)////////.. / Tww for any Y E y and D D Lemma A.2. Let BERM denote the optimal model porameter learned by ERM in (3) using fa(z) w +b and Ý [[f((x)= 1/2). Under Assumptions 3.3 to 3.6
||A To ||
WGA(BERN)
(12)
22[|Abl1 + Exo Ac
where 0., == - 4m0)/11 + 2mo - 2nT) 12 and |||||| == VoLI-le.
Proof. Since the model learned by ERM with no data augmentation is invariant to domain label noise by Lemma A.I we derive the the general form for the WGA of a model fe under the assumption of having clean domain label, and therefore using the original data parameters. We begin by deriving the individual accuracy terms Alv.d) (fa), dv, {0, 13 (R, B}, with fo(x) = w - b and Y I(fo(x) > 1/2), as follows:
(0.d) (fo) = P (1 w x 1/2] = Y Y = y D
Y
P (w= X + 1/2 Y = D, = d)
1/2 1/2- (w (( + b)
Vu Ew
((l,a)) + b- 1/2
$
Tww
(f0))(f) = P (1 (w ToTT -
= P Pw X + b 1/2 Y
= 1/2 (w (0,0) +b)
v u Ew
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We now derive the optimal model parameters for ERM for any 1/4. In the case of ERM, c(y, d) for
(v, d) E E x D, so the optimal solution to (3) with fo(x) = w + b and y = ([)(z)) > 1/2) is
WERM Var(())-Cor(x,1), and DERM B [x]]
(13)
Note that
B[Y] = 2'
B[x] = E D,
E
[1d= R) - (l.BB1) + (1 v0.B + B))
(1i0.R) + n (I.B))
Let x (d(a) = P(D d/Y = y) for (y,d) E e D, n B[X|Y = y) for y E y and A p(1) - -1(0) We
compute Var(X) as follows:
Var(X) ([[Va((X])) + (ar(E[X|
(14)
E [E[ D)
Var(E[X[X))
(15)
Σ. + E|Var([[X)), DJj V))
(16)
Σ E)Var(1(D= 00.8) - - (.) + -1-11 (1- 0.B y
+ (ar(E(
(17)
E++ AcA (1D==))))] Var(Y( -1110 (0) ()
(18)
E (DI + A Var(V)
(19)
Σ + ACA (1 (B(1) (1 Y)m (110) (110) (B[0) ÂÄT (1)
(20)
Σ + 2 (1 AC + AAT.
(21)
Next, we compute Cov(X, Y) as follows:
Cov(X,Y) = -E(Cov(X, + Cor(E[X|)),
(22)
Y)),
(23)
(ov( +Y
(24)
= Cov(Y
(25)
Var(Y)
(26)
π (0)
(27)
1 A.
(28)
In order to write 21 and 28 only in terms of Ac and Ap and to see the effect of no, we show the following relationship between Á, Ac and Ap.
We introduce the following two minor lemmas that allow us to obtain clean expression for the optimal weights.
Lemma A.3. Let À = (())) (0)) Then
AD A = (1 4TO)
Proof. We first note that
(1) = 2 (I (1.1))) + (1.00 = 2 + (1.88)
Similarly,
(0) 20. (. (0.B) - + (0..))
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Combining these with the definitions of Ao and A, get
DD A AD (1(²) - 100))
1! 11 -2T -00.00 2mo + b10.B
pl (10000 4TOAc
(1 4TO)
From 21
28
and Lemma
A.3 we then obtain
1 + ) A Σ + 20o 2TTO
WERM 4
(29)
where A = =1(1)) -1:00) AD - (1 4 and
UERM
1
(WERR)) ( (4 + (l..)))
(30)
2 2
Therefore,
A (1.d) (fornx)) = (WERM)) T (ullid) (4(00) (II.B)))
(31)
((UERM)"EWENT (WEER)) T (p(0.M) (p ((.BB1))
A (0.d) (ferns) = +
(32)
(WERR)) \ EWERM
We simplify the expressions in 31 and
32
by using the following relations:
(0.00
(n
11 (1
2 (10 (0.20 -n (LBB)))
1
(1 (2.10 + (1 - (1 - - An),
a (0BB)
(1 (I)
(1 (0,B) 100000 + 2 (110.B) -10.0)) = (Ac-ADD)
2
((IBB)
(W(0.R) (()
2 (L. - -00 (1(1. (1..) + (1(11 - (1(00.8)
1 _ + AD).
(I.
(u(0,.R)
(1BB))
2 (1.) -((0.R)) + " (1(1.)) -,(1BB) 2
1
1 (AD -Ac).
Plugging these into
31 and
332 for each group (y. {0,1) 13 (R, B} yields
1 (WWRR)) T (Ac + Ap) (WWRR) )zr EWERM
A (). (forns) = (1, (fermM)) = ②
[((UTORN)) T (Ap Ac)
A (). (fenns) = ((I.)) (feERn) +
((WERM EWEER
Thus,
WGA(OFRM) min ( + [((WEus)) (Ac + +AD) ((WERM) EWERM
+ (W(EE)))) (AD - Ac)
(33)
((EERM)" EWERM
In order to rewrite 29 to be able to simplify
33 will use the following lemma.
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Lemma A.4. Let A Rmxm be symmetric positive definite (SPD) and u, Rm.. Then
1
and cu = 0 A
vv + uu ) cu (A-'u aarlu-ch - with Cu :- 1 B-B-tu
1 A-1
Proof. Let B = A vv- Then
(A + vo + ) = (B + uu )
l-l B-1
B
1 u²² B-1
u
(Sherman-Morison formula)
u² B-t
B B-1
u
B-1
1 + u² B-lu
= Cu B-1
A A
A
(Sherman-Morrion formula).
1 v A-1o
The assumption that A is SPD guarantees that A-1 exists, B is SPD, and co and well-defined.
Applying Lemma A.4 to 29
with u 2/2 and v3Ac, where 3 = 2no(1 - 2 yields
BATE A
1+ 1+BATE E- AC 5-1A0
WERM = 7ERM
6 BATEAAE-AA AA ADD-IAN (5-AA))
YERM
AD
1+ EATE-IA
(substituting = AD - -6Cc)
NERM
E
AD C. Σ E-AAc)
with
8 + 3--AEE-1A
7ERM 4+ AT
and Cra
1+ BAAEE-IA
FRM
Let ||0|| = Vor--a be the norm induced by the I-l-inner
iiner product. Then
WGA((ERM) min {
(1 - Cxg A AD + ||D1| Cup ||
{ +
2 D Cao Acl
(Cro + +)A nー - + A + CFo AAolll))
A CTO Acll
Under Assumption 3.6
Cap
= En. = (1 - 4TT)/(1
(1 + 2To 2 Ac/12 and
| 2 2 A 1
|| ET Boll
WGA((EEMM = min
(34)
2 A 2 22
Ac
2 1 22
where the first term is the accuracy of the minority groups and the second is that of the majority groups. In order to compare the WGA of ERM with the WGA of DS, we first show that under Assumption 3.6 the WGA of ERM is given by the majority accuracy term in 334 Since ER. 0 for To I 1/4, we have that
|| 2..
|| + 3T ||
+>
TT l 12 2 0,
2 A 2 + 2 Ac
2 A 1 22 A
which is satisfied for all < 1/4 with equality at 1/4. Since & is increasing, get
WGA(OERM) = || 1|2 2no |
(35)
2
Ap 22 |
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Lemma A.5. Learning the model in 3 after downsampling according to noisy domain labels using the noisy minority prior = = (1 p) + p(1/2- - mO) for p E [0, 1/2] is equivalent to learning the model with clean domain labels (no noise) and using the minority prior
(p) DS
no
pno
(36)
4m 0
(p) 4(1/2 70
Proof. We note that the model learned after downsampling is agnostic to domain labels, only the true proportion of each group, not the noisy proportion, determines the model weights. We derive the equivalent clean prior. We do so by examining how true minority samples are affected by DS on the data with noisy domain labels. When DS performed on the data with domain label noise, the true minority samples that are kept can be calegorized as (i) those that are still minority samples in the noisy data and (ii) proportion of those that have become majority samples in the noisy data.
The first type of samples appear with probability
(1 - p) m): mo:
(37)
i.c., the proportion of true minority samples whose domain was not flipped. The second type of samples are kept with probability
pwo
1/2 00 (p)
T
(38)
where the factor dependent To to be the same size as the noisy minority groups.
(p) is the factor by which the size of the noisy majority groups will be reduced
Therefore, the unnormalized true minority prior can be written as
(p)
(1 po + pmo
To
(39)
1/2 "0
(p)
We repeat the same analysis for the majority groups to obtain the unnormalized true majority prior
(p)
To 1/2
p(1/2 mo) (1 (1-p)) (1/2 TO)
(40)
(p)
m
In order for the true minority and true majority priors to sum one over the four groups, we divide by the normalization factor 4m so our final minority prior is given by
(p)
(1 - p) + pio
1/2-5!1
no
pio
(41)
4mp
(p)
4m
(p)
4(1/2 - x (p)
DS is usually a special case of ERM with To = 1/4. However, since DS uses domain labels and therefore is not agnostic to noise, we need to use the prior derived Lemma A.5 to be able to analyze the effect of the
(p) noise while still using the clean data parameters. Note that T defined in (36) decreases from 1/4 to the noise increases from 0 to 1/2. Since we can interpolate between 1/4 to Ag using p. we can therefore
(p) substitute un in 122 with mDs and then examine the resulting expression function of p for any no- Using
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the WGA of ERM from Lemma
A.2
take the following derivative:
(p) 2 (DS)
|
(p)
|
- -1AD|1
(000 Ds
+
-2 16
-8 +3 || Acll
Di
X
Op
2,
A
+
82 (p)
Ac 12
3/2
(1 11+2zDps (p)
(1-2TD3) ||a|12)
DS
2 ||An||
22 DD
A
To Amo 12 1) -
2 (To 4p) + p)² (To - 2) - +) 1)²
which is strictly negative for < 1/2 and To < 1/4 Therefore, for any no < 1/4, the WGA DS is strictly decreasing in p and recovers the WGA of ERM when p 1/2 or when To 1/4. Thus, for p S 1/2 and
mo 1/4,
WGA(OERRM S WGA(O))) = |A 2
(90) DS
Acll
(42)
2 ||abll
(p) Ds
Acll)
with equality when p 1/2 or To 1/4. Additionally, by Proposition 3.1
||An|l
Ac
WGA(0 WGA( +
De
(43)
2
( + (p> | DD
B
Datasets
Table 2: Dataset splits
Group, g Domain, d
Data Quantity
Dataset
Class, y
Train
Val
Test
non-blond
female
71629
8535
9767
non-blond
male
66874
8276
7535
CelebA
blond female
22880
2874
2480
blond male
1387
182
180
landbird land
3506
462
2255
landbird water
185
462
2255
Waterbirds
waterbird land
55
137
642
waterbird water
1049
138
642
0-4 green rod green red no nogation
1527
747
786
0-4
13804
6864
6868
CMNIST
5-9
13271
6654
6639
5-9
1398
735
707
contradiction contradiction entailment
57498
22814
34597
negation no negation
11158
4634
6655
67376
26949
40496
MultiNLI
entailment neither no negation
negation
1521
613
886
66630
26655
39930
neither
negation
1992
797
1148
C Experimental Design
For the image datasets, we use a Resnet50 model pre-trained on ImageNet, imported from torchvision as the upstream model. For the text datasets, we use a BERT model pre-trained on Wikipedia, imported from the transformers package as the upstream model. In our experiments, we assume access validation sot with clean domain annotations, which we use tune the hyperparameters. For all methods, we tune the inverse of X, where À is the regularization strength, 20 (equally-spaced log scale) values ranging from
20

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Published in Transactions on Machine Learning Research (12/2024)
1e 4 to 1. RAD-UW has more hyperparameters to tune, which we discuss in detail below for each dataset. For all the methods we tested, for each noise level, we perform ten rounds of hyperparameter tuning over ten seeds of adding domain annotation noise. We then fix the most commonly chosen value across the ten rounds. With the fixed hyperparameters, we rerun the algorithms over 10 random seeds of noise and report the mean and standard deviation across the len seeds. RAD-UW uses a regularized linear model implemented with pytorch for the pseudo-annotation of domain labels (henceforth referred to as the pseudo-annotation model) and uses cRegresiioo model imported from sklearn.. ealeeannnninarr Linear_model _model as the retraining model with upweighting. The annottainn model uses weight decay of le 3 with the AdamW optimizer from pytorch. For all datasets except Waterbirds, the pseudo-annotation model is trained for 6 epochs. Waterbirds is trained for 60 epochs. For all datasets except CMNIST, we tune the inverse of \ιd for the pseudo-annotation model over 20 (equally-spaced on a log scale) values ranging from le - to le - 3. For CMNIST, we tune the inverse of ÅLD 20 (equally-spaced on a log scale) values ranging from 1e - 1 to 1e2. For the retraining model, we tune the inverse of X over 20 (equally-spacod on a log scale) values ranging from le to 1.
C.1 Waterbirds
For the upstream ResNet55 model, we use a constant learning rate of le 1e-3, 3, momentun of 0.9, and weight decay of 1.-3. We train the upstream model for 100 epochs. We leverage random crops and random horizontal flips as data-augmentation during the training. For RAD-UW, we tune À for both the pseudo-annotation model and the retraining model. We tune the upweighting factor, for the retraining model over 5 equally spaced values ranging from 5 to 20. The pseude-annotation model uses a constant learning rate of 1e- 5.
C.2 CelebA
For the upstream ResNet50 model, we use a constant learning rate of le 1 3, momentum of 0.9 and weight decay of le- - 4. We train the upstream model for 50 epochs while using random crops and random horizontal flips for data augmentation. We tune the upweighting factor, c, for the retraining model over equally spacod values ranging from 20 to 40. The pseudo-annolation model is trained with an initial learning rale of le with CosineAnnealingla. learning rate scheduler from pytorch.
C.3 CMNIST
For the ResNet50 model, use constant learning rate of le 3, momentum of 0.9 and weight decay of 1e - 3. We train the model for 10 epochs without any data augmentation. We tune the upweighting factor, c, over 5 equally spaced values ranging from 20 to 40. The pseudo-annotation model is trained with an initial learning rate of 1e-
- 5 with CosineAnneal ingLR learning rate scheduler from pytorch. The spurious correlations in CMNIST is between the digit being between less than and the color of the digit. We note that this simple correlation is quite casy to learn, so the l penalty needed in quite small.
C.4 MultiNLI
We train the BERT model using code adapted from [Iamailov et al., 2022 We train the model for 10 epochs with an initial learning rale of le 4 and weight decay of le We use the linear learning rate scheduler imported from the transformer. library. The upweight factor is tuned over 5 equally spaced values ranging from 4 to 10. The pseudo-amnotaton model is trained with an initial learning rate of 1c 4 with bosineennealinglle learning rate scheduler from pytorch.
C.5 Civil Comments
Similar to MultiLII, We train the BERT model using code adapted from (Izmailov et al. 2022). We train
the model for 10 epochs with an initial learning rate of 1e - 5 and a weight decay of le 4. We use the linear lcarning rate scheduler imported from the transformers library. The upweight factor is tuned over equally spaced values ranging from to 10. The psendo-annotation model is trained with an initial learning rate of le 4 with CosineAnneal inngLR learning rate scheduler from pytorch.
21

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Published in Transactions on Machine Learning Research (12/2024)
Table 3: M-SELF Hyperparametens
Datasct
fine-tuning steps
learning rate range
num points range
CelebA
500
[1e-6, 1e-5, le-4]
[2, 20, 100]
Waterbirds
500
[1o-4, 1e-3, 1e-2]
[20, 100, 500]
CMNIST
500
[le-5, le-4, 1e-3]
[100, 500, 700
Civilcomments
200
[1c-6, 1e-5, lc-4]
200 100, 500]
Table 4: CelebA group downsampling WGA
Label Noise
Method
0%
5%
10%
15%
20%
Averaged
87.33:10.46
79.22:12.14 1.33
77.33:13.03 78.67
Single 33.25
81.56:3.005
76.4443.82
78.67+4.67
76.89+3.06
D M-SELF Implementation
We implemented misclassifccation-SELL using code adapted from LaBonte et al. 2023 that it would be compatible with our setup, where we use pre-generated embeddings from the base models. We fix the finetuning steps, which is the number of steps of fine-tuning we perform once we construct the class- balanced error set. We tune the learning rate and the number of points that are selected for class balancing. The hyperparameter values and ranges used are given in Table 3
E
Model Averaging
DFR (Kirichenko al. 2023 emphasizes the importance of model averaging in their setting seeing different downsampled retraining sets can dramatically change the fair classifier. To examine these effects we train GDS 10 times and average the weights over those 10 runs. We report the mean and standard deviation of the worst-group accuracy of this averaged model over 10 independent runs.
We see in Tables
4 to [hat for each dataset, averaging helps to reduce variance and provides modest increases in performance for both CelebA and CMNIST. This same model averaging could be performed both for SELF and RAD, but would have effect in GUW the weighting set is fixed is the upweighting factor.
F
Additional Tables
Methods which require domain annotations (DA) are denoted with "Y" in the appropriate column, while those that are agnostic to DA are denoted as "N" We collate the results similar methods and separate those for different approaches in our tables by horizontal lines. Finally, results for methods designed to annotate domains before using data augmentations, namely RAD-UW and SELF (LaBoute al., 2023), are collected the bottom of each table.
G Robustness to Noisy Embeddings
We note in Table 13 and Table 14 that M-SELF has significantly worse performance than RAD-UW when using noisy embeddings, likely because M-SELF additionally reuses the final classification layer of the base
Table 5: CMNIST group downsampling WGA
Label Noise
Method
0%
5%
10%
15%
20%
Averaged
96.1210.21 95.08::..25
94.62-0.41
94.42-0.54
93. 78.59
Single
95.76-10.33
94.42+0.55
94.31+0.34
94.26+00.4
93.41+00.73
22

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Published in Transactions on Machine Learning Research (12/2024)
Table 6: Waterbirds group downsampling WGA
Label Noisc
Method
0%
5%
10%
15%
20%
Averaged
91.78+0.68
91.81+0.81
92.06-00622
91.78-10.68
91.84+0.67
Single
91.59:1..61
91.40:10.51
91.3441.655 91.78:10.48
91.00::0.78
Table 7: CivilComments group downsampling WGA
Label Noise
Method
0%
5%
10%
15%
20%
Averaged
80.4520.43
80.27:0.335
80. 70.53
80.6410.64
80.57
Single 80.47+0.33
80.11+0.447
80.6440.61
80.53+0.57
80.45+1.110
model. Previous work (Iscen et al.)
2019 2022) has shown that most of the drop in performance when training deep models with noisy data comes from poor classification head.
23

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Published in Transactions on Machine Learning Research (12/2024)
Table CMNIST WGA under domain label noise. CMNIST has a relatively small spurions correlation and as such even LLR performs quite well. Additionally, CMNIST is already class balanced so class downsampling and upweighting have effect. (LaBonte et al. 2023 do not provide WGA for CMNIST; RAD-UW matches the performance of group-dependent methods at 10% and surpasses it beyond that.
Domain Annotation Noise (%)
Method
DA
5
10
15
20
Group Downsample
Y
95.73 0.58
94.77 0.46
94.26 0.33
93.90 + 0.58
93.15 0.41
Group Upweight
Y
95.19 =
94.60 0.22
94.03 = 0.22
93.54 0.31
93.12 0.28
Class Downsample
N
91.47 = 0.13
91.47 0.13
91.47 0.13
91.47 0.13
91.47 0.13
Class Upweight
91.94 = 0.09
91.94 0.09
91.94 0.09
91.94 0.09
91.94 0.09
LLR
N
91.81 0.08
91.81 = 0.08
91.81 0.08
91.81 0.08
91.81 0.08
RAD-UW
N
94.06 0.15
94.06 0.15
94.06 0.15
94.06 = 0.15
94.06 0.15
M-SELF (Our Imp.)
N
92.04 0.20
92.04 0.20
92.04 = 0.20
92.04 0.20
92.04 0.20
Table 9: CelebA WGA under domain label noise. RAD-UW outperforms domain annotation-dependent methods at only 5% noise and existing misclassification--ased domain annotation-free baselines at every noise level.
Domain Annotation Noise (%)
Method
DA
10
15
20
Group Downsample
Y
0.84 86.05
84.05 + 1.83
83.00 1.17
81.67 + 1.89
78.83 + 1.98
Group Upweight
Y
86.11 =
82.55 = 0.67
82.39 0.43
81.72 + 0.52
78.72 + 0.96
Class Downsample
N
74.5
0.94
74.5 0.94
74.5 + 0.94
74.5 0.94
74.5 + 0.94
Class Upweight
N
73.89 0.00
73.89 + 0.00
73.89 0.00
73.89 + 0.00
73.89 + 0.00
LLR
N
44.28 0.5
44.28 0.5
44.28 0.5
44.28
44.28 + 0.5
RAD-UW
N
83.51
0.02
83.51 + 0.02
83.51 0.02
0.02
0.02 83.51
83.51 + 0.02
M-SELF (Our Imp.)
N
83.48 0.02
83.48 0.02
83.48 0.02
1.48
83.48 + 0.02
M-SELF
[LaBonte et al.)
N
83.0 6.1
83.0 6.1
83.0 6.1
83.0 6.1
83.0 + 6.1
Table 10: Waterbirds WGA under domain label noise. The validation (retraining) split for Waterbirds is domain balanced already, so class and group balancing perform equivalently. All domain ion-fation-free methods show improvement over baselines.
Domain Annotation Noisc (%)
Method
DA
5
10
15
20
Group Downsample
Y
92.14 + 0.99
91.73 + 0.44
92.07 + 0.27
92.19 + 0.73
92.44 + 0.65
Group Upweight
Y
90.92 + 0.07
90.98 + 0.13
90.95 + 0.15
90.86 + 0.16
90.89 + 0.25
Class Downsample
N
91.44 + 0.31
91.44 - 0.31
91.44 + 0.31
91.44 0.31
91.44 + 0.31
Class Upweight
N
91.40 + 0.06
91.40 + 0.06
91.40 + 0.06
91.40 0.06
91.40 + 0.06
LLR
N
87.35 + 0.06
87.35 + 0.06
87.35 + 0.06
87.35 0.06
87.35 + 0.06
RAD-UW M-SELF (Our Tmp.)
N
92.52
0
92.52 0
92.52 -
92.52
N
92.83 + 0.49
92.83 0.49
92.83
0.49
92.83 + 0.49
92.83 0.49
M-SELF (LaBonte al.)
92.6 + 0.8
92.6 + 0.8
92.6 0.8
92.6 + 0.8
92.6 0.8
24

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Published in Transactions on Machine Learning Research (12/2024)
Table 11: MultiNLI WGA under domain label noise. SELF's reported result performs strongly on this dataset, perhaps due the structure of the spurious correlation. We were unable to replicate the results of LaBonte al. (2023) with our implementation. Regardless, both SELF and RAD-UW outperform group-dependent methods at label noise above 5%.
Domain Annotation Noise (%)
Method
DA
5
10
15
Group Downsample
Y
73.19 + 1.16
67.96 + 1.14
65.94 0.39
64.93 + 0.24
65.31 0.13
Group Upweight
Y
74.31 0.07
69.21 + 0.46
66.22 0.24
65.26
0.24
65.87 0.19
Class Downsample
65.50 + 0.07
65.50 0.07
65.50 = 0.07
65.50
0.07
65.50 0.07
Class Upweight
N
65.05 0.15
65.05
65.05
0.15
65.05 0.15
65.05 0.15
LLR
N
65.36 0.35
0.31 65.47
65.47 0.31
65.47 0.31
RAD-UW
N
0.14 68.53
68.53
68.53
68.53 0.14
M-SELF (Our Tmp.)
N
64.02
64.02
64.02
64.02
64.02 + 0
M-SELF
(LBoonee al.)
N
72.2
72.2
2.2
2.2
72.2 + 2.2
Table 12: CivilComments WGA under domain label noise. RAD-UW dramatically outperforms SELF
which is unable to learn with the severe class imbalance present in CivilComments.
Domain Annotation Noise (%)
Method
DA
5
10
15
20
Group Downsample
Y
80.66 + 0.21
80.42 0.24
81.14 : 0.09
81.07 0.15
81.25 + 0.17
Group Upweight
Y
81.08 = 0.01
80.96 = 0.02
80.87 = 0.01
80.78 = 0.03
80.73 + 0.02
Class Downsample
N
81.56 + 0.12
81.56 0.12
81.56 = 0.12
81.56
81.56 + 0.12
Class Upweight
N
81.50 + 0.03
81.50 + 0.03
81.50 0.03
81.50
81.50 + 0.03
LLR
N
58.59 + 0.01
58.59 - 0.01
58.59 = 0.01
58.59 0.01
58.59 + 0.01
RAD-UW
N
81.57 + 0.03
81.57 0.03
81.57 + 0.03
81.57 0.03
81.57 + 0.03
M-SELF
(Our Imp.)
N
60.61 + 0.04
60.61 = 0.04
60.61 0.04
0.04 60.61 - 0.04
60.61 + 0.04
M-SELF (LaBonte et al.)
N
62.7 + 4.6
62.7 = 4.6
62.7 = 4.6
62.7 + 4.6
62.7 4.6
Table 13: CelebA WGA (std. dev.) using embeddings from noisy base model. We that RAD-UW is significantly more robust to than M-SELF as M-SELF reuses the base model's noisy classifier.
Base Model Label Noise
Method
%
20%
RAD-UW
83.51 0.02
80.55 + 0.02
M-SELF
83.48 + 0.02
31.86 = 2.32
Table 14: Waterbirds WGA (std. dev.) using embeddings from noisy base model, Again RAD-UW is more robust than M-SELF.
Base Model Label Noise
Method RAD-UW
0%
20%
92.52 +
86.12 + 0.05
M-SELF
92.83 0.49
67.43 + 4.48
25


Reviews:
[{"review_id": "E7vppG7YMO", "reviewer": "Reviewer_RrSN", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths:  \nThis paper is well written, the organization follows relatively clear logic and the methodology part is reasonable.  \nThe theoretical contribution is intuitive and beneficial to the field of distribution robust optimization.  \nThe experimental evaluations are quite exhaustive, which shows the effectiveness of the proposed method.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "Summary:\nThis paper studies the distribution robust optimization problem where there is subpopulation shift across different distributions, which is a very practical problem and could have potential applications in realistic situations. Specifically, there are different groups in training dataset, each of them is identified by a group annotation. However, in practice, the group annotation is normally not given. As a result, the difficulty of learning from groups of distributions is normally quite hard, and the performance on worst-case group is poor. Under this setting, the authors conduct thorough theoretical analysis to show that under symmetric group noise, the upweighting strategy and downweighting strategy achieve the same results. Further, the authors propose a novel method which simply uses a l1 regularization to ensure the performance of minor group data detection. Through extensive experimental evaluation, the performance of the proposed method is carefully justified.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "Weaknesses:  \n- The proposed method shows too much similarity to existing methods, as the authors stated in the paper, many works have already leveraged l1 penalty to regularize the performance worst-case optimization, which makes the studies of this paper more of an incremental work. Please provide more justification on the novelty of this work.  \n- The experiments are quite extensive, various datasets and baseline methods are included in this paper. However, intuitive understanding of the proposed method is still unclear to me. For example, why not choosing the l2 or lp regularization? How will the strength of regularization affect the learning performance or group detection performance?  \n- There are several DRO references are missing:  \n  - Huang et al., Robust Generalization against Photon-Limited Corruptions via Worst-Case Sharpness Minimization, in CVPR 2023.  \n  - Indyk et al., Worst-case performance of popular approximate nearest neighbor search implementations: Guarantees and limitations, in NeurIPS 2023.  \n  - Chaudhuri et al., Why does throwing away data improve worst-group error? In ICML 2023.", "broader_impact_concerns": "The author have stated broader impact, no ethical concerns.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "t4ORQBqzU9", "reviewer": "Reviewer_7RCn", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "# Strenghts\n- Relevant problem setting: Worst-group accuracy optimization is an important topic, as spurious correlations are often learnt by deep learning models. \n- Sensible proposed approach: The novel approach using high l1 penalization to identify minority samples is well-motivated.\n- Empirical evaluation covers datasets similar to competitors: The chosen datasets seem sufficient to make claims\n- Results show improvement of performance under group label noise against chosen competitors: Although the approach is not always the best compared to the baselines, it wins on average and show small variance over the runs.\n\n# Weaknesses\n- The empirical evaluation section is not convincing yet. \n    - 1) The description states that the approach is evaluated against class-only upweighting/downsampling, but the results are not to be found in the main paper. They are only the the appendix and should be highlighted more.\n    - 2) It seems the authors only compare to the worst version of LaBonte et al. (2023) with no clear argumentation. The exact method (M-Self) is mentioned directly, but why did the authors not compare against, for example, the early stop version or the best-performing disagreement version? It should be clearly stated, as this is the comparison of the State-of-the-Art. I understand that M-Self also uses misclassifications, which might be similar to the proposed approach using l1 loss, but if there are better strategies, why not bulid on these?\n- Related work could give a better overview of other methods next to upweighting / downsampling. For example, recent methods  use SSL, such as Tsirigotis et al. (2023).\n- Minor: \n    - ERM is never introduced - only the abstract mentions empirical risk minimization but never refers to ERM.\n    - In-sentence citations often miss surrounding brackts\n\nReferences:\nTsirigotis, C., Monteiro, J., Rodriguez, P., Vazquez, D. and Courville, A.C., 2024. Group robust classification without any group information. Advances in Neural Information Processing Systems, 36.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "No", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "The paper proposes a novel approach for worst-group accuracy optimization, where a classifiers a trained to overcome spurious correlations by focussing on achieving sufficient performance for all available groups. Groups are determined by an extra set of labels, although several approaches exist which achieve the same goal without using them.\n\nThe first contribution of the paper are a theortical analysis of downsampling and upweighting of majority groups or minority examples, respectively, under group label noise. The authors show, among others, that under symmetric label noise both upweighting and downsampling lead to the same degradation of worst-group accuray.\n\nHaving shown the effect of group label noise, the authors propose a new approach which trains a linear model with high l1 penalty and uses the misclassifications to detect minority points. These are then upweighted to train the final model using a logistic loss with another l1 penalty.\n\nThe paper is empirically evaluated for CMNIST, CelebA, Waterbirds, MultiNLI and CivilComments by comparing the proposed approach against main competitor misclassification SELF (M-Self) and group-only upweighting and -downsampling (+ class-only methods,  vanilla last layer retraining in the appendix). The results show that the proposed approach is often superior to the baselines when more group label noise is added. The authors also show ablation studies of adding more group noise as well as increasing penalties during training.", "claims_and_evidence_yn": "No", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "- Please improve the presentation and discussion of the empirical results wrt class-only upweighting and downsampling. If this is mentioned as part of the evaluation, one should add the performances to the main line charts next to the other methods. Otherwise, one has to show tables of complete results in the main paper.\n\n- Please clearly motivate the chosen main competitor misclassification SELF and resulting questions: Why can't one choose the best version of the respective paper, e.g., a disagreement variant? Would this use information you not allow in the problem statement? Otherwise I see no point in not comparing against this variant.  Lastly, if the overall goal of the paper is another, it should not be claimed that the approach beats the SotA under group label noise.\n\n- Exending on that, it might be good to better explain how the proposed method differs to M-Self if one ignores the early stopping and drop out rates.\n\n- Minor: It would be beneficial to add a short section or clear sentences what other techniques are currently investigated in recent papers, such as the mentioned SSL.", "broader_impact_concerns": "There are no concerns on ethical implications of the work.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "m9tVRsFe6F", "reviewer": "Reviewer_ct71", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths:\n- The target problem is clearly stated and motivated.\n    \n- The related works section covers the relevant approaches.\n    \n- The theoretical analysis provides a deeper understanding of the two common methods in this field.\n    \n- The methodology is clearly explained.\n\nWeaknesses:\n\n- In the abstract, the authors state: “Our results show that RAD is competitive with other recently proposed domain annotation-free techniques. Most importantly, RAD outperforms state-of-the-art annotation-reliant methods even with only 5% noise in the training data for several publicly available datasets.” In my understanding, these mean that in terms of performance, recent domain annotation-free methods >= this paper’s method > SOTA domain annotation-reliant methods. Since the annotation-free methods do not require domain labels and thus cost less than annotation-reliant methods (meanwhile, perform better), I cannot see why the comparison with domain-reliant methods matters.\n    \n- I think that conceptually, there are only two differences between the proposed RAD-UW and M-SELF proposed by LaBonte et al (2023): RAD-UW uses explicit l1 regularization for domain labelling and adopts UW for WGA optimizing, whereas M-SELF uses implicit early-stopping regularization and adopts DS. As l1 regularization is a basic concept in ML and UW is a common method in optimizing WGA, I think the novelty of the proposed method is quite limited. The experimental results showing that the proposed method failed to outperform existing methods in many settings also limit its significance.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This paper deals with the challege of optimizing worst-group accuracy under the setting of training with imbalanced data where the domain labels are noisy. The authors first present a theoretical analysis arguing that the two common methods in the literature of optimizing WGA have the same theoretical guarantee, which degrades as the domain labels get noisier. They further propose to use an explicitly regularized model that learns spuriously correlated features to label minority data to enhance the common UW method. The experimental results show that the proposed method achieves competitive results.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "Please see the weaknesses stated above.", "broader_impact_concerns": "I have no concerns about the ethical implications of the work.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Meta-review: After a thorough evaluation of the submission and the reviewers' feedback, I recommend accepting the paper with minor revisions. The paper makes a contribution by introducing a method that is both theoretically justified and empirically validated. The reviewers generally agree on the paper's strengths, particularly its clear problem statement, theoretical analysis, and extensive experimental evaluation.


Recommendations for Improvement:

- Enhance the discussion on how the proposed method differs from and improves upon methods like M-SELF. Emphasize the unique aspects, such as the use of L1 regularization for spurious feature identification and robustness to noise.

- Incorporate the experimental results comparing the proposed method with class-only upweighting/downsampling in the main paper to strengthen the empirical evidence.

- Expand the related work to include recent methods employing semi-supervised learning and other techniques relevant to worst-group accuracy optimization without group annotations.

- Address minor issues such as the introduction of ERM (Empirical Risk Minimization) and correct any citation formatting errors.
Decision: Accept (poster)