Hyper-parameter Tuning for Fair Classification without Sensitive Attribute Access
Authors: Akshaj Kumar Veldanda
Ivan Brugere
Sanghamitra Dutta
Alan Mishler
Siddharth Garg
Venue: Submitted to ICLR 2023 (2023)

Abstract: Fair machine learning methods seek to train models that balance model performance across demographic subgroups defined over sensitive attributes like race and gender. Although sensitive attributes are typically assumed to be known during training, they may not be available in practice due to privacy and other logistical concerns. Recent work has sought to train fair models without sensitive attributes on training data. However, these methods need extensive hyper-parameter tuning to achieve good results, and hence assume that sensitive attributes are known on validation data. However, this assumption too might not be practical. Here, we propose a framework to train fair classifiers without access to sensitive attributes on either training or validation data. Instead, we generate pseudo sensitive attributes on the validation data by training a biased classifier and using the classifier’s incorrectly (correctly) labeled examples as proxies for minority (majority) groups. Since fairness metrics like demographic parity, equal opportunity and subgroup accuracy can be estimated to within a proportionality constant even with noisy sensitive attribute information, we show theoretically and empirically that these proxy labels can be used to maximize fairness under average accuracy constraints. Key to our results is a principled approach to select the hyper-parameters of the biased classifier in a completely unsupervised fashion (meaning without access to ground truth sensitive attributes) that minimizes the gap between fairness estimated using noisy versus ground-truth sensitive labels.

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HYPER-PARAMETER TUNING FOR FAIR CLASSIFICA- TION WITHOUT SNSSTIVVE ATTRIBUTE ACCESS
Anonymous authors Paper under double-blind review
ABSTRACT
Fair machine learning methods seek to train models that balance model perfor- mance across demographic subgroups defined over sensitive attributes like race and gender. Although sensitive attributes are typically assumed to be known dur- ing training, they may not be available in practice due to privacy and other logis- tical concerns. Recent work has sought to train fair models without sensitive at- tributes on training data. However, these methods need extensive hyper- parameter tuning to achieve good results, and hence assume that sensitive attributes are known on validation data. However, this assumption too might not be practical. Here, we propose Antigone, a framework to train fair classifiers without access sensitive attributes either training validation data. Instead, we generate pscudo sensitive attributes on the validation data by training a biased classifier and using the classifier's incorrectly (correctly) labeled examples as proxies for minority (majority) groups. Since fairness metrics like demographic parity, equal opportunity and subgroup accuracy can be estimated within a proportionality constant even with noisy sensitive attribute information, we show theoretically and empirically that these proxy labels can be used to maximize fairness under average accuracy constraints. Key to our results is a principled approach to select the hyper-parameters of the biased classifier a completely unsupervised fashion (meaning without access to ground truth sensitive attributes) that minimizes the gap between fairness estimated using noisy versus ground-truth sensitive labels.
INTRODUCTION
Deep neural networks have achieved sfate-of-the-art accuracy on many tasks including face recog-
nition (Buolamwini & Gebru 2018 Grother et al., 2010) Ngan & Grother] 2015). autonomous driving (Zhang et al.] [202]] | Chitta et al. 2021). medical image diagnosis (Litjens et al. [017 Chep- Chep-
lygina et al.] 2019), etc. But, prior work (Hovy & Søgaard 2015 Oren et al. 2019 Hashimoto et al.)
2018ah has found that state-of-the-art networks exhibit unintended biases towards specific popula- tion groups, especially harming minority groups. Seminal work by [Buolamwini & Gebru (2018)
demonstrated, for instance, that commercial face recognition systems had lower accuracy on darker skinned women than other groups. A body of work has sought to design fair machine learning al- gorithms that account for a model's performance on per-group basis (Prost et al. 2019 Sagawa*
al. 2020 Liu et al. 2021 Sohoni et al. 2020).
Much of the prior work assume that demographic attributes like gender and race on which we seek train fair model, which we refer to as sensitive attributes, are available on training and validation data Saaawaa et al. (2020); Prost et al.] (2019). However, there is a growing body of literature (Veale & Binns [001]] Holstein et al. 2019) highlighting many real-world settings in which sensitive attributes may not be available. This is for multiple reasons. For example, the data subject may abstain from providing sensitive information to eschew potential discrimination
which the model discriminates might not even be known (Citron & Pasquale 2014, Pasquale| 2015). For instance, in algorithmic hiring decisions, Köchling & Wehner (2020) highlight that bias and discrimination are recognized only after making real world decisions on applicants due to unknown attributes on which the model discriminates during training. Consequently, a large American e- e-commerce company had to cease using algorithmic tools for hiring purposes as it was unintentionally discriminating female appli- cants (Dastin 2018
in future (Markos et al., (017). In other settings, the attributes

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Recent work seeks to train fair classifiers without access to sensitive attributes on the training set (Luu et al. 2021 Creager et al. 2021; Nam et al. 2020 Hashimoto et al.) 2018a). The common theme across these methods is to up- weight misclassified examples either by splitting the training stage into
two separate stages Liu et al. (02T) (identify mis-classified examples in stage and upweight in stage 2) or by alternating between these stages across training epochs Nam et (2020) (identifying misclassified examples in one epoch and upweighting in the next). However, Liu et al.] (2021) has shown that these methods are highly sensitive to choice of hyper-parameters: the up-weighting factor, for example, can have a large impact on the resulting model's fairness. Some methods, therefore, tune nyper-parameters assuming access sensitive information on the validation dataset. In fact, without this information, [iu et al. (2021) observed that these methods sometimes do worse than using standard ERM. But, sensitive information on the validation dataset may not available for the same reasons they are hard to acquire on training data.
In this paper, we propose Antigone, simple, principled approach that enables hyper-panee prrammprr tuning for fairness without access to sensitive attributes on validation data. Antigone can be used to tune hlper-parametert for any prior method, for instance, JTT (Liu et al., 202T). LIF (Nam et al. 2020), CVaR DRO (Hashimoto et al., 8a), that trains fair models without sensitive attributes on training data, and for several fairness metrics including demographic parity, equal opportunity and worst sub-group accuracy. We note that these prior methods also address the problem of spurious correlations (Sagawa et al., 2020) Wang & Culotta 202T) and their impact on accuracy. As such, Antigone can also be used address spurious correlations, but we focus on fairness in this paper.
Antigone builds on the same intuition as in prior work: mis-classified examples of a classifier trained with standard empirical risk serves as an effective proxy for minority groups. Accordingly, Antigone trains a biased classifier as a noisy sensitive attributes labeller on the validation data, labelling cor- rectly and incorrectly classified examples as majority and minority groups, respectively. But this raises a key question: how do we select the
of the noisy labeler?
Intuitively, maximize utility of the noisily labelled validation set, we seek to maximize the frac- tion of minority (majority) samples in the incorrect (correct) sets. Since this cannot be measured directly, Antigone instead maximizes the distance between the data distributions of the two sets, which we measure using the Euclidean distance between the means (EDM) of the two distribu- tions. We provide theoretical justification for our choice under the mutually contaminated (MC) noise model (Scott et al. 2013) that assumes that fraction of majority (minority) group labels are contaminated with labels from minority (majority) group. Lamy et al. (2019) et al. show that com- mon fairness metries can be estimated up proportionality constant under the MC model. We show that Antigone's 's EDM criteria maximizes this proportionality constant, thus providing the most reliable estimates of fairness.
We evaluate Antigone in conjunction with Liu al. (2021) on the CelebA, Waterbirds and Adult datasets which are commonly used in faimess literature. We compare Antigone with baselines that assume ground-truth knowledge of sensitive attributes and standard ERM on demographic parity, equal opportunity, and worst subgroup accuracy. Antigone significantly closes the fairness gap between standard ERM training and fairness with ground truth sensitive attributes. Compared with GEORGE that estimates majority/minority group labels by clustering the activations of an ERM model, Antigone produces more accurate labels and results in improved fairness. Ablation studies demonstrate the effectiveness of Antigone's EDM based seper-paramett tuning.
2
PROPOSED METHODOLOGY
We now describe Antigone, starting with the problem formulation (Section followed by de- scription of the Antigone algorithm (Section 2.2
2.1 PROBLEM SETUP
Consider a data distribution over set D = X' x X y, the product of input data (2²), sensitive
attributes (A) and target labels ()) triplets. We are given training set D {x*",a aa"" vf" Her with R training samples, and a validation set D = {agaa apal yf " samples. We will assume binary sensitive attributes (AA (0. 1}) and target labels ()' e {0, 1)). We note that for now Antigone is limited to binary sensitive attributes, but can be extended to multiple target labels.
Nest with Nreat validation
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We seek to train machine learning model, say deep neural network (DNNN, which can be repre- sented as a parameterized function fo : - + E {0,1}, where 8 E θ are the trainable parameters, e.g,, DNN weights and biases. Standard fairness unaware empirical risk minimization (ERM) opti- mizes over trainable parameters 0 to minimize average loss LERAS:
LERM
N
on Der where (z, y1) is the binary cross-entropy loss.
Optimized model parameters O are obtained by invoking a training algorithm, for instance stochas- tic gradient descent (SGD), the training dataset and model, i.e., 0 MERM (D fo, 7), where y E 2 are hyper-panee paramettes of the training algorithm including learning rate, training epochs etc. sapperpparaeeter
tuned by evaluating models fe-.x for all y I D and picking the best model. More sophisticated algorithms like Bayesian optimization can also be used.
Since standard ERM models suffer from unintended biases in their predictions, fair ML algorithms seek instead to optimize metrics that explicitly account for the performance on demographic sub- groups. We review three commonly used metries below:
Demographic parity (DP): DP requires the model's outcomes to be independent of sensi- tive attribute. In practice, we seek to minimize the demographic parity gap:
A DP [P (x())= = 1|A = 1] P[f = 1|A = 0))
(2)
Equal opportunity (EO)): EO aims to equalize only the model's 's true positive rates across sensitive attributes. In practice, we seek to minimize
A5 = (())(X) = 1|A 1,Y = ( = 1 =, 0, = =].
(3)
Worst-group accuracy (WGA)) WGA seeks to maximize the minimum accuracy over all sub- sub-groups over sensitive attributes and target labels. That is, we seek to maximize: min WGAp (E.0
P(f(2) y A a, Y v).
In all three settings, we seek to train models that optimize fairness under a constraint on average accuracy. For example, for equal opportunity, we seek 8 arg minøee A such that (z) Y| 2 Acc, where Acc is a user specified constraint. With access to sensitive attributes, the fairness metric (and average accuracy) be evaluated on the validation set. The challenge here is that sensitive attributes are unavailable.
2.2 ANTIGONE ALGORITIIM
We describe the Antigone algorithm which consists of three main steps. In step train multiple intentionally biased ERM models that each provide pseudo sensitive attribute labels on validation data. We view each model noisy sensitive attribute labeller on the validation set. In step 2, we use the proposed EDM metric to pick a noisy labeller from step with the least noise. Finally, in step we use the labelled validation from step to tune the hyper- paremerrrssssrss of methods like JTT that train fair classifiers without sensitive attributes on training data.
Step 1: Generating sensitive attribute labels validation set. In step 1, we use the training dataset and standard ERM training to obtain a set of classifiers, 0*:2 = MERM f), each corresponding to different value of training hyper-parameterrs 7 As we discuss in Section 2.1 these include learning rate, weight decay and number of training epochs. Each classifier is used to generate pseudo sensitive attribute labels on the validation set by assigning correctly (incorrectly) classified examples to the majority (minority) groups. That is, each classifier yields a validation set Neal Jizl
Dval {azaaa ,a, mai,y y.
V
(5)
where:
mal, [1, if Sa (x.al) ya
a, (0 otherwise.
(6)
From these noisily labelled validation sets, now seek to pick the whose pseudo sensitive attribute labels match most closely with true (but unknown) sensitive attributes. That is, we seek to pick the pareee-prraetter corresponding to the "best" noisy labeller.
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Step 2: Picking the best noisy labeller. The noisy labellers in Step 1 partition inputs in the validation set into two sets containing correctly and incorreetly classified inputs. These serve as proxies for majority and minority groups, respectively. Specifically, let the correct set (or noisily labeled set of majority examples) be X pai,7 Aml,nnisy {s.aal a val,y 1} and the incorrect set (or val.y = 0}.
noisily labeled set of minority examples) be X X
{x.all a;
A=D,noiey
To estimate fairness accurately, we would like our noisy labeler to be biased, i.e., to place all majority (minority) group inputs the correct (incorrect) set. In the absence of true sensitive attribute labels, we can measure bias using the distance between the data distributions in the correct and incorrect sets. In Antigone, we pick the simplest distance metric between two distributions, i.c., the Euclidean distance between their means (EDM). Formally,
EDM = (X val.a
val.y A=l,noiay) xxX X 112
where ja()) represents the empirical mean of dataset. In Section 2.3 we theoretically justify this choice. We pick 7- = arg max EDM". Note that in practice we pick two different noisy labellers corresponding to target labels = 10.
Step 3: Training a fair model. Step 2 yields Dval,"", a validation dataset with (estimated) sen- sitive attribute labels. We can provide D as an input to any method that trains fair models without access to sensitive attributes training data, but requires a validation attribute labels to tune its own hyper-parameters. In our experimental results.
D to
tune the hyper-parameters of JTT (Liu et al. (021) and GEORGE (Sohoni et al. (2020). We note that GEORGE proposes its method to obtain sensitive attributes labels on validation data, but replacing it with Antigone improves on GEORGE's performance.
2.3 ANALYZING ANTIGONE UNDER MC NOISE
Prior work Lamy et al. 2019) has modeled noisy sensitive attributes using the mutually contami- nated (MC) noise model Scott al. (201)). Here, is assumed that have access to noisy datasets, noiey and Dois, corresponding to minority and majority groups, respectively, that are mixtures of their ground-truie -ruth datasets Do and D, Specifically,
D==lmoiss aa) + ADD
(8)
noidy = 3D + (1-33)DA- A=D
where and 3 are noise parameters. Note that strictly speaking Equation InquationSSshuulle Ishoull refer to the prob- ability distributions of the respective datasets, but we will abuse this notation to refer to the datasets themselves. As such Equation says that fraction of the noisy majority group. Do=i.noisyr contaminated with data from the minority group, and fraction 8 of the noisy minority group, D D==0,noisp noisy. is contaminated with data from the majority group. An extension of this model as- sumes that the noise parameters are target label dependent, i.e., (00.30) for Y = and (01,31) 31) for ==
Note that the MC model assumes that noisy datasets are constructed by sampling independently from the ground-truth distributions. While this is not strictly true in our case since the noise in our sensitive attribute labels might be instance dependent, the MC model can still shed light on the design of Antigone.
Proposition (Lamy al. 2019) Under the MC noise model in Equation demographic parity and equal opportunity gaps measured on the noisy datsets are proportional to the true DP and EO gaps. Mathematically:
A DP (DA=0,noisy U DA=1,noisy) = (1- a DDA=D(DADD DA=1);
and
FO (D O.noisy U D AmmL,,nn))))) = 11-a1- - -1)A R0 (D UD
(10)
From Equation 9 and Equation 10 we can conclude that under the MC noise model, the DP and
EO gaps can be equivalently minimized using noisy sensitive attribute labels, assuming independent
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Moan Image
Men
Women
ColebA
Ground-Truth Blond (Correct Set)
Validation Data
114
2770
Blond
Non- Bon-Bllon
Predicted Blond
Pseudo Majority Labels
Ground-Truth Non Blond (Incorrect Set)
182
1077
Men
Women
(2874)
(8276)
Ground-Trud Trunh Non Blond (Corret Set)
8094
7458
Predicted Non-blond
Pseudo Minority Labela
Mon
Women (8535)
Biased Classifir
Ground-Truth Blond (Incorrect
(182)
Figure I: Figure illustrates the schematic of Antigone generating pseudo sensitive attributes on CelebA validation data by training a biased classifier and using the classifier's incorrectly (correctly) labeled examples as proxies for minority (majority) groups.
contamination and infinite validation data samples. In practice, these assumptions do not hold, however, and therefore seek maximize the proportionality constant 1 3 (or 1 31) to minimize the gap between the true and estimated fairnsss values.
Lemma Assume X n and A=m.mois correspond to the input data of noisy datasets in the MC model. Then, maximizing the EDM between the X Ammonn and X Am m,nispp i.e., (In(X (u((X== (.miin - ((( mooissy)) maximizes 1
Proof. From Equation we can see that |I A=U,noisy) - (((A=1nnnisy))) = (1 3){1)((XA=o)) (x(x A=1)l2- Here (]ı(( - ((xA= (AA=))lle is the EDM between the ground truth majority and minority data and is therefore a constant. Hence, maximizing EDM between X noiey and A= maximizes aa ---a B.
In practice we separately maximize EDM for target labels Y 10 and hence maximize both Ogg 3o and 1 01 31. We note that our theoretical justification motivates the use of EDM for DP and EO fairness. While not exact, minimizing + 3 using EDM proxy is still helpful for WGA because it reduces contamination and, empirically, provides more reliable estimates for sub-grou uub-group accuracy.
EXPERIMENTAL SETUP
We empirically evaluate Antigone the CelebA, Waterbirds and UCI Adult datasets which have been extensively studied fairness literature. In this section, we present the details about Antigone's 's implementation, evaluation and network architecture used for these three datasets. To begin, note Antigone can be deployed in conjunction with any method that trains fair classifiers without sensitive attributes on training data. We evaluate Antigone with one such state-of-the-art method, JTT (Liu et al. 2021) We begin by briefly describing how Antigone is deployed in conjunction with JTT.
JTT Antigone: JTT operates in two stages. In the first stage, a biased model is trained using T epochs of standard ERM training identify the incorrectly classified training examples. In the second stage, the misclassified examples are upsampled times and the model is trained again to completion with standard ERM. The hyperparameters of stage I and stage 2 classifiers, including early stopping epoch T' and upsampling factor X, are jointly tuned using a validation dataset with ground-truth sensitive attribute labels. We replace the ground-truth validation dataset with noisy sensitive attributes obtained from Antigone.
3.1 CELEBA DATASET
Dataset details: CelebA (Liu et al. 2015) is image dataset, consisting of 202.599 celebrity face images annotated with 40 attributes including gender, hair colour, age, smiling, etc. The task is to predict hair color, which is either blond y 1 or non-blond Y = 0 and the sensitive attribute is

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gender A {Men, Women). The dataset is split into training, validation and test sets with 162770, 19867 and 19962 images, respectively. Only 15% of individuals in the dataset are blond, and only 6% of blond individuals are men. Consequently, the baseline ERM model under-performs the blond men.
Hyper-parameter settings: In all experiments using CelebA dataset, fine-tune a pre- trained ResNet50 architecture for a total of 50 epochs using SGD optimizer and a batch size of 128. We unne Antigone and JTT over three pairs of learning rates and weight decays, (le 04, le 04), (le - 04, le 02), (le 05, le - -1), which are also the values used in JTT. For Antigone, we also explore early stopping at any of the 50 training epochs. Antigone's nyper-parameters are tuned using the EDM approach. 21,2,5, 10, 15, 20, 25, 30,35, 40, 45, 50} and À (20, 50, 100} as reported in their paper. JTT's hyper-parameters are tuned using the validation dataset produced by Antigone. We report results for DP, EO and WGA fairness metries. each case, we seek to optimize fairness while constraining average accuracy ranges {[90, 91), [91, 92), [92, 93), [93, 94), [94, 95)}.
For JTT, we explore over T
3.2 WATERBIRDS DATASET
Dataset details: Waterbirds a synthetically generated dataset, containing 1 11,788 images of water and land birds overlaid top of either water or land backgrounds (Sagawa* al., 2020 The task is to predict the bird type, which is either a waterbird = 1 or a landbird Y O and the sensitive attribute is the background A (Water background, Land background). The dataset is split into training, validation and test sets with 4795, 1199 and 5794 images, respectively. While the validation and test sets are balanced within each target class, the training set contains majority of waterbirds (landbirds) in water (land) backgrounds and minority of waterbirds (landbirds) on land (water) backgrounds. Thus, the baseline ERM model under-performs on the minority group.
Hyper-parameter settings: In all our experiments using Waterbirds dataset, we train a pre- trained ResNet50 architecture for a total of 300 epoch using the SGD optimizer and a batch size of 64. We tune Antigone and JTT over three pairs of learning rates and weight decays, (le - 03, 1e - 04), (le 04, le 01), (le 05, 1.0). which are also the values used in JTT. For JTT, explore over T {25, 40, 50, 60, 75, 100, 125, 150, 175, 200, 225, 250, 275, 300} and E {20, 50, 100} as reported their paper. each case, we seek to optimize fairness while constraining average accuracy ranges [194, 94.5), (94.5, 95), (95, 95.5), (95.5, 96), [96, 96.)).
3.3 BASELINES FOR COMPARISONS
We evaluate Antionge against several baselines.
Standard ERM: A naive baseline standard ERM model that only seeks maximize average accuracy and does not consider faimess. We train standard ERM models using the same network architectures and training pypee-parameters used for Antigone + JTT as reported above.
JTT + Ground-truth sensitive attributes: An upper bound for UTT+Atigonee is a JTT model trained with ground-truth sensitive attributes on validation data, i.e., the overall approach used in JTT. For this, we used the reference implementations provided by JTT.
GEORGE Sohoni et al. 2020); GEORGE competing approach Antigone that does not assume access to sensitive attributes on either training or validation data. GEORGE operates in two stages: stage an ERM model is trained until completion on the ground-truth target labels. The activation in the penultimate layer of the FRM model are clustered into k clusters to generate pseudo sensitive attributes on both the training and validation datasets. These pscudo sensitive attributes are used to train and tune the hyper-parametert of a Group DRO model model Sagawa* et al. (2020).
For fair comparison with GEORGE, we replace its stage with Antigone, and use the resulting pseudo sensitive attribute labels to tune the hyper- of Group DRO model Sagawa* et al. 2020). We refer to this approach as GEORGE+Antigone.
4 EXPERIMENTAL RESULTS
We now discuss the results of our empirical evaluations. We begin by analyzing the quality of sensitive attribute labels produced by Antigone and evaluate JTTGGEORGE+Antigoee

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Women
Men
Waterbkgd
Landbkgd
Waterbirds Dataset: Waterbirds Class
Waterbirds
Blond
DAL AY
0.8
0.6
47%
47%
Non- -B---doddd
Landbirds
MysteeSpoto Aone May. Aup
h
16
26%
24%
2%
48%
CelebA Dataset
Waterbirds Dataset
50
100
150
200
250
300
(a) Dataset Details
(b) EDM and noise parameters on Waterbirds
Figure 2: Figure (a) illustrates CelebA and Waterbirds datasets along with fraction of each sub-group examples in their respective training dataset. Figure (b) shows Euclidean Distance between Means (EDM) and noise parameters (a1, 91 and 1 - a 31) for the positive target class of Waterbirds dataset. The noise parameters are unknown in practice. Blue dot indicates the model that we pick to generate pseudo sensitive attributes, while black star indicates the model that maximizes 1-a --1-
Quality of Antigone's sensitive attribute labels: Antigone seeks to generate ac- curate sensitive attribute labels on vali- dation data based on the EDM criterion (Lemma M. In Figure [ we empiri- cally validate Lemma by plotting EDM and noise parameters da (contamination minority group labels), 81 (contamination in minority group labels) and 1 - 01 81 (proportionality constant between true and estimated fairness) on Waterbirds dataset (similar plot for CelebA dataset is Ap- pendix Figure 3). As per Lemma 1 EDM allows us to maximize is ideally proportional to this value. From the figure, we observe that in both cases the EDM metric indeed captures the trend in 01 31, enabling early stopping at an epoch that minimizes contamination.
Table 1: FI Scores and Accuracy of the pseudo sensitive attribute labels generated by Antigone (w/o EDM), GEORGE, GEORGE with k 2 clusters and Antigone (w/ EDM) on CelebA and Waterbirds datasets. Bold indicates higher FI Scores/Accuracy across different methods. For CelebA, BM, BW, NBW and NBM refer to Blond Men, Blond Women, Non- blond Women and Non-blond Men, respectively. For Waterbirds, WL. WW, LW and LL refer waterbirds landbkgd, waterbirds waterbkgd, landbirds waterbkgd and landbirds landbkgd, respectively.
Antigone (w/o EDM)
GEORGE
GEORGE 2)
Antigone (w/ EDM)
01 31 since it
CelebA (FI Scores)
BM
0.28 1 0.01
4: 0.02
0.01
0.04
BW
0.95 1 0.01
0.43 0.04
0.51 0.02
0.96 1 0.00
NBW
0.22
1 0.02
0,42 : 0.01
0.6 : 0.01
0.22 : 0.01
NBM
0.67 + 0.01
0.4 0.02
0.31 + 0.01
0.68 + 0.01
Acc.
0.59 + 0.01
0.33 + 0.01
0.48 + 0.00
0.60 + 0.00
The early stopping points based on EDM and oracular knowledge of a 31 are shown in a blue dot and star, respectively. For Waterbirds these are very close.
Waterbirds (FI Scores)
WL
0.41 + 0.02
0.43 + 0.02
0.52 1::::0000 0.01
0.76 + 0.03
WW
0.72
1 0.00
0.36 0.02
0.43 1: 0.02
0.83 +: 0.01
LW
0.58
: 0.02
0.44
0.55 : 0.03
0.04
LL
0.76 4 0.01
0.34 0.02
0.55 0.03
0.84
0.02
Next, we evaluate the Fl scores of Antigone's noisy sensitive attributes for all four subgroups in the CelebA and Water-
Acc.
0.68 1 0.01
0.30 0.02
0.53 0.03
0.81 + 0.02
birds datasets. In Table we compare Antigone's F1 Score to GEORGE with the baseline number of clusters and GEORGE with & = 2 clusters. Across CelebA and Waterbirds datasets and all four subgroups, we find that Antigone outperforms GEORGE except for one sub-group CelebA dataset. In the Appendix Table 4 we also include precision and recall values and reach similar con- clusion. Additionally, we note that the pscudo label generated by Antigone are 1.25 and 1.5 times more accurate than GEORGE's pseudo labels CelebA and Waterbirds datasets, respectively.
To understand the benefits of the proposed EDM metric, we implement a version of Antigone but tune byper-parameters using standard ERM. We refer to this Antigone (w/o EDM) and find in Table I that Antigone with EDM outperforms the version without EDM. We later report on the fairness achieved by these different versions.
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Table 2: (Avg. Accuracy, Fairness) on test data for different validation accuracy thresholds on the CelebA dataset. Lower DP and EO gaps are better. Higher WGA is better.
Val. Thresh.
Method
DP Gap
EO Gap
Worst-group Acc.
Antigone + JTT
(94.6, 15.0) = (0.2, 0.7)
(94.7. 30.1) + (0.2, 3.2)
(94.4, 59) (0.2, 4.7)
[94, 95)
Ground-Truth + JTT
(94.7, 14.9) = (0.2. 0.6)
30.45, (0.2. 2.3)
(94.3, 62.1) + (0.3, 3.2)
Antigone + JTT
(93.7, 13.1) 1 0..2.0.7)
(93.6, 26.4) 1 (0.4, 5.0)
(93.4, 62.6) 1 (0.2, 7.0)
[93, 94)
Ground-Truth + JTT
(93.6, 13.1) (0.1.0.)
(93.6, (2.7) (0.3, 2.7)
(93.4, 67.9) + (0.1, 1.9)
Antigone + JTT
(92.7, (92.7,11.1) = 0.5)
(92.3, 20.2) + (0.2,
(92.7, 68.1) + (0.4, 3.7)
[92, 93)
Ground-Truth + JTT
(92.7. (1.2) = 0..3.
(92.7, 16.9) (0.4,
(92.7. 72.5) + (0.2. 1.3)
Antigone + .TTT
(91.7,9.6 + 0.5)
(9.55 16.3) (0.3,3.4)
(91.3, 63.2) + (0.3, 2.6)
[91. 92)
Ground-Truth + JTT
(91.8. 9.7) # 0.5).
(918,, 10.1) (0.3.4.1)
(91.8, 77.3) = (..1.
Antigone JTT
(91.0, 8.3) (0.2. 0.4) (91.0, 8.4) + (0.2,
(90.9, 13.1) 3.61, (90.7, 6.8) - (0.4,
(90.9, 63.1) (0.5, (91.4, 78.6) + (0.2, 2.0)
(90, 91)
Ground-Truth + JTT
ERM
(95.8, 18.6) 1 (0.0, 0.3)
(95.8, 46.4) (0.0, 2.2)
(95.8, 38.7) (0.0, 2.8)
Antigone + JTT: Next, in Table 2 compare the test accuracy and faimess achieved by Antigone with JTT (Antigone+ JTT) versus a baseline ERM model and with JTT using ground -oouhd-truth sensitive attributes (Ground-Truthen Truth+JTT), As expected, baseline ERM yields unfair outcomes on all three fairness metries: DP, EO and WGA. We observe that Antigone + JTT improves fairness over the baseline ERM model and closes the gap with
On DP, Antigone JTT is very close to Ground Truth JTT results. Antigone JTT substantially improve upon the EO Gap achieved by standard ERM. Antigone JTT improves WGA from 38.7% using standard ERM to 68. 1% at the expense of 3% accuracy drop. Ground-Truth + JTT improves WGA further up 78.6% but with larger average accuracy drop. Antigone + JTT achieves highest fairness for relatively high average accuracy values, although one would expect fairness to reduce with higher average accuracy. We believe this in part due to the noise in sensitive attribute labels that Antigone generates. Data for Adults (shown in the Appendix Table 8) and Waterbirds (shown in the Appendix Table 6 have the same trends.
with GEORGE: Like Antigone, GEORGE also generates pseudo-sensitive attributes on validation data, but as we noted in Table D Antigone's labels are more accurate and have higher Fl scores for different sub-groups.
Comparison
Table 3: Performance of GEORGE using Antigone's noisy valida- tion data compared with GEORGE by itself. We observe that on CelebA and Waterbirds dataset, GEORGE + Antigone out-performs GEORGE, even if GEORGE assumes knowledge of number of clus- ters (k- 2) in its clustering step. We show errors for over five runs.
CelebA
Waterbirds
Method
Avg Ace
WGA
Avg Ace
WGA
We now compare the faireess in terms of WGA achieved by GEORGE versus Antigone +GEORGE in which we use Antigone's 's labeled validation data to tune GEORGE's training algorithm. Antigone GEORGE is more fair than GEORGE alone on CelebA and Waterbirds (Table 3). On CelebA, Antigone GEORGE has a small drop in average accuracy compared GEORGE, while on Waterbirds, both average accuracy and fairness are better. In interpreting the errors on Waterbirds dataset, we should note that Antigone GEORGE's WGA is atleast 8.4% higher than GEORGE's in each one of our multiple runs, except in one run where GEORGE has 1 1% higher WGA compared to Antigone + GEORGE, whereas on CelebA, Antigone + GEORGE'S WGA was equal to or better than GEORGE's in each one of our multiple runs. Similar trend holds for Antigone GEORGE (k = 2) and GEORGE (k- = 2).
ERM
95.7 0.1
34.5 = 3.1
95.9 + 0.2
29.7 1.6
GEORGE
93.6
60.4 2.3
95.5 0.7
50.0 5.8
Antigone GEORGR
93.3 + 0.3
62.1 + 1.2
96.0 + 0.2
57.4 + 6.6
GEORGE (k=2)
9.1
62.6 2.1
95.0
46.7 1: 11.7
Antigone + GEORGE (k=2)
0.3
65.3 2.9
95.8
54.4 = 7.1
Impact of EDM metric on fairness: We already noted in Table Antigone with the proposed EDM metric produces higher quality sensitive attribute labels compared to a version of Antigone that picks perameess using standard ERM. We evaluated these two approaches using JTT's training algorithm and find that Antigone with EDM results in a 5.7% increase in WGA and a small 0.06% increase in average accuracy.
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5 RELATED WORKS
Several works have observed that standard ERM training algorithms can achieve state-of-the-art accuracy on many tasks, but unintentionally make biased predictions for different sensitive attributes failing to meet the fairness objectives (Hovy & Søgaard 2015 Oren et al. 2019 Hashimoto et al.)
2018a
Buolamwini & Gebru 2018).
Fairness objectives can be broadly categorized into two types: individual fairness and group fair- ness. Individual fairness (Dwork et al., 2012 Kusner et al. 2017) requires similar individual to be treated similarly. Whereas, group fairness Prost et al. (2019 Quadriaato et al. (2019); Hardt et al.] (2016) requires the groups of individuals divided based on a sensitive attribute like race, gender, etc., be treated equally. In this paper, we focus on the popular group fairness notions that include Demographic Parity, Equal Opportunity and Worst-group performance.
Methods that seek to achieve group faireess three types: pre- processing, in processing and post- processing algorithms. Pre-processing (Quadrianto et al., 2019. Ryu et al. 2018) methods focus on curating the dataset that includes removal of sensitive information or balancing the datasets. In-processing methods (Hashimoto et al. 2018b Agarwal et al. 2018 Zafar et al. 2019 Lahoti et al. 2020; Prost et al.) [209]]Liu Liu al.) 202 Sohoni al. 2020) alter the training mechanism by using adding fairness constrains to the loss function or by training an adversarial framework to make predictions independent of sensitive attributes Zhang al. (2018). Post-processing methods (Hardt et al. 2016 Wang et al. 22200 Savani et al. 2020) alter the outputs, for e.g. use different threshold for different sensitive attributes. In this work, we focus on nn-prceessing algorithms.
Prior in-processing algorithms, including the ones referenced above, assume access to sensitive attributes on the training data and validation dataset. Recent work sought to train fair model without training data annotations Liu et al. (202T); Nam et al. (2020); Hashimoto et al. (2018a); Creager al. (02T)) but, except for GEORGE (Shoni et al. (2020). require sensitive attributes on validation dataset to tune the hyperparameters. Like GEORGE, we seek to train fair classification models without ground-truth sensitive information on either training or validation dataset.
Antigone is different from GEORGE in three ways: (1) Unlike GEORGE, we account for the model prediction and the ground-trutt target label to generate pseudo-sensitive attributes. (2) The hyper- parameters of the clustering step in GEORGE are fixed from literature and not specifically tuned for each dataset. In this paper, we propose a more principled approach to tune the model's hyperparam- eters in unsupervised fashion to obtain noisy sensitive features. And finally, (3) GEORGE only focuses on worst-group accuracy, whereas Antigone can be adapted to different notions of fairness.
A related body of work develops post-processing methods to improve fairness without access to sensitive attributes but assuming a small set of labelled data for auditing Kim et al. (201)). One could use Antigone create this auditing dataset, albeit with noise. Evaluating Antigone with these post-pree post-processing methods is an important avenue for future work.
6 CONCLUSION
In this paper, we propose Antigone, a method to enable hyper-paramette tuning for fair ML models without access to sensitive attributes on training or validation sets. Antigone generates high-quality pseudo-sensitive attribute labels on validation data by training family of biased classifiers using standard ERM and using correctly (incorrectly) classified examples as proxies for majority (minor- ity) group membership. We propose novel EDM metric based approach to pick the most biased model from this family and provide theoretical justification for this choice using the MC noise model. The resulting validation dataset with pseudo sensitive attribute labels can then be used to tune the parameerrssssrs of fair training algorithm like JTT or GEORGE. We show that Antigone produces the highest precision sensitive attributes compared to the state-of-art. Future work will also seek to address the variance in fairness metrics (Mozannar et al. 2020) introduced by finite sam- ple size under the MC noise model, extend Antigone to multiple-sensite attributes, inter-sectional fairness and active learning of sensitive attributes.
AVAILABILITY
Code with README.1x file is available at: fa i rness_ w www.thtttooodoopohhhhccoooo wttp://raappaaaaaa///aaaa/aaaaaa md

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Under review as a conference paper at ICLR 2023
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A APPENDIX
A.1 UCI ADULT DATASET
Dataset details: Adult dataset (uaa Graff 2017) used to predict if an individual's annual income is S 50K (Y 0) or >> 50K (Y 1) based on several continuous and categorical attributes like the individual's education level, age, gender, occupation, etc. The sensitive attribute gender A = [Men, Women } Zemel et al. (2013). The dataset consists of 45,000 instances and is split into training, validation and test sets with 12, 9049 and 15060 instances, respectively.
Hyper-parameter settings: In all experiments using Adult dataset, train multi-layer neural network with one hidden layer consisting of 64 neurons. We train for a total of 100 epochs using the SGD optimizer and batch size of 256. We tune Antigone and JTT by per- forming grid search over learning rates E {1e 03, le 04, le - 05) and weight decays {le-01 le 03). For JTT, we explore over 7 21, 5, 10, 15, 20, 30, 35, 40, 45, 50, 65, 80, 95) and À E (5, 10, 20 In each case, we seek to optimize fairness while constraining average accuracy ranges {[82, (8155, 82), [81, 81.5), [80.5, 81), [80, 80.5)
A.2 QUALITY OF ANTIGONE'S s SENSITIVE ATTRIBUTE LABELS
EDM
an
CelebA Dataset: Blond Class
0.6
0.4
10
20
30
40
50
Epochs
Figure 3: Euclidean Distance between Means (EDM) and noise parameters 01, 31 and and 1 1 31 for the positive target class of CelebA dataset. The noise parameters are unknown in practice. Blue dot indicates the model that pick to generate pseudo sensitive attributes, while black star indicates the model that maximizes 01 - 31.
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Table 4: We tabulate the precision, recall, F1-score of the noisy validation groups generated from ERM model, GEORGE, GEORGE with number of clusters 2 and Antigone. We observe that Antigone has higher precision and Fl scores across different noisy groups on CelebA and Water- birds, respectively.
Antigone (w/o BDM)
GEORGE
GEORGE
Antigone (w/ EDM)
2)
CelebA (Precision, Recall, F1 Scores)
0.26, 0.31, 0.28
0.09, 0.32, 0.13
0.06, 0.70, 0.12
0.36, 0.34, 0.35
Blond Men
(0.02, 0.03, 0.01)
(0.01, 0.09, 0.02)
(0.01, 0.05, 0.01)
(0.05, 0.04, 0.04)
0.95, 0.94, 0.95
0,94, 0.28, 0.43
0.95, 0.35, 0.51
0.96, 0.96, 0.96
Blond Women
(0,01, 0.01, 0.01)
(0.01, 0.04, 0.04)
(0.00, 0,02, 0.02)
(0.0, 0.0, 0.0)
0.82, 0.13, 0.22
0.51, 0.36, 0.42
0.5, 0.76, 0.6
0.86, 0.13, 0.22
Non-blond Women
(0.01, 0.01, 0.02)
(0.00, 0.01, 0.01)
(0.00, 0.01, 0.01)
0.01, 0.01)
0,52, 0.97, 0.67
0,53, 0.33, 0.40
0.47, 0.23, 0.31
0,52, 0.98, 0.68
Non-blond Men
(0.00, 0.00, 0.01)
(0.01, 0.02, 0.02)
(0.01, 0.01, 0.01)
0.0, 0.60 1 0.00
CelebA Accuracy
0.59 i 0.01
0.33 0.01
0.48 1 0.00
Waterbirds (Precision, Recall, F1 Scores)
0,94, 0.26, 0.41
0.56, 0.34, 0.43
0,48, 0.57, 0.52
0.96, 0.63, 0.76
Waterbirds Landbkgd
(0.01, 0.02, 0.02)
(0.03, 0.02, 0.02)
(0.01, 0.01, 0.01)
(0.01, 0.04, 0.03)
0,57, 0.98, 0.72
0.55, 0.27, 0.36
0.48, 0.39, 0.43
0.73, 0.97, 0.83
Waterbirds Waterbkgd
(0.01, 0.00, 0.00)
(0.07, 0.03, 0.02)
(0.02, 0.02, 0.02)
(0.02, 0.01, 0.01)
0.96, 0.42, 0.58
0.57, 0.36, 0.44
0.55, 0.55, 0.55
0.97, 0.65, 0.78
Landbirds Waterbkgd
(0.00, 0.03, 0.02)
(0.04, 0.03, 0.03)
(0.03, 0.03, 0.03)
(0.00, 0.05, 0.04)
0,63, 0,98, 0.76
0.55, 0.24, 0.34
0.55, 0.56, 0.55
0.74, 0.98, 0.84
Landbirds Landbkgd
(0.01, 0.00, 0.01)
(0.04, 0.04, 0.02)
(0.03, 0.04, 0.03)
(0.03, 0.00, 0.02)
Waterbirds Accuracy
0.68 + 0.01
0.30 0.02
0.53 0.03
0.81 = 0.02
Table 5: We tabulate the precision, recall, F1-score, accuracy of the noisy validation groups gen- crated by varying the fraction minority group examples each class of CelebA dataset. We observe that Antigone has higher precision, recall, Fl score and accuracy if the imbalance is more in the training dataset.
Fraction Minority
5%
20% Precision, Recall, F1 Score
35%
50%
Blond Men (Minority) Blond Women (Majority) 01 31 Blond Acc.
0.57, 0.40, 0.47
0.81, 0.17, 0.29
0.67, 0.15, 0.24 0.68, 0.96. 0.79
0.75, 0.14, 0.24
0.97, 0.98, 0.98
0.83, 0.99, 0.90
0.53, 0.95, 0.68
0.54
0.64
0.35
0.28
0.95
0.83
0.68
0.55
Non-blond Women (Minority) Non-blond Men (Majority) 0g So
0.45, 0.26, 0.33
0.59, 0.26
0.63, 0.18, 0.28
0.63, 0. 0.26
0.96, 0.98, 0.97
0.82. 0.97, 0.89
0.68, 0.94, 0.79
0.52. 0.91, 0.66
0.41
0.41
0.31
0.15
blondlond Acc.
0.94
0.81
0.67
0.54
Overall Acc.
0.95
0.81
0.67
0.54
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A.3 ANTIGONE JTT
Table 6: We report the (Test Average Accuracy, Test Fairness Metric) for different validation ac- euracy thresholds Waterbirds dataset. We observe that Antigone JTT (our noisy sensitive attributes) improves faimess over baseline ERM model and closes the gap with Ground-Trun + JTT (ground-truth sensitive attributes).
Val. Thresh.
Method
DP Gap
EO Gap
Worst-group
Antigone + JTT
(95.8,3.9) 1 (0.4, 0.4)
(96.2, 10.7) 1 (0.3, 7.1)
(96.3, 83.0) 1 (0.4, 1.3)
196, 96.5)
Ground-Truth + JTT
(95.8, + (0.4,
(96.0, 7.1) = (0.3, 1.4)
(96.3, 83.0) + (0.4, 1.3)
Antigone JTT
(95.4, 2.8) 0.11
(96.0, 7.5) (0.2, 1.5)
196.3,83.22 (0.3, 0.6)
[95.5, 96)
Ground-Truth JTT
(9544 = (0.4, 1.1)
(95.6, 6.0) = 2.13,
(96.1, 83.5) (0.5, 0.8)
Antigone JIT
(95.5. (0.6, 0.6)
(94.7, 4.2) = (0.9.
(94.7, 85.9) (0.9. 1.4)
(95, 95.5)
Ground-Truth JTT
(94.4, 1.7) + (0.7, 0.7)
(94.3, 1.1) (0.5, 0.6)
(95.1, 86.8) (0.6, 1.1)
Antigone JTT
(94.2, 0.4) (0.4, 0.4)
(93.8, 2.0) = (0.5, 1.4)
(94.2, 86.7) (0.8, 1.8)
[94.5, 95)
Ground-Truth JTT
(93.6, 0.6) (0.5,
(93.8, 2.0) (0.5, 1.4)
(94.1, 88.2) (0.6, 0.7)
Antigone + JTT
(93.0, 1.5) (0.6, 0.3)
(93.6, 4.8) = (1.2.
(93.7, 87.9) (0.5. 1.4)
[94.0, 94.5)
Ground-Truth + JTT
(93.1, 1.5) (0.3, 0..3
(93.2, 4.0) = (1.0, 2.1)
(93.8, 88.1) (0.7, 1.1)
ERM
(1.33 = (0.2. 1.1)
(97.3, 35.0) = 3.4)
(97.3, 59.1) + (0.2. 3.8)
Table Antigone + JTT vs Ideal MC Model + JTT (Avg. Accuracy, Fairness) comparison on test data for different validation accuracy thresholds the CelebA dataset. Lower DP and EO gaps are better. Higher WGA better.
DP Gap
EO Gap
WGA
Antigone + JTT Ideal MC JTT
(94.9, 14.7) (94.9, 14.7)
(94.6, 33.7)
(94.5, 61.7)
>=94 and <95
(94.4, 34.1)
(94.4, 58.3)
Antigone + JTT
(93.7, 12.2)
(93.9, 30.3)
(93.3, 60.0)
>=93 and
Ideal MC JTT
(93.7, 12.2)
(93.5, 26.3)
(93.7, 65.0)
Antigone + JTT
(93.1, 12.1)
(92.4, 22.9)
(92.9, 65.6)
>=92 and <93
Ideal MC JTT
(93.1, 12.1)
(93.0, 22.7)
(93.2, 69.4)
Antigonc + JTT
(91.9, 9.3) (91.9,
(91.1, 13.9)
(91.1, 66.7)
>=91 and <92
Ideal MC JTT
(92.2, 19.1)
(91.8, 73.9)
Antigone
(91.1, 7.9) (90.9, 8)
(91.1, 13.9)
(91.1, 66.7)
>=90 and <91
Ideal MC JTT
(90.4, 18.9)
(91.4, 72.2)
15

---

Under review as a conference paper at ICLR 2023
Table 8: (Avg. Accuracy, Fairness) on test data for different validation accuracy thresholds on the UCI Adult dataset. Lower DP and EO gaps are better. Higher WGA is better.
Val. Thresh.
Method
DP Gap
EO Gap
Worst-group Acc.
Antigone + JTT
(81.9, 11.7) (81.8, 11.9)
(81.9, 0)
(81.7, 54.6)
[82, 82.5)
Ground-Truth JTT
(81.4, 3.3)
(81.7, 54.6)
Antigone + JTT
(81.5, 9.3)
(81.5, 1.9)
(81.0, 56.0)
[81.5, 82)
Ground-Truth JTT
(81.5, 9.3)
(81.1,
(81.0, 56.0)
Antigone + JTT
(80.8, 7.1)
(80.9, 0.9)
(81.0, 57.1)
[81, 81.5)
Ground-Truth JTT
(80.8, 7.1)
(81.0, 2.4)
(81.0, 57.1)
Antigone + JTT
(80.4, 7.2)
(80.1, 1.9)
(80.4, 58.2)
[80.5, 81)
Ground-Truth JTT
(79.8,
(80.5,
(80.5, 58.0)
Antigone + JTT
(79.7, 5.4)
(79.7, 1.4)
(80.4, 58.0)
180, 80.5)
Ground-Truth JTT
(79.5,
(80.4, 4.2)
(80.4, 58.0)
ERM
(84.8, 53.8)
(84.8, 10.6)
(84.8, 52.4)
16


Reviews:
[{"review_id": "uZXJA-zQJU", "reviewer": "Reviewer_qHvW", "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 presents a method for performing hyperparameter tuning without access to a sensitive attribute. Instead of obtaining ground-truth sensitive attribute labels on the validation set, the proposed method uses \"pseudo\" attribute labels, which are simply whether an observation is correctly predicted or not. They use these labels for performing hyperparameter tuning on JTT and George for two datasets.\n", "summary_of_the_review": "Overall, the paper presents an interesting, if somewhat ad hoc seeming, approach. However, I think the exposition of the method is fairly confusing, and more importantly, I have some concerns about the empirical evaluation -- they are missing any estimates of statistical uncertainty/variability, and the empirical results are mixed and missing some clear baselines (see other comments).", "strength_and_weaknesses": "## Major comments\n\n* It seems there is a clear baseline that is not evaluated here: simply use some of the (fully-labeled) training data as a held-out validation set. In that case, ground-truth attribute labels would be available. It is not clear why the paper doesn't compare to this?\n\n* It would be helpful if the authors formally state the problem they are trying to solve (P3 simply says \"we seek to train models that optimize fairness under a constraint on average accuracy\").\n\n* Similarly, it seems like the works on multicalibration/multiaccuracy are trying to solve a similar problem (\"fair\" classification without access to any sensitive labels); it seems particularly the fair boosting approach in (Kim et al, \"Multiaccuracy: Black-box post-processing for fairness in classification\") as a postprocessing method with a strong backbone model is relevant to compare to as well.\n\n* The notation in the paper was quite confusing for me to read. There are many different sub- and superscripts, and D and X both denote (different) datasets. It also seems like \\mathcal{A} is used to refer to the set of potential sensive labels (2.1) and a function class (in definition of \\theta^*)? The intution of using the max-EDM model is also not clear to me; why do the authors state \"we would like our noisy labeler to be biased\"? It seems that *we would like to obtain accuracy pseudo-labels for the sensitive attribute* (see next comment), which is not the same thing. It is also not even clear what \"bias\" means in this context.\n\n* It seems the key empirical/theoretical result for the entire paper is to show that the pseudo- attribute labels are good estimates of the true attribute labels on the validation set. The only evidence we have of this is Table 1, which strangely gives the precision (not the accuracy?) of these attribute labels. It would be useful to (1) provide the *accuracy* of these labels, (2) perhaps give some examples of data points in each (pseudo) class to see whether these match our expectation since the attribute in each dataset are easily interpretable from images, (3) perform some simulated analyses to demonstrate that under ideal conditions the pseudo-labels correctly recover the true attribute labels.\n\n## Minor comments\n\n* Please provide (a) the size of the data subsets in Table 1 (how many \"blond men\" in the validation set of CelebA?) and (b) Clopper-Pearson confidence intervals on the accuracies shown in the tables, or some other measure of statistical uncertainty of these point estimates. As is, the authors use some very fuzzy language (\"JTT+Antigone is very close\" and \"[b]oth substantially improve upon\").\n\n* It is not clear why the method is called Antigone. This name is also not mentioned in the abstract.\n\n* Table 3 is way too small.\n\n\n## Typos etc.\n\nThere are many typos in the paper. I list a few below.\n\nP2 \"incorrectly classifier examples\"\n\nAfter Proposition 1: \"From ... that\" -> \"From ... we can conclude that\"\n\nLemma 1 \"inputs data\" -> input data\n\nP7 \"tune it's hyperparameters\" -> tune its hyperparameters\n\n* 3.2 why is GEORGE \"a competing approach\"? Competing against what? Please clarify.", "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": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}, {"review_id": "r1T_hElDcfp", "reviewer": "Reviewer_pAmd", "summary": "", "questions": "", "limitations": "", "rating": 8, "confidence": 3, "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": "In this paper, the authors propose an algorithm for mitigating unintended bias without requiring access to the sensitive attribute. The intuition is similar to some recent works, which assume that the errors of a model provide a noisy proxy for the sensitive attribute (e.g. minorities would have a disproportionately larger error). There have been some recent works along this direction but it has been observed that their performance was sensitive to the choice of hyper-parameters. In this paper, the authors introduce a method for hyper-parameter selection without requiring access to the sensitive attribute in both training and validation data and demonstrate experimentally (using CelebA and WaterBirds) that it performs better than previous methods.", "summary_of_the_review": "I think the paper is novel and the experimental results show a significant improvement. The paper is clearly-written and well-motivated, particularly for such a challenging topic. ", "strength_and_weaknesses": "**Strengths**\n\nOverall, the paper is clearly written and the proposed algorithm Antigone is well-motivated. The experimental results show a significant improvement compared to previous methods. In addition, Antigone can be applied to any prior method for hyper-parameter selection, such as JTT (Liu et al., 2021). I think the method is neat and the motivation behind the EDM criterion using the mutually contaminated (MC) noise model is elegant.\n\n\n**Weaknesses**\n\nThe primary weakness is that the method only applies to binary sensitive attributes. Often, sensitive attributes are non-binary, such as based on age, race, or nationality. \n\nSecond, the authors argue that their method would also work with other techniques, such as LfF (Nam et al., 2020) and CVaR DRO (Hashimoto et al., 2018a). However, they do not report any experiments to support this claim. While I don’t expect a different conclusion, it would be useful to include one or two additional methods.\n\nThird, the hyper-parameters the authors experiment with are quite limited. They only consider three pairs of learning rate and weight decay combination and the choice of those parameters seem odd to me. A learning rate of 1e-4 is very small for a ResNet50 architecture while a weight decay of 1e-1 seems extremely large! Have the authors tried other combinations but decided not to include them because the model failed to train or did they simply stick to the choices used in JTT? \n\nFinally, the authors experiment with two vision datasets only. Is there a reason the authors did not try additional datasets, such as Adult Income or Credit Score? It would be interesting to see how the method performs in such cases. My concern is that this line of work assumes that the error of the model is a proxy for the sensitive attribute so it would be useful to see how well this assumption holds in other settings.\n\n**Typos**\n\nThere is a typo in Section 4: “on validation data based the EDM criterion” → “on validation data based on the EDM criterion”.\n", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "4: All of the claims and statements are well-supported and 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": "9uEH9-3Fsk", "reviewer": "Reviewer_DQeE", "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": "This paper propose a fair model training method (called Antigone) without sensitive attribute access. The idea is to train a biased classifier where all its correctly-labeled examples are considered to be the majority sensitive group, and all its incorrectly-labeled examples form the minority group. The measure of success for such a biased classifier is the Euclidean distance between the means of the two groups (EDM) where a classifier with a larger EDM is best. As a justification, an mutually contaminated noise model is used where maximizing EDM results is shown to minimize DP and EO gaps. Experiments show that Antigone outperforms the competing method GEORGE.", "summary_of_the_review": "This paper solves the challenging and important problem of fair training without sensitive attributes. There is theoretical support on why the biased classifier should maximizd EDM. However, the key assumption that training the desired biased classifier is possible is a bit questionable. In addition, the MC noise model seems quite simplistic and should be verified using the datasets. Finally, the experiments are a bit thin using only two real datasets and not fully analyzing how Antigone behaves.", "strength_and_weaknesses": "Strengths\n- Solves the realistic and challenging problem of fair training without sensitive attributes.\n- The EDM maximization strategy is supported by theoretical results.\n- Antigone outperforms GEORGE on real datsets.\n\nWeaknesses\n- The key assumption that there can be a bias classifier where all its correct (incorrect) predictions form the majority (minority) group seems a bit unrealistic. This means that minority group examples are extremely difficult to classify while majority group examples are much easier. If we consider the motivating examples mentioned in the Introduction like algorithmic hiring, is hiring female and male applicants that different in difficulty? I would argue that making predictions on the two sensitive groups is quite similar in difficulty, so it is not clear if the paper's assumption holds. Perhaps the assumption holds for applications where there is severe class imbalance, but in fairness problems, the gap can be more subtle than obvious. The paper does not attempt to demonstrate the key assumption empirically either. There are two real datasets CelebA and Waterbirds, and it is not clear how imbalanced their sensitive groups are. \n- While the theoretical justification of EDM using the MC noise model is useful, it is not clear if the MC noise model itself really holds on real datasets. One way to verify is to add a synthetic dataset that clearly follows the MC noise model first, and then show that the Antigone results are similar on real dataset. It is often the case that real datasets have all sorts of noise that makes it difficult to understand why the proposed method is working well. \n- It seems like EDM is only justified because the MC noise model is quite simplistic. Intuitively, is maximizing the Euclidean distance really all we need to do to tune the bias model? Should we not care about say the variance of the two distributions? If not, why? \n- Can Antigone be extended to support more than two sensitive groups? The MC noise model seems to be limited to the binary case.\n- Only experimenting on CelebA and Waterbirds seems a bit thin. What about other fairness benchmarks like AdultCensus, COMPAS, and the recent ACSIncome? More importantly, it would be informative to know how each dataset is useful in showing the advantages of Antigone. Also, it would be nice to have datasets with varying imbalances where if the imbalance is small, Antigone actually does not perform well, which is expected.\n", "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": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}, {"review_id": "1qYHZlDVr9Q", "reviewer": "Reviewer_iLMB", "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 focuses on the problem of accessing sensitive group attributes in the validation set for hyperparameter tuning. To solve this issue, the paper proposes Antigone, a hyper-parameter tuning framework for fairness techniques that do not access sensitive group attributes in training data. The proposed framework is inspired by a prior work (Lamy et al., 2019), which has been proposed for fair training under noisy sensitive attributes. This algorithm is evaluated on two datasets, including CelebA and Waterbirds, with some baselines.", "summary_of_the_review": "Although the paper tries to solve a practical problem, there seems some room for improvement in 1) clarification on the importance of the work, 2) justification of the design choices, and 3) enhancement of the experimental results. Overall, I think that this paper is on the borderline.\n", "strength_and_weaknesses": "[Strength]\n\nS1: The paper tackles the practical problem of accessing sensitive attributes in the validation set. \n\nS2: The paper utilizes an idea from fair training under noisy sensitive attributes, and such inspiration gives an interesting approach. \n\n\n[Weakness]\n\nW1: The significance of the proposed algorithm seems a bit limited, as it only targets fairness techniques that do not access sensitive attributes in training data. Since many more algorithms have been proposed for fair training with sensitive attributes, it would be helpful if the paper can clarify 1) the significance of this work and 2) how the proposed algorithm can be extended in other scenarios.\n\nW2: Several design choices in the proposed framework Antigone are not fully justified. For example, why using the previous idea of handling noisy group attributes is the most appropriate way to solve the target problem? Why the current approach is better than other approaches like training a weak-labeler on groups?\n\nW3: More importantly, the experimental results are insufficient. \n- The baselines are not enough. One of the key advantages the paper argues is that Antigone can be used for any algorithm of not accessing sensitive attributes on training data. However, the paper only shows its effectiveness on JTT. Thus, it is hard to believe that Antigone will effective in other algorithms like LfF and DRO.\n- Also, all experimental results are reported without error range, which makes the observations less reliable. For example, in several rows of Table 1, the improvements in Antigone compared to GEORGE are a bit marginal, so it is questionable how it changes after multiple runs. It would be much better if the paper shows the results with error ranges to clarify the performance gain.\n\nMinor Typo: First paragraph in Section 2.1) target labels (X) => target labels (Y)\n", "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": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}]

Author rebuttal:

Decision: Reject