Revisiting Group Robustness: Class-specific Scaling is All You Need
Authors: Seonguk Seo
Bohyung Han
Venue: Submitted to ICLR 2023 (2023)
Keywords: Group robustness
spurious correlation
debiasing
worst-group accuracy
unbiased accuracy
performance evaluation

Abstract: Group distributionally robust optimization, which aims to improve robust accuracies such as worst-group or unbiased accuracy, is one of the mainstream algorithms to mitigate spurious correlation and reduce dataset bias. While existing approaches have apparently gained performance in robust accuracy, these improvements mainly come from a trade-off at the expense of average accuracy. To address the challenges, we first propose a simple class-specific scaling strategy to control the trade-off between robust and average accuracies flexibly and efficiently, which is directly applicable to existing debiasing algorithms without additional training; it reveals that a naive ERM baseline matches or even outperforms the recent debiasing approaches by adopting the class-specific scaling. Then, we employ this technique to 1) evaluate the performance of existing algorithms in a comprehensive manner by introducing a novel unified metric that summarizes the trade-off between the two accuracies as a scalar value and 2) develop an instance-wise adaptive scaling technique for overcoming the trade-off and improving the performance even further in terms of both accuracies. Experimental results verify the effectiveness of the proposed frameworks in both tasks.


Under review as a conference paper at ICLR 2023
REVISITING GROUP ROBUSTNESS: CLASS-SPECIFIC SCALING IS ALL YOU NEED
Anonymous authors Paper under double-blind review
ABSTRACT
Group distributionally robust optimization, which aims to improve robust accu- racies such as worst-group or unbiased accuracy, is one of the mainstream al- gorithms to mitigate spurious correlation and reduce dataset bias. While exist- ing approaches have apparently gained performance in robust accuracy, these im- provements mainly come from trade-off at the expense of average accuracy. To address the challenges, we first propose simple class-specific scaling strategy control the trade-off between robust and average accuracies flexibly and effi- ciently, which is directly applicable to existing debiasing algorithms without addi- tional training; it reveals that naïve ERM baseline matches even outperforms the recent debiasing approaches by adopting the class-specific scaling. Then, we employ this technique to I) evaluate the performance of existing algorithms in comprehensive manner by introducing a novel unified metric that summarizes the trade-off between the two accuracies as a scalar value and 2) develop an instance- wise adaptive scaling technique for overcoming the trade-off and improving the performance even further terms of both accuracies. Experimental results verify the effectiveness of the proposed frameworks in both tasks.
INTRODUCTION
Machine learning models have achieved remarkable performance in various tasks via empirical risk minimization (ERM). However, they often suffer from spurious correlation and dataset bias, failing to learn proper knowledge about minority groups despite their high overall accuracies. For instance, because digits and foreground colors have a strong correlation in the colored MNIST dataset (Ar-) jovsky et al. 2019 Bahng et al.) 2020). a trained model learns unintended patterns of input images and performs poorly in classifying the digits in minority groups, in other words, when the colors of the digits are rare in the training dataset.
Since spurious correlation leads to poor generalization performance minority groups, group dis- tributionally robust optimization (Sagawa al., 2020) has been widely studied in the literature about algorithmic bias. Numerous approaches (Huang et al. 2016 Sagawa et al.) 2020; Sco et al. 2022al Nam et al. 2020 Sohoni et al. 2020 Levy et al., 2020 Liu et al. 2021) have presented high bust accuracies such as worst-group or unbiased accuracies in a variety of tasks and datasets, but, although they clearly sacrifice the average accuracy, comprehensive evaluation jointly with aver- age accuracy has not been actively explored yet. Refer to Figure [ about the existing trade-off's of algorithms.
This paper addresses the limitations of the current research trends and starts with introducing a simple post-processing technique. robust scaling, which efficiently performs class-specific scaling on prediction scores and conveniently controls the trade-off between robust and average accuracies. allows us to identify any desired performance points, e.g., for average accuracy, unbiased accuracy, worst-group accuracy, balanced accuracy, on the accuracy trade-off curve using a single model with marginal computational overhead. The proposed robust-scaling method can be easily plugged into various existing debiasing algorithms to improve the desired target objectives within the trade- off. One interesting observation is that, by adopting the proposed robust scaling, even the ERM baseline accomplishes competitive performance compared to the recent group distributionally robust
optimization approaches (Liu et al. 2021] Nam et al. 2020 Sagawa et al. 2020; Kim et al. 2022
Seo et al. 2022a Creager al. 2021 Levy 2020 Kirichenko al. 2022 Zhang al.
2022

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Worst Accuracy
10-
Umbrased
65
60
BRD 3r -0.21
UNO ff -0/7
-0.73
GR -0.57)
.0.11)
-0.78)
Average Accuracy (%)
Average Accuracy (361
(a) Worst-group accuracy
(b) Unbiased accuracy
Figure 1: The scatter plots that illustrate trade-off between robust and average accuracies CelebA dataset using ResNet-18, We visualize the results from multiple runs of each algorithm and present the relationship between the two kinds of accuracies. The lines denote the linear regression results of individual algorithms and r in the legend indicates its Pearson coefficient correlation, which validates the strong negative correlation between both accuracies.
without extra training, as illustrated in Figure 2 algorithms in the experiment section.
We will present the results from other debiasing
By taking advantage of the robust scaling technique, we develop novel comprehensive evaluation metric that consolidates the trade-off of the algorithms for group robustness, leading a unique perspective of group distributionally robust optimization. To this end, we first argue that comparing the robust accuracy without considering the average accuracy is incomplete and a unified evaluation of debiasing algorithms is required. For a comprehensive performance evaluation, we introduce a convenient measurement referred to as robust coverage, which considers the trade-off' between average and robust accuracies from the Pareto optimal perspective and summarizes the performance of each algorithm with a scalar value. Furthermore, we propose a more advanced robust scaling algorithm that applies the robust scaling each example adaptively based on its cluster membership at test time to maximize performance. Our instance-wiss adaptive scaling strategy effective to overcome the trade-off between robust and average accuracies and achieve further performance gains in terms of both accuracies.
Contribution. We present a simple but effective approach for group robustness by the analysis of trade-off between robust and average accuracies. Our framework captures the full landscape of robust-average accuracy trade-offs, facilitates understanding the behavior of existing debiasing techniques, and provides way for optimizing the arbitrary objectives along the trade-off using a single model without extra training. Our main contributions are summarized as follows.
We propose a training- free class-specific scaling strategy to capture and control the trade- off between robust and average accuracy with marginal computational cost. This approach allows us to optimize a debiasing algorithm for arbitrary objectives within the trade-off.
We introduce a novel comprehensive performance evaluation metric via the robust scaling that summarizes the trade-off between robust and average accuracies as scalar value from the Pareto optimal perspective.
We develop an instance-wist robust scaling algorithm by extending the original class- specific scaling with joint consideration of feature clusters. This technique is effective to overcome the trade-off and improve both robust and average accuracy further.
The extensive experiments analyze the characteristics of existing methods and validate the effectiveness of our frameworks on the multiple standard benchmarks.
2 RELATED WORKS
Mitigating spurious correlation has been emerged as an important problem in a variety of areas in machine learning. Sagawa al. (Sagawa al., 2020) propose group distributionally robust opti-
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Unbblased Acc (15)
08
Worst grst-geuupp Arc.
00
60
C1M
BMK
LPF
FRM
50
ITT
LI
Group BR
70
CAR D&O Group DRC
CFR
UNBC
Drh
Average Acc. 196
Average Acc. 0%5
(a) Worst-group accuracy
(b) Unbiased accuracy
Figure 2: Comparison between the baseline ERM and existing debiasing approaches on CelebA dataset using ResNet-50. Existing works have achieved meaningful improvements in robust ac- curacy over ERM, but our robust scaling strategies (RS, IRS) enable ERM to catch up or even outperform them without any training.
mization (Group DRO) and provide practical assumption; training examples given in groups, and arbitrary test distribution represented by a mixture these groups. Because models which rely on the spurious correlation yield poor worst-group performance, group distributionally robust optimization, which aims to maximize worst-group accuracy, is widely adopted to deal with spurious correlation, and the methods can be mainly categorized into three folds as follows.
Sample Reweighting The most popular approaches are assigning different training weights to each samples to focus on the minority groups, where the weights are based on the group frequency or loss. Group DRO (Sagawa al. 2020) minimizes the worst-group loss by reweighting based on the average loss per group. Although Group DRO achieves robust results against group distribution shifts, it requires training examples with group supervision. To handle this limitation, several un- supervised approaches have been proposed that do not exploit group annotations. George (Sohoni al. 2020) and BPA (Seo et al. 2022a) extend Group DRO in an unsupervised way, where they first train the ERM model and use this model to infer pscudo-groups via feature clustering. CVaR DRO
Levy et al. 2020) minimizes the worst loss over all a-sized subpopulations, which upper- bounds the worst group loss over the unknown groups. LfF (Nam et al.) (2020) simultaneously trains two models, one with generalized cross-entropy and the other one with standard cross-entropy loss, and reweights the examples based on their relative difficulty score. JTT (Liu al. (02I)) con- ducts a two-stage procedure, which upweights the examples that are misclassified by the first-stage model. [drissi et al. (2022) analyze simple data subsampling and reweighting baselines based on group or class frequency to handle dataset imbalance issues. LWBC (Kim et al.] (022) employs an auxiliary module identify bias-conflicted data and assigns large weights to them.
Representation Learning On the other hand, some approaches aim to learn debiased represen- tations directly to avoid spurious correlation. ReBias (Bahng al., 2020) adopts Hilbert-SShhidt independence criterion (Gretton et al. 2005) to learn feature representations independent of the pre- defined biased representations. Cobias (Seo et al.) 2022b) defines conditional mutual information between feature representations and group labels bias measurement, and employ it debias- ing regularizer. IRM (Arjovsky et al. 9019) learns invariant representations to diverse environments, where the environment variable can be interpreted the group. While IRM requires the supervi- sion of the environment variable, EIIL (Creager et al. 2021) and PGI (Ahmed et al. 2020) are the unsupervised counterparts, which assign each training example to the environment that violates the IRM objective maximally.
While most previous studies are in-processing approaches that perform feature representation learning sample reweighting during training to improve group robustness, our framework does not fall into those categories; deals with group robust optimization by simple post-procee poscesrocessin with class-spechs score scaling, which does not require any additional training. Similar to our method, some prot-procsssing techniques, including temperature (Guo et al., 2017) or Platt (Plati 2000) scaling, are widely exploited in the literature of confidence calibration, but
Post-processing
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Wers:group Accuracy (9%
vold
80-
Accuracy
Pareto Optimal
85.0
Pareto Optimal
60
82.5
50
85.0
71.5
94
54
86
Average Accuracy
Average Accuracy (9)
(a) Worst-group accuracy
(b) Unbiased accuracy
Figure 3: The relation between the robust and average accuracies obtained by varying the class-
specific scaling factor with ERM model on the CelebA dataset. The black marker denotes the origi- nal point, where the scaling is not applied. The points, located within the green area, the trade-off curve represent the Pareto optimums.
not applicable in our task because it scales the prediction scores equally for each class and does not change the label predictions. Recently, DFR (Kirichenko et al. 2022) demonstrated that retraining only the last layer of the model with group group-balanced dataset can match the performance of existing approaches, but they still require additional training different from our framework.
FRAMEWORK
This section first presents a class-specific scaling technique, which captures the landscape of trade-off and identifies the optimal performance points for desired objectives along the trade-off curve. Based on the scaling strategy, we introduce a novel unified metric for evaluating the group robustness of an algorithm with consideration of the trade-off. Finally, propose instance-wist class-specific scaling approach to overcome the trade-off and further improve the performance.
3.1 PROBLEM SETUP
Let consider triplet (I, a)) consisting of input feature E X. target label D. and an attribute a E A. We construct a group based on a pair of target label and an attribute, 9 = (y,a) y x A G. We are given training examples without attribute annotations, e.g., (111,1),,.. (Nnr Yn)), while m validation examples have group annotations for model selection, e.g., ((11, (00,,114, ).... (Imm 9m)) (x11, y/, 01), ... (Im, Um, Um,am)) am)).
Our goal is to learn a model fo(.) : X - y that is robust to group distribution shifts. To measure the group robustness, typically refer the robust accuracy such unbiased accuracy (UA) and worst-group accuracy (WA). The definitions of UA and WA require the group-wise accuracy (GA), which is given by
GM = Σ, )
= 91 Σ, 1gg =))
(1)
where 11.) denotes an indicator function and GA(r) is the accuracy of the th group samples. Then, the robust accuracies are defined by
1 UA
Σ GA and WA == min GA(r)-
rEg
The goal the group robust optimization is to ensure robust performance by improving UA and WA regardless of the group membership of sample.
3.2 ROBUST SCALING:
SCALING FOR GROUP ROBUSTNESS
We perform a simple non-uniform class-specific scaling of the scores corresponding to individual class and potentially change the final decision of the classifier to achieve the robustness by improving
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Werstgroup gropp Accuracy (%)
vold
Unblosed Accuracy (99
wlld Best
50
30
10-1
10a1
10'
scale
(a) Worst-group accuracy
(b) Unbiased accuracy
Figure 4: Effects of varying the class-specific scaling factors on the robust accuracy using ERM model on the CelebA dataset. Since this experiment is based on the binary classifier, a single scaling factor is varied with the other fixed one. This shows that the optimal scaling factor identified in the validation set can be used in the test set to get the final robust prediction.
worst-group or unbiased accuracies while sacrificing the average accuracy. Formally, the prediction with the class-specific scaling is given by
arg max (s + )),,
where & E C is prediction score vector, C' is the number of classes, E RC is C-dimensional scaling coefficient vector, and @ denotes the deement-wise product operator.
Based on the ERM model, obtain set of the average and robust accuracy pairs using wide range of the class-specd caas--pecific scaling factors and illustrate their relations in Figure The black markers indicate the point with a uniform scaling, i.e., (I...., 1) RCC The graphs show that simple class-specific scaling effectively captures the full landscape the trade-off of the two accuracies. We also visualize the relationship between scaling factors and robust accuracies in Figure 4 where the curves constructed based on validation and test splits are sufficiently well-aligned to each other. This validates that can identify the desired optimal points between robust and average accuracies in the test set by following simple strategy: 1) finding the optimal class-specific scaling factors that maximize the target objective (UA, WA, or AA) in the validation set, and 2) apply the scaling factors to the test set. We refer to this scaling strategy for robust prediction as robust scaling.
To find the optimal scaling factor s, we adopt a greedy searct and the entire process takes less than second. Note that the robust scaling is any kinds of existing robust optimization methods without extra training. Moreover, our method can find any desired performance points on the trade-off envelop using a single model. For example, there may be scenarios in which multiple objectives are required to solve problem, but the robust scaling approach is flexible enough to handle the situation as we only need to apply a robust scaling for each target metric using a single model. Meanwhile, other existing robust optimization methods have limited flexibility and require training of separate models for each target objective.
praterrrcssing method, so it can be easily applied to
3.3 ROBUST COVERAGE FOR COMPREHENSIVE PERFORMANCE EVALUATION
Although the robust scaling identifies the desired performance point on the trade-off curve, from the perspective of performance evaluation, still reflects only single point on the trade-off curve while ignoring all other possible Pareto optimums. For more comprehensive evaluation of an algorithm, we propose convenient evaluation metric that yields scalar summary of the robust- average accuracy trade-off. Formally, we define the robust coverage as
D-1 max WAA 2 1
Coverage == max [WA 2 ofdc Σ
(4)
c=
where WA and AA* denote the worst-group and average accuracies given by the scaled prediction using 3 with the scaling factor s. and D = 1000 is the number of slices for discretization. The
We search for the scaling factor of each class in greedy manner. Specifically, we first find the best scaling factor for a class and then determine the optimal factors of the remaining classes sequentially conditioned on the previously estimated ones.
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Table Experimental results of the robust scaling (RS) the CelebA dataset using ResNet-18 with the average of three runs (standard deviations in parenthesis), where RS is applied to maximize each target metric independently. On top of all existing approaches, RS can maximize all target metrics consistently. Gain indicates the average (standard deviations) of performance improvement of RS for each run.
Group Supervision
Robust Coverage
Accuracy (%)
Method
Worst-group Unbiased
Worst-group
Unbiased
Average
ERM
34.5(6.1)
71.7(1.8)
95.5(0.4)
ERM + RS
83.0(0.8)
88.1(0.6)
82.8(3.3)
91.2((0.5)
95.8(0.2)
Gain
+47.7(7.8)
+13.3(2.0)
+0.4(0.2)
CR
70.6(6.0)
88.7(1.2)
94.2(0.7)
CR RS
82.9(0.5)
88.2(0.3)
82.7(5.2)
91.0(1.0)
95.8(0.5)
Gain
+12.2(7.5)
+2.2(113)
+1.6(0.4)
SUBY ldrissi et al. 2022
65.7(3.9)
87.5(0.9)
94.5(0.7)
SUBY RS
81.5(1.0)
87.4(0.1)
80.8(2.9)
90.5(0.8)
95.5(0.6)
+15.1(3.))
43.000.9)
+1.1(0.6)
LIF Nam 2020
55.6(6.6)
81.5(2.8
92.4(0.8)
LfF RS
74.1(3.5)
79.7(2.6)
78.7(4.1)
85.4(2.4)
93.4(0.7)
Gain
+23.2(2.5)
+4.0(0.8)
+1.)
JIT (Liu et al 2021
75.1(3.6
85,9(1.4)
80.8(0.8)
JTT RS
77.3(0.7)
81.9(0.7)
82.9(2.3)
87.6(0.5)
90.3(1.3)
Gain
+7.8(3.0)
+1.7(0.4)
+0.6(0.1)
Group DRO Sagawa et al. 2020
88.4(2.3)
92.0(.4)
93.2(088)
Group DRO
87.3(0.2)
88.3(0.2)
89.7(1.2)
92.3(0.1)
93.9(0.3)
Gain
+1.4(1.)
+0.4(0.2)
+0.7(0.5)
GR
88.6(1.9)
92.0(0.4)
92.9(0.8)
GR RS
86.9(0.4)
88.4(0.2)
90.0(1.6)
92.4(0.5)
93.8(0.4)
Gain
+1.4(1.1)
+0.5(0.4)
+0.8(0.5)
SUBG ldrissi et al. 2022
87.8(1.2)
90.((1.2)
91.9(.3)
SUBG RS
83.6(1.6)
87.5(0.7)
88.3(0.7)
90.9(0.5)
93.9(0.2)
+0.5(0.44
+0.5(0.5) +1.9(0.6)
robust coverage measures the under the Pareto frontier of the robust-average accuracy trade- off curve, where the maximum operation (4) finds the Pareto optimum for each threshold, as visualized Figure Tigure|5cJand55 5dl Note that the robust accuracies such WA and UA are two popular target metrics and we can adjust class-specific scaling factors depending on the objectives. Please refer Appendix B.I for more discussions.
3.4 INSTANCE-WIS! ROBUST SCALING FOR IMPROVING GROUP ROBUSTNESS
We claim that the optimal scaling factor can be applied adaptively to each test example and has the potential to overcome the trade-off and improve accuracy even further. Previous approaches (Seo) et al, 2022a| Sohoni al. 2020 have shown the capability to identify hidden spurious attributes via clustering on the feature space for debiased representation learning. Likewise, we take advantage of feature clustering for adaptive robust scaling; we obtain the optimal class-specific scaling factors based the cluster membership for each sample. The overall algorithm of instance-wise robust scaling (IRS) is described as follows.
1. Clustering the examples in the validation split on the feature space and store the centroids of the clusters.
2. Find the optimal scaling factors for each cluster in the validation split.
3. Assign the examples in the test split to the clusters by selecting their nearest centroids obtained from step
4. For each sample in the test split, apply the optimal scaling factor obtained in step 2 based its cluster membership.
In step 1, we use the naive k-means algorithm for clustering. The number of clusters K a hy- perparameter but it can be easily tuned by selecting the one that gives the highest robust coverage in the validation set. Empirically, sufficient number of K 10 gives stable and superior results, compared to the original robust scaling.

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Table Experimental results of robust scaling (RS) on the Waterbirds dataset using ResNet-50 with the average of three runs (standard deviations in parenthesis). Gain indicates the average (standard deviations) of performance improvement of RS for each run.
Group Supervision
Robust Coverage Worst-group Unbiased
Accuracy (%)
Method
Worst-group
Unbiased
Average
ERM
76.3(0.8)
89.4(0.6)
97.2(0.2)
ERM RS
76.1(1.)
82.6(1.3
81.6(1.9)
89.8(0.5)
97.5(0.1)
Gain
+5.3(1.3)
+0.4(0.4)
+0.440022
CR
76.1(0.7)
89.10077)
97.100.)
CR RS
73.6(2.3)
82.0(1.5)
79.4(2.4)
89.4(1.0)
97.5(0.3)
Gain
43,4(1.8)
+0.3(0.4)
+0.4(0.1)
SUBY (Idrisii el al. 2022
72.8(4.1)
84.9(0.4)
93.8(1.))
SUBY RS
22.5(1.)
81.2(1.4)
75.9(4.4)
86,3(0.9)
95.5(0.2)
Gain
+3.4(1.88
+0.3(0.4)
+I7(I1
LIF (Na et al. 2020
77.0227)
87.1(1.9)
93.((1.)
LIF
75.7(2.7)
80.9(0.4)
79.5(2.5)
88.2(1.1)
94,8(1.9
Gain
+2.6(2.1)
+I.10.99)
JTT
eiu 2021
86.7(0.3)
90.2(0.2)
92.6(0.3)
JTT
RS
83.0(0.5)
84.6(0.))
88.2(0.7)
90.3(0.2) 92.9(0.4)
Gäin
+1.3(0.7)
+0.[0.1
+0.40.2
Group DRO (Sagawa al. 2020
88.0(1.0)
92.5(0.9)
95.8(18)
Group DRO FRS
83.4(1.1)
87.4(1.4)
89.1(1.7)
92.7(0.8) 96.4(1.55
Gain
+1.I(0.8)
+0.2(0.1) +0.5(0.5)
GR
86.1(1.3)
89.3(0.9)
95.1(1.)
GR + RS
83.7(0.3)
86.8(0.7)
89.3(1.3)
92.0(0.7)
95.4(1.3
+3.2(2.0)
+0.7(0.6)
+0.4[0.2]
SUBG (ldiissi el 2022
86.5(0.9)
88.2(1.)
87.3(L.))
SUBG
80.6(2.0)
82.3(2.0)
87.1
88.5(1.))
913(0.4)
Gain
+0.6(0.5)
+0.3(0.3)
+4.0(0.9)
4 EXPERIMENTS
4.1 EXPERIMENTAL SETUP
Implementation details We adopt a ResNet-18 18 and ResNet-50 (He et al. 2016), which is pre- trained on ImageNet (Deng et al., 2009), our backbone network for CelebA and Waterbirds datasets, respectively. We train our models using the stochastic gradient descent method with the Adam optimizer for 50 epoch, where the learning rate is 1 10-4, the weight decay is 1 X 10 and the batch size 128. We adopt the standard K-means clustering and set the number of clusters K 20 in Section 3.4 for all experiments. We select the final model which gives the best unbiased coverage in the validation split. Our algorithms are implemented in the Pytorch (Paszke et al. 2019) framework and all experiments previous works (Sagawa et al. 2020 Liu et al. 2021). we report the adjusted average accuracy as the average accuracy for Waterbirds dataset; we first calculate the accuracy for each group and then report the weighted average, where the weights corresponds to the relative portion of each group in training set. Please refer the supplementary file for the dataset usage.
conducted on a single unit of NVIDIA Titan XP GPU. Following
Evaluation metrics
Following prior works, evaluate all the compared algorithms with the average, unbiased and worst-group accuracies, and also with the proposed unbiased and worst-group coverages for comprehensive view.
4.2 RESULTS
Plugging RS into the existing methods Table and present the experimental results of our original robust scaling (RS) on top of the existing approaches (CR, SUBY. LIF, JTT, Group DRO, GR, SUBG on the CelebA and Waterbirds datasets, respectively. In these tables, RS is applied to maximize each target metric (worst-group. unbiased, and average accuracies) independently | We conducted three experimental runs and reported the average and the standard deviation of the results.
2 Please refer to Appendix A for hrief introduction comparisons.
Note that, since our robust scaling strategy is simple post-processing technique, do not need to retrain the model for each target metric and the cost negligible, e-g., only few seconds for each target metric.

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Table 3: Results of our robust scaling methods on the CelebA and Waterbirds datasets with the average of three runs (standard deviations in parenthesis). Blue color denotes the target metric that the robust scaling aims to maximize. Compared to RS, IRS improves the overall trade-off.
Robust Coverage
Accuracy (%)
Accuracy (%)
Datasel
Method
Worst. Unbiased
Worst.
Unbiased
Average
Worst.
Unbiased
Average
ERM
34.5(6.1)
77.7(188
95.5(004)
34,5(6.1)
(7.7(1.))
90.5(0.4)
ERM + RS
83.0(0.7)
88. (0.5)
82.1(3.7)
91.1(0.6) 1 92.2(1.))
45.0(7.4)
81.7(188)
95.8(0.2)
ERM + IRS
83.4(0.1)
88.4(0.4)
87.2(2.0)
91.7(0.2) 91.5(0
44.1(4.2)
81.3(0.8)
95.8(0.1)
CR
70.6(6.0)
88.7(1.2) 94.22(0.7)
70.666.0)
88.7(1.2)
94.2(0.7)
CelebA
CR RS
82.9(0.5)
88.2(0.3)
82.7(5.2)
91.0X1.0)
(91.711))))))
48.5(8.9)
82.5(2.2)
95.8(0.1)
CR IRS
83.6(1.1)
88.6(0.5)
91.3(0.4) 84.8(1.5)
99..7(13)
48.8(9.1)
82.7(2.4)
95.8(0.1)
GroupDRO
88.4(2.3)
92.0(0.4)
93.2(00.8
88.4(2.3)
92.000.4)
93.2(0.8)
Gro + RS
87.3(0.2)
88. (0.2(
92.3(0.1) 89.7(1.2)
93.7(0.55)
64.9(3.3)
80.1(
93.9(0.3)
GroupDRO + IRS
87.5(0.4)
88.4(0.2)
90.0(2.3)
92.6(0.6) (93.500.4
60.4(5.4)
84.4(0.6)
94.7(0.3)
ERM
89,4(0.6) 76.3(0.8)
97.2(00.2)
76.3(0.8)
89.4(0.6)
97.2(0.2)
ERM + RS
76.1(0.4)
82.6(0.3)
81.6(19)
89.8(0.5) 1 97.2(0.22
79.1(2.7)
89.7(0.6)
97.5(0.1)
FRM IRS
83.4(1.1)
(0.9(
89.3(0.5)
92.7(0.4) (4.1(
77.6(7.0)
19.6(1.1)
97.5(0.3)
CR
76.1(077)
89.1(0.7) 1 97.1(0.55
((0.7
89.1(0.7)
(0.1(
Waterbirds
CR + RS
73.6(2.3)
82.0(1.5)
79.4(2.4)
89.4(1.0) 96.8(0.8)
76.4(1.5)
89.3(0.8)
(7.5(0.3)
CR + IRS
84.2(2.5)
88.3(1.0)
88.2(2.7)
92.1(0.7) 95.7(1.1)
77.3(4.7)
88.6(1.2)
97.4(0.2)
GroupDRO
92.5(0.9) 88.0(1.)
8)..(
88.0(1.0)
92.5(0.9)
85.8(1.8
GroupDRO- RS
83.4(L.1)
87.4(1.4)
89.1(1.7)
92.7(0.) %6.((.))
80.9(4.4)
91.3(1.0)
97.1(0.3)
GroupDRO IRS
86.3(2.3)
92.1(2.6)
90.8(1.3)
93.9(0.2) 96.0(0.6)
83.2(1.7)
91.5(0.8)
97.1(0.4)
Group supervision indicates that the method requires training examples with group supervision. As shown in the tables, no matter what the backbone method is, our robust scaling strategy consistently improves the performance for all target metrics. Based on the robust coverage and robust accuracy after scaling, LIF and JTT are not superior ERM on the CelebA dataset, though their initial robust accuracies without scaling are much higher than ERM. GR and SUBG are reweighting and subsam- pling baselines based on group frequency, respectively. Although two method achieve competitive robust accuracy on the Waterbirds dataset, the average accuracy of SUBG is far below than GR, mainly because SUBG drops a large portion of training samples to make all groups have the same size. This supports our argument that we need to evaluate in more comprehensive way beyond robust accuracy. On the other hand, the methods that leverages group supervision (Group DRO, GR) achieve better robust coverage results than others on both datasets, which validates that group supervision helps to improve the trade-off itself. For the group supervised methods, our scaling pro- vides relatively small performance gains in robust accuracy, the gaps between robust and average accuracies are already small and the original results are already close to the optimal for maximizing robust accuracy.
Instance-wise Robust Scaling We evaluate all the proposed methods on the CelebA and Water- birds datasets and present the results in Table We employ ERM, class reweighting scheme (CR), and Group DRO as baselines, and apply our robust scaling methods, including the standard robust scaling (RS) and instance-wise robust scaling (IRS), to them. We test robust scaling strategies with two scenarios, each aimed at maximizing unbiased or average accuracies, respectively, where each target metric is marked in blue in the tables. Compared to RS, IRS improve the robust cov- erage itself as well as the accuracy of the target metric for each scenario. In particular, although Group DRO have already achieved high robust accuracy and coverage, IRS further improves their results on both datasets. This validates that our instance wise class-specific scaling strategy is effec- tive to overcome the trade-off between robust and average accuracies and truly improve the group robustness of baseline models.
4.3 ANALYSIS
Visualization of the trade-off curve and its Pareto frontier We visualize the robust-average accuracy trade-off curve and its corresponding robust coverage curve in Fig. the CelebA dataset.
In Fig. 5a and 5b the black markers indicate the points where the scaling factor is not applied,
indicating that there is room for improvement in robust accuracy along the trade-off curve. Fig. [5c and 5d present the corresponding robust coverage curves, which represents the Pareto frontiers of
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20.0
50-
Wersi group Accuraty
50.0
70-
Worsk group Accu
FRM
$2.5
30.0
40-
DRD
75.0
04
90
02
95
Average Accuracy (56
Average Accuracy (%)
(a) Worst-group accuracy
(b) Unbiased accuracy
Wersk Werst-group group Accuracy (%)
Unbisee Accuracy 1%6
8
60
EIM (85.2) [8B.2)
40-
GR
BRD
08
9:
97 21
97
50
92
Average Accuracy (36)
Avaraçe Accuracy (96)
(c) Worst-group accuracy
(d) Unbiased accuracy
Figure 5: The robust-average accuracy trade-off curves ((a), (b)) and the corresponding robust cov-
erage curves ((c), (d)), respectively, the CelebA dataset. The curves in (c) and (d) represent the Pareto frontiers of the curves (a) and (b), respectively. In (c) and (d), the numbers in the legend denote the robust coverage, which measures the area under the curve.
90
85
90
80
Worst-graup Accurary (%)
Accuracy
group Coverage (validatio)
Unblased Coverage (valldation)
15
10
15
The number of clusters (K)
The number clusters (K)
(a) Worst-group accuracy
(b) Unbiased accuracy
Figure 6: Sensitivity analysis on the number of clusters in the instance-wise robust scaling on the Waterbirds dataset. The robust coverage in the validation split (orange line) tends to be similar to the robust accuracy in the test split (blue line).
Fig. aaland 5b
respecitvely. The area under the curve in Fig. 5c aeanddd indicates indicatees the robust coverage. which is reported in the legend.
Sensitivity analysis on the number of clusters We conduct the ablation study on the number of clusters for feature clustering in instance-wic robust scaling method the Waterbirds dataset. Fig. 6 shows that the worst-group and unbiased accuracies are stable with a sufficient number of K 10. We also plot the robust coverage results in the validation split, which tends almost consistent with the robust accuracy. This presents that we can select the optimal K based on the robust coverage results of the validation split.
CONCLUSION
We presented a simple but effective post post-processing framework that provides a novel perspective of group robustness. Our work started from the observation that there exists clear trade-off between robust and average accuracies existing works, and argued that comparing only the robust accuracy should be regarded incomplete. To deal with this issue, first proposed the robust scaling strategy, which can capture the full landscape of trade-off and identify the desired performance point the trade-off curve. Based this strategy, introduced novel convenient measurement

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that summarizes the trade-off from Pareto optimal perspective for the comprehensive evaluation of group robustness. Moreover, we proposed an mnstance-wise robust scaling algorithm with adaptive scaling factors, which is effective to improve the trade-off itself. We analyzed the characteristics of existing methods and demonstrated the effectiveness of our proposed frameworks and measurements with extensive experiments. We believe that the proposed approaches exact behavior of existing debiasing techniques and paving the way in the future research direction.
helpful for analyzing the
Ethics Statement As model learning focuses unconditionally on improving the overall perfor- mance, there is room for risks such fairness bias issues caused by dataset algorithmic bias. With the careful and comprehensive consideration of robust performance such as worst-group or unbiased accuracies, we believe framework help alleviate this potentially harmful risks in model use. We also acknowledge that we have read and commit to adhering to the ICLR code of ethics.
Reproducibility Statement We provide the dataset usage, implementation details, and evaluation metric in Section 4.1 We reported all experimental results the main tables based on the average of three runs with standard deviation.
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A COMPARISONS
Below is brief introduction of the comparisons used in our experiments.
ERM Given loss function (()), the objective of empirical risk minimization is optimizing the
following loss over training data:
min
((fo(x)).i))
(5)
Class reweighting (CR) To mitigate the class imbalance issue, we can simply reweight the sam- ples based on the inverse of class frequency in the training split,
min Σ wrl(fo(Fs)) mil where Wi Σ, 1g; = Mi
(6)
LfF Motivated by the observation that bias-aligned samples are more easily learned, LIF (Nam et al. 2020) simultaneously trains a pair of neural network Jf). The biased model I' is trained with generalized pross-entropy loss which intends to amplify bias, while the debiased model fo is trained with a standard cross-entrope loss, where each sample (Iz, Vi) is reweighted by the following relative difficulty score:
EUP (UP( U:
((f (2:),
JTT JTT (Liueuu 2021) consists of two-stage procedures. In the first stage, JTT trains standard ERM model /(-) for several epochs and identifies error set E of training examples that misclassified:
E = (Zi, 9:) s.t. f(x;) + wi
Next, they train a final model fo(-) by upweighting the examples in the error set E as
min 9
uup
Σ
((fol)).))
Σ (lo(o).
(E.
(F.))E
Group DRO formulated as:
Group DRO (Sagawa et al. 2020) aims to minimize the empirical worst-group loss
Fy Σ igg=9g
min
max gEG
[(fo(z)).
(10)
where ny is the number of samples assigned to 9h group. Unlike previous approaches, group DRO requires group annotations (y, a) on the training split.
Group reweighting (GR) Using group annotations, we can extend class reweighting method to group reweighting based on the inverse of group frequency in the training split, i.e.,
min
ure(fo(as)) where WA E, a =a)
(11)
To mitigate the data imbalance issue, SUBY subsample majority classes, all classes have the same size with the smallest class on the training dataset, as Idrissi et al.] (2022). Similarly, SUBG subsample majority groups.
SUBY/SUBG
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Table A4: Realized robust coverage results on the Waterbirds and CelebA datasets with the average of three runs (standard deviations in parenthesis).
Robust Coverage
Realized Robust Coverage
Dataset
Method
Worst-group
Unbiased
Worst-group
Unbiased
Waterbirds
ERM
70.3(1.3)
79.4(0.7)
69.0(1.5)
78.7(0.8)
Waterbirds
CR
68.9(1.1)
78.5(0.5)
67.8(1.2)
77.9(0.4)
Waterbirds
Group DRO (Sgawa et al. 2020
80.8(0.6)
85.2(0.1)
78.6(1.0)
83.8(0.4)
Waterbirds
GR
78.8(5.6)
83.7(0.7)
77.9(1.4)
82.8(0.8)
CelebA
ERM
78.9(1.7)
86.0(0.6)
75.9(2.2)
85.4(0.7)
CelebA
CR
77.2(2.8)
85.6(0.9)
71.8(1.)
85.0(0.)
CelebA
Group DRO Sagawa et al. 2020
84.2(0.6)
86.7(0.5)
81.((1.)
86. 86.1(0.2)
CelebA
GR
84.2(0.5)
87.5(0.3)
81.2(1..)
87.0(0.5)
B CLARIFICATION
B. ROBUST COVERAGE IN THE TEST SPLIT
In Sec. 4.3 of the main paper, defined robust coverage
D-1 Σ max [WA d=0
Coverage ==
max 2
2 cfdc
D
(12)
c=0
The robust coverage can be directly calculated in the validation split, but unfortunately, it basically unavailable the test split. This is because we need to know the values of WA* in advance to conduct max operation in (12). but we cannot use the information in the test split.
To bypass this issue, we report the robust coverage of validation split in this paper, which tends to be similar to those of the test split. We also validate the reliability of the robust coverage of the test split. We first obtain a optimal scaling factors for each threshold in the validation split S as
Shal = max (WA AA 2 d I
for 0 d D 1
(13)
then the realized robust coverage of test split is calculated by
Realized Coverage
WAS BES.
(14)
SSall
Table A4 presents the original robust coverage and realized robust coverage results on the test splits of Waterbirds and CelebA datasets. Both coverage results are almost similar, because the optimal scaling factors identified in the validation split are close to optimal in the test split as well.
C ATTRIBUTE-SPEGE ROBUST SCALING WITH GROUP SUPERVISION
the supervision of group (spurious-attribute) information can be utilized during our robust scaling, it will provide flexibility further improve the performance. To this end, we first partition the examples based on the values of spurious attributes and find the optimal scaling factors each partition separately. Like the original robust scaling procedure, factors for each partition in the validation split and apply them to the test split. However, this partition-wise scaling is basically unavailable because do not know the spurious attribute values of the examples in the test split and thus cannot partition them, In other words, we need to estimate the spurious-attribute values in the split for partitioning. To conduct attribute-speiifie robust scaling (ARS), we follow a simple algorithm described below:
obtain the optimal scaling
1. Partition the examples in the validation split by the values of the spurious attribute.
2. Find the optimal scaling factors for each partition in the validation split.
3. Train independent estimator model to classify spurious attribute.
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Table A5: Results of the attribute-specific robust scaling (ARS) on the CelebA and Waterbirds datasets with the average of three runs (standard deviations in parenthesis), where ARS is applied to maximize each target metric independently. Note that our post-processing strategy, ARS, allows ERM to achieve competitive performance Group DRO that utilizes the group supervision during training.
Robust Coverage
Accuracy (%)
Dataset
Method
Worst.
Unbiased
Worst.
Unbiased
Average
ERM
34.5(6.1) 1)
77.7(1.8)
95.5(0.4)
CelebA
ERM ARS
87.6(1.0)
89.0(0.2)
88.5(1.8)
91.9(0.3)
95.8(0.1)
Group DRO
87.3(02))
88.3(0.23
88,42.3)
92.0(0.4)
93.27033
ERM
76.3(0.8)
89.4(0.6)
97.2(0.2)
Waterbirds
ERM ARS
84,4(1.9)
87.8(1.7)
89.3(0.4)
92.510.4)
97.5(1.0)
Group DRO
83.4(1.1)
87.4(2.3)
88.0(1.0)
92.5(0.9)
95.8(188
Table A6: Effects of the size of group-labeled examples on the attribute-ppecffic robust scaling on the CelebA dataset. Group-labeled size denotes ratio of group-labeled samples among all training examples for training estimators. Spurious accuracy indicates the average accuracy of spurious- attribute classification using the estimators the test split.
Accuracy (%)
Accuracy (%)
Robust Coverage
Group-laheled 100%
Spurious
Worst-group
Unbiased
Average
Worst-group
Unbiased
98.
83.1(3.0)
92.4(1.1)
93.1(1.2)
87.6(10)
89.0(0.5)
10%
97.7
88.5(1.8)
91.9(0.3)
92.8(0.6)
86.8(0.4)
89.0(0.2)
1%
95.8
88.5(1.8)
91.9(0.3)
92.9((06)
87.1(0.3)
89.0(0.2)
0.1%
92.6
88.4(2.1)
91.8(0.5)
92.4(0.8)
87.1(0.3)
89.0(0.2)
4. Estimate the spurious attribute values of the examples in the test split using the estimator, and partition the test samples according to their estimated spurious attribute values.
5. For each sample in the test split, apply the optimal scaling factors obtained in step based on its partition.
To find a set of scale factors corresponding to each partition, we adopt a naïve greedy algorithm that performed in one partition time. This sttribute-specifi robust scaling further increases the robust accuracy compared to the original robust scaling, and also improves the robust coverage, as shown in Table A.5 Note that attribute-specific scaling strategy allows ERM match the supervised state-of-thc-as approach, Group DRO (Sagawa et al. 2020
One limitation that it requires the supervision of spurious attribute information to train the es- timator model in step 3. However, we notice that only a very few examples with the supervision enough train the spurious-attribut estimator, because is much easier to learn as the word "spurious correlation" suggests. To determine how much the groupelabeled data is needed, we train several spurious- attribute estimators by varying the number group-labeled examples, and conduct ARS using the estimators. Table A6 validates that, compared to the overall training dataset size, very small amount of group-labeled examples enough to achieve high robust accuracy.
D EXPERIMENTAL DETAILS
D.1 DATASETS
CelebA (Liu et al., 2015) is a large-scale dataset for face image recognition, consisting of 202,599 celebrity images, with 40 attributes labeled on each image. Among the attributes, we primarily ex- amine hair color and gender attributes as target and spurious attributes, respectively. We follow the original
split (Liu et al. 2015) for all experiments in the paper. Water- birds (Sagawa et al. 2020) is synthesized dataset. which created by combining bird images in the CUB dataset Wah et al. (21IT) and background images from the Places dataset (Zhou et al. 2017), consisting of 795 training examples. The two attributes- one is the type of bird, [waterbird,
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Table A7: Ablation study on the size of validation set in our robust scaling strategies on the CelebA
dataset.
Method
Valid size
Worst-group Acc.
Unbiased Ace.
Average Acc.
ERM
34.5(6.1)
77.7(1.)
95.5(0.4)
RS
100%
82.8(3.3)
91.2(0.5)
95.8(0.2)
+ RS
50%
83.3(3.7)
91.5(0.9)
95.8(0.2)
+ RS
10%
82.4(4.3)
91.4(0.8)
95.8(0.2)
+ RS
1%
79.2(10.3)
90.8(2.2)
95.5(0.4)
IRS
100%
88. (609)
92.0(0.5)
95,8(0.1)
+ IRS
50%
86.9(2.0)
91.8(0.4)
95.9(0.2)
+ IRS
10%
84.4(6.3)
91,4(1.0)
95.6(0.4)
+ IRS
1%
60.4(14.4)
85.8(3.2)
94.7(1.5)
Table A8: Variations of robust scaling methods tested on the FairFace dataset.
Method
Cost
Worst-group Acc.
Unbiased Acc.
Average Acc.
ERM
15.8
47.0
54,1
RS (2 super classes)
((n)
18.6
51.8
52.9
RS (greedy search)
O(n)
19.2
52.3
53.3
RS (full grid search)
(n
19.0
52.8
53.1
landbird} and the other is background places, {water, land], used for the experiments with this dataset.
D.2 CLASS-SPECIFIC SCALING
To identify the optimal points, we obtain a set of the average and robust accuracy pairs using a wide range of the class spess--e scaling factors, i.e., S; (1.05)" for 200 I < 200 for 1th class. Note that we search for the scaling factor of each class in greedy manner, as stated in Section 3.2
D.3 HYPERPARAMETER TUNING
We tune the learning rate (10-3, 10-1, 10-53 and the weight decay in {1.0, 10-10002,0011 for all baselines. We used 0.5 of for LfF. For JTT, we searched Xup in (20, 50, 100} and updated the error set every epoch for CelebA dataset and every 60 epochs for Waterbirds dataset. For Group DRO, we tuned C' in {0, 1, 3, 4), and used 0.1 of 17.
E ADDITIONAL ANALYSIS
Ablative study on the size of validation set Our robust scaling strategies need held-out valida- tion set to identify the optimal scaling factors, like other existing approaches for early stopping and hyperparameter tuning. Note that early stopping is essential to achieve high robust accuracy in other approaches. To validate the robustness of our frameworks, we conduct the ablation study by varying the size of validation set. Table A7 presents the ablative results using ERM baseline on the CelebA dataset, where the size of validation set is varied by (100%, 50%, 10%, 1%). As shown in the table, with only 10% or 50% of the validation set, both our robust scaling (RS) and instance- wise robust scaling (IRS) achieves almost competitive performance with the results using the full size of validation set. Surprisingly, even only 1% of the validation set is enough for RS to achieve sufficiently high robust accuracy, but inevitably entails a large variance results. On the other hand, IRS suffers from performance degradation when only 1% of the validation set is avail- able. This mainly because IRS takes advantage of feature clustering on the validation set, which needs some validation samples. Nevertheless, our robust scaling strategies can achieve meaningful performance improvement with a limited number of validation samples for all cases, which validates the robustness of our method.
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Table A9: Results of our robust scaling methods on top of various baselines on the CelebA and Waterbirds datasets with the average of three runs (standard deviations in parenthesis). Blue color denotes the target metric that the robust scaling aims to maximize. Compared to RS, IRS improves the overall trade-off.
Robust Coverage
Accuracy (%)
Accuracy (%)
Datasel
Method
Worst. Unbiased
Worst.
Unbiased
Average
Worst.
Unbiased
Average
ERM
34.5(6.1)
71.7(1.8) 95.3(
34.5(6.1)
77.7(1.8)
95.5(0.4)
ERM RS
83.0(0.7)
88.1(
82.1(3.7)
91.1(0.6) 92.2(1.)
45.00..4)
81.7(1.8)
95.8(0.2)
ERM + IRS
83.4(0.1)
88,4(0.4)
91.7(0.2) 87.2(2.0)
91.55(0.8
44.1(4.2)
81.3(0.8)
95,8(0.1)
CR
76.606.0)
88.7(1.2) (1.7(1.),99.0000 94..2(0.7) ((.1.2),4..200.7
70.6(6.0)
88.7(1.2)
94.2(0.7)
CR + RS
82.9(0.5)
88. 88.2(0.3)
82.7(5.2)
91.0(1.0) 10011110 91.7(1.3) 48.5(8.9)
82.5(2.2)
95.8(..1)
CR + IRS
83.6(1.1)
88.6(0.5)
84.8(1.5)
91.3(0.4)
90.7(1.3)
48.8(9.1)
82.7(2.4)
95.8(0.1)
SUBY
65.1(5.9)
87.5(0.9)
94.5((0.7)
65.7(339)
87.3(0.9)
94.5(0.7)
SUBY RS
81.5(1.))
87.4(0.1)
80.8(2.9)
90.5(0.8) 91.1(1.7)
45,4(6.7)
81.4(2.0
95.5(0.0)
SUBY IRS
82.3(1.1)
87.8(.2))
82.3(2.0)
90.8(0.8) 90.7(1.9) 46.0(6.9)
81.5(2.1)
95.5(0.1)
CelebA
SUBG
8788(12)
90.4(1.)) 91.9((0.)
87.8
90.4(12)
91.9(0.3)
SUBG + RS
83.6(1.6)
87.5(0.7)
88 88.3(0.7)
90.9(0.5) 90.6(1.)
67.8(6.5)
85.2(2.0)
93.9(0.2)
SUBG + IRS
84.5(0.8)
87.9(0.1)
88.7(0.6)
91.0(0.3) 90.6(0.8
68.5(6.5)
85.5(1.9)
94.0(0.2)
GR
92.000.4) (2.9(
11.6
92.000.4
92.9(0.8)
GR RS
46.9(044)
88.4(0.2)
90.0(1.)
92.4(0.5) 92.5(0.5)
66.5(0.3)
85.4(0.4)
90.)(
GR IRS
87.0(02))
88.6(0.2)
90.0K2.3)
92.6(0.6) 92.5(0.4) 62.0(5.3)
84.5(0.7)
94.2(0.3)
Grou
38.4(233)
92.0(0.4) 993.2
92.000.3)
93.2(0.8)
GROupDRO + RS
87.30.2)
88. 88.30.2)
89.7(1.2)
92.3(0.1) 93.7(0.5)
64.9(3.3)
(0.7
93.9(0.3)
GroupDRO + IRS
87.5(0.4)
88.4(0.2)
90.0(2.3)
92.6(0.6) 93.5(0.4)
60.4(5.4)
84.4(0.6)
94.7(0.3)
ERM
76.3(0.8)
89.4(0.6) 97.2(0.2)
76.3(
89.4(0.6)
27.2(0.2)
ERM RS
(6.1(0.4)
82.6(0.3)
81.6(19)
89.8(0.5) 97.2(0.2)
79.1(2.7)
89.7006)
90.5(
ERM IRS
83.4(1.1)
(6.9()
89.3(0.5)
92.7(0.4) 94.1(0.3)
77.6(7.0)
89.6(1.))
97.5(0.3)
CR
76.1(0.7)
89.1(0.7) 97.1(0.5)
76.1(0.7)
89.1(0.7)
90.1(
CR + RS
73.6(2.3)
82.0(1.5)
79.4(2.4)
89.4(1.0 96.8(0.8)
76.5(1.5)
89.3(0.8)
97.5(0.3)
CR + IRS
84.2(2.5)
88.3(1.)
88.2(2.7)
92.1(0.7) 95.7(1.1)
77.3(4.7)
88.6(1.2)
97.4(0.2)
SUBY
728(4117
84.9(0.4)
193.8(T.5))
S4.9
93.8(1.5)
SUBY RS
72.5(1.)
81.2(1.4)
75.9(4.4)
86.3(0.9) 95.2(1.4)
70.7(5.8)
85.4(1.6)
(5.5(0
SUBY IRS SUBG
78.8(2.7)
85.9(1.0)
82.1(4.0)
89.1
92.6(2.2)
74.1(4.1)
86.3(0.9
96.2(0.6)
Waterbirds
86,5(0997
28.2(1.2) 17...3(T.))
86.5(07)
88.201.)
87.3(1.1)
SUBG + RS
80.6(2.0)
82.3(200)
87.1(0.7)
88.5(1.) 87.9(1.1)
74.0(5.6)
85.9(2.8)
91.3(0.4)
SUBG + IRS
82.2(0.8)
84.1(0.8)
87.3(1.3)
88. 88.2(1.2) 87.6(1.2)
70.2(1.6)
84.5(1.0)
(3.5(0.4)
GR
86.1(1))
89.3(0.9) (9..1(1.3)
86.1(133
89.3(0.]
95.1(1.3)
GR RS
83.7(0.3)
86.8(0.7)
89.3(1.3)
92.0(0.7) (3.1)3.2)
82.2(1.3)
90.((0.5)
95.((1.)
GR IRS
84.8(1.7)
87.4(0.4)
(9.
92.2(1.0) 92.9(2.1)
((.4(114)
90.5(0.7)
95.6(0.8)
GrüupDRO
86,00100)
92.5(0.9) 193.8((T8))
88001100
92.5(0.9)
95.8(1.8)
GroupDRO + RS
83.4(1.1)
87.4(1.4)
92.7(0.8) 89.1(1.7)
96.5((..)
80.9(4.4)
91.3((.0)
97.1(0.3)
GrouDRO + IRS
86.3(2.3)
90.1(2.6)
90.8(1.3)
93.9(0.2) 96.0(0.6)
83.2(1.7)
91.5(0.8)
97.1(0.4)
Scalability As mentioned in Sec. 3.2 we actually search for the scaling factor of each class in greedy manner. Hence, the time complexity increases linearly with respect to the number of classes instead of the exponential growth with the full grid search; even with 1000 classes, the whole process takes less than a few minutes practice, which is negligible compared the model training time. Moreover, we can reduce the computational cost even further by introducing the superclass concept and allocating single scaling factor for each superclass. We compare three different options greedy search, superclass-level search, and full grid search-on on the FairFace dataset Kärkkäinen & Joo| (202T) with 9 classes. Table [A8 shows that our greedy search is as competitive as the full grid search despite the time complexity gap in several orders of magnitude in computational complexity and the superclass- search is also effective to reduce cost. Note that the superclasses are identified by the feature similarity of class signatures.
F ADDITIONAL RESULTS
Table A9 presents the full experimental results with our robust scaling strategies (RS, IRS) top of existing models, which supplement Table 3 of the main paper.
16


Reviews:
[{"review_id": "y6hubZfHVKQ", "reviewer": "Reviewer_3mfo", "summary": "", "questions": "", "limitations": "", "rating": 8, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "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": "", "main_review": "", "summary_of_the_paper": "This work presents a simple post-training strategy to balance the worst-group and average-case accuracies of a classifier. In addition, it proposes a new metric to summarize this tradeoff. An extension on the simple method is also proposed to achieve better results. The proposed method outperforms several existing baselines and helps to put prior work on group robustness in context.", "summary_of_the_review": "This paper presents some important insights regarding the tradeoff between worst and average accuracy. It presents a simple method to allow trading off the two. At the same time, this work lacks some experimental rigor (only 2 datasets and missing subsampling baseline) and clarity in exposition (the RS & IRS results are difficult to compare to each other). If these last two points were done well, there would be a nice takeaway along two directions: 1) worst and avg accuracy can be traded off for all models, and 2) RS & IRS are two simple methods that do this with strong empirical performance. Due to the limitations outlined, however, I can only have confidence and clarity in takeaway #1. This is the reason for my rating.\n\n------------------------ UPDATE AFTER REBUTTAL --------------------\n\nMy main criticisms with this work are around clarity and the small number of datasets. The authors have addressed clarity somewhat, and importantly have added results on two more datasets - CivilComments and FMOW. The results on CivilComments are just as impressive/notable as those on CelebA. The results on FMOW are a bit muddied, which is due to ERM performing worse than GDRO, so the story here is a bit nuanced but I am glad the authors included the results nonetheless. Given that evaluation has been much improved, I have updated my rating of this paper to accept. That being said, I would like to see a couple things in the camera ready:\n- Full evaluation results of all the baselines on the new datasets.\n- A figure or table within the main text or appendix that averages the numbers across all datasets (to provide a wholistic view of the method).", "strength_and_weaknesses": "Strengths:\n- the proposed method (RS) and its extension (IRS) are both simple and effective\n- the robust coverage method is a nice way to summarize the worst-avg accuracy tradeoff and is a strong contribution\n- the related works section is written very well.\n\nWeaknesses:\n- Evaluation on more datasets would help to strengthen the analysis. In particular, the BalancingGroups codebase (https://github.com/facebookresearch/BalancingGroups) would be a great point for this to add 2 text classification tasks.\n- Following the above work, this work should also compare against subsampling baselines (SUBG/SUBY).\n- The results are often not presented in the clearest way (elaborated in more detail below).\n- In general, it is unclear to me whether this paper thinks RS or IRS should be the main method (there is also a discussion of ARS in the appendix, which seems to have very strong results but confusingly was not even discussed in the main text). It seems that IRS does have strong results on Waterbirds and should be highlighted more - in fact, I would suggest adding IRS to figure 2 and presenting all results (tables 1 & 2) with both RS and IRS. (As a side note, it is also unclear why IRS was not evaluated on GDRO/JTT etc in table 3). This point may seem small, but it has a significant impact on how the results are interpreted overall.", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "4: The contributions are significant, and do not exist in prior works."}, "extra_text": {}}, {"review_id": "qz9w9SBRfy", "reviewer": "Reviewer_yYTs", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "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": "", "main_review": "", "summary_of_the_paper": "This paper suggests rescaling the output probability to achieve group robustness. The idea is to find the scale factor using the unbiased validation set to minimize the balanced group accuracy on the validation set. Once the scale factor is found, it is applied during the test as a post-process module to the test prediction. ", "summary_of_the_review": "The paper proposes a simple yet novel technique to post-process the network prediction to achieve group robustness. The method is well-motivated and experiments are conducted to validate its effectiveness.  ", "strength_and_weaknesses": "Strength:\n- The proposed method is simple yet very effective and can be easily added to previous methods. \n- The paper proposes a new metric to both evaluate average accuracy and worst-group accuracy. \n\nWeakness:\n- It is clear to me that the proposed method is able to maximize the robust accuracy, it remains unclear to me why it can achieve better balance between robust accuracy and worst-group accuracy than the other methods. \n- The method may heavily rely on the validation set to work and requires access to the group information of the validation set which sometimes is not necessarily available. \n- The method might also need a large validation set to work as the validation set is used to estimate the scaling factor and the centroid. It would be nice if an ablation study can be performed for different sizes of the validation set. \n\n\nQuestion:\n- Wondering instead of searching the scaling factor, can it be learned?\n- does adding a bias factor be more effective than scaling factor along? ", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}, {"review_id": "k-nw0Dutha", "reviewer": "Reviewer_2hCQ", "summary": "", "questions": "", "limitations": "", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "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": "", "main_review": "", "summary_of_the_paper": "The paper proposes a test-time rescaling strategy to address the trade-off between worse-case and average accuracy. The rescaling coefficient is optimized on a validation set to maximize a certain objective function, e.g., the worse-group accuracy. With different rescaling coefficients, the method is claimed to find a Pareto frontier of the two objectives (worse-case and average accuracy). The proposed method is compared with different baselines in the experiment and is shown to be effective on two datasets.", "summary_of_the_review": "Given the weaknesses, I would like to give a conservative score and encourage the author to do a more rigourous experiment in the next version to show the real effect of robust scaling. Otherwise, I cannot agree with the argument that class-specific scaling is ALL you need. ", "strength_and_weaknesses": "Strength:\nThe paper is clearly written and the proposed method is straightforward. The experiment looks extensive. \n\n\nWeaknesses:\n\nThe reported baselines in this paper are not consistent with their official results. For example, GroupDRO has 93.5% average accuracy and 91.4% worse-case accuracy with ResNet50, but this paper's Table 2 reports a much lower accuracy for GroupDRO with ResNet18. The result of JTT has the same concern. So I cannot say the experiment is convincing to me.  Please show the experiment using the same backbone with baselines. \n\nOnly two binary classification datasets are used in the main experiment. It will be more convincing if the method works in more challenging tasks like CivilComments, WildCam or FMoW in WILDS benchmark, which contain more classes and groups. The FairFace with 9 classes are used to show the scalability of robust rescaling, but not compared with any baselines. I would like to see a fair comparison with existing baselines on more challenging and real-world datasets.\n\nThe title has a very strong statement that class-specific scaling is all you need, which is not supported by the experiment as least for me.", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}, {"review_id": "C4jFlEKMN0", "reviewer": "Reviewer_TDJz", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "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": "", "main_review": "", "summary_of_the_paper": "This paper proposes a rescaling-based postprocessing method that is applied to the output of any machine learning model with the goal of making the predictions more robust. They conduct experiments comparing the proposed method used to postprocess the outputs of several existing robust learning techniques, along with an ERM baseline, on two standard robustness datasets (CelebA, Waterbirds).", "summary_of_the_review": "I have several concerns with the paper. In addition to the proposed method being neither well-motivated nor well-described, the experimental results also show only very small improvements (in most cases, within the realm of statistical variation) and over baselines that appear not to be tuned at all and perform far below the original published results of the baseline works. I think it is not ready for publication in its current form. ", "strength_and_weaknesses": "\n## Major comments\n\n* The paper lacks any motivation for the proposed method. While of course robustness is a worthy goal, why *rescaling* would be a useful or appropriate technique to advance the community toward this goal is not obvious -- and there is no discussion in the paper for why either.\n\n* The method is not well-described. The equation (3) does not fully define the problem being solved. For example, what is really meany be a \"scaling coefficient vector\" -- does it need to have unit norm? Why do we take arg max in (3)? What are the practical implications of using this method? There is no discussion of this in the paper; lacking any theoretical results, there should be strong empirical or intuitive support for why this is a reasonable postprocessing choice.\n\n* The implementations of \"baseline\" or prior works are not faithful, and report much lower numbers than those works on the same datasets. For example, JTT reports much higher worst-group and average accuracies on Waterbirds (Table9 listd their best as 88.6% and 93.1% in Table 9, see also Table 7,8; these are lower than in the current paper Table 2) and Group DRO reports mich higher Waterbirds worst-group and average accuracies in Table 3. I am concerned that this is due to poor hyperparameter tuning or model architecture selection; the approach to tuning is not described at all in the paper so it is difficult to tell (if no tuning were performed, this would also be a concern).\n\n* The empirical results are weak. For example, only 4/18 comparisons in Table 2 show an improvement greater than two standard deviations, and only one of the eight comparisons on Table 3 (for the blue \"target metric that robust scaling aims to maximize\" columns) is greater than two standard deviations.\n\n* Small contribution - beyond the rescaling method, the proposed metric is not a standalone contribution. I think the metric is lacking a thorough discussion or motivation.\n\n# Minor comments\n\n* Figure 1 needs more detail. What dataset/task is this? Are the different points different initializations, hyperparameter configurations? There is very weak evidence of a tradeoff here, but the details are far too murky to draw much of a conclusion; if there were not lines drawn on the graphs I would not conclude there was any relationship.\n\n* Figure 2 also doesn't describe (a) the dataset/task, or (b) what models are used for each method, how they were selected, or give any notion of variability (i.e. Clopper-Pearson confidence intervals). Again, it is hard to learn much without this information.\n\n* It seems Figure 3 is missing any reference to a baseline; can this comparison be made e.g. to ERM? Also, how are we supposed to conclude that any other scaling (s \\neq 1) is an improvement based on this plot?\n\n* Other hyperparameters also seem to be selected in an ad hoc manner. Why is k=20 chosen? How does varying the number of clusters impact the experimental results?\n\n# Typos etc.\n\nPage 2: Footnote 1 should probably be in main text.\n\nPage 4: \"given n training examples without group annotations\" --> without *attribute* annotations (since group is attribute + label)", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "2: Several of the paper’s claims are incorrect or not well-supported.", "technical_novelty_and_significance": "1: The contributions are neither significant nor novel.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}]

Author rebuttal:

Decision: Reject