Hyper-parameter Tuning for Fair Classification without Sensitive Attribute Access
Authors: Akshaj Kumar Veldanda
Ivan Brugere
Sanghamitra Dutta
Alan Mishler
Siddharth Garg
Venue: Accepted by TMLR ()

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 sough 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 Antigone, 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 ERM model and using the classifier’s incorrectly (correctly) classified examples as proxies for disadvantaged (advantaged) 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 ERM model 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. We demonstrate that Antigone outperforms existing methods on CelebA, Waterbirds, and UCI datasets.

Published in Transactions on Machine Learning Research (03/2024)
Hyper-parameter Tuning for Fair Classification without Sen- sitive Attribute Access
Akshaj Kumar Veldanda
aku275
Electrical and Computer Engineering Department New York University
Ivan Brugere" JP Morgon Chase AI Research
ioan. brugere @ipmchase.ccmm
Sanghamitra Dutta"
sanghamd@uum..cm edu
Electrical and Computer Engineering Department University of Moryland College Park
Alan Mishler"
alan, connmmshherr Biinhber@@pmmhhse.cccm
JP Morgon Chase Al Research
Siddharth Garg
sg1 75 25@yy...co edu
Electrical and Computer Engineering Department
New York University
Reviewed on OpenReview: https: oppnreevee. net/ per/forum? id- 2SWKdR12cU
Abstract
Fair machine learning methods seek to train models that balance model performance across demographic subgroups defined over sensitive attributes like and gender. Although sensitive attributes 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 altributes 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 to sensitive attributes on either training or validation data. Instead, we generate pseudo sensitive attributes the validation data by training ERM model and using the classifier's incorrectly (correctly) classified examples as proxies for disadvantaged (advantaged) 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 principled approach to select the syper-parameters of the ERM model in completely unsupervised fashion (meaning without. access lo ground truth sensitive attributes) that minimizes the gap between fairness estimated using noisy versus ground-trute truth sensitive labels. We demonstrate that Antigone outperforms existing methods on CclebA, Waterbirds, and UCI datascts.
1 Introduction
Despite their success on a range of real-world tasks, prior work (Hovy & Søgaard 2015 Oren et al. 2019 Hashimoto al. 2018a) has found that state-of-the-at deep neural networks exhibit unintended biases
"Equal Contribution

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towards specific subgroups, for instance towards disadvantaged subgroups because of tendency to learn spurious correlations and simplicity bias, especially harming disadvantaged groups. Seminal work by Buo- lamwini & Gebru (2018) demonstrated, for instance, that commercial face recognition systems had lower accuracy on darker-skinned women than other groups. body work has sought to design fair machine
learning algorithms that account for a model's performance on per-group basis Prost el al. 2019 Liu
ct al. 2021 Sohoni et al. 2020).
Mean Image
Men
Women
CelebA Validation Data
Ground-Truth Blond (Correct Set)
114
2770
Blond PSA =1
Blond
Non-Blond
Predicted Blond
Ground-Truth Non-Blond (Incorrect Set)
1077
Non-Blond PSA 0
Women (2874)
Men (8276)
Men
Women
Ground-Truth Non-Blond (Correct Set)
8094
7458
Non-Blond PSA
BAL
Predicted Non-blond
Men (182)
Women (8535)
ERM classilier (noisy sensitive attribute labeler)
Ground-Truth Blond
68
104
Blond PSA
(Incorrect Set)
Figure Antigone on CelebA dataset with hair color as larget label and gender as (unknown) sensitive attribute. Blond men are discriminated against. Correspondingly, the mean image of the Blond class incorrect set (row 4) has more male features than that of its correct set (row 1), reflecting this bias. Similarly, bias against non-blond woren is also reflected. PSA = 0 corresponds to disadvanlaged groups, and PSA = 1 corresponds to advantaged groups.
Prior work typically assumess that attributes, e.g. gender and race, on which we seek to train fair models are available on training and validation data (Sagawa* * al. 2020; Prost et al., 2019). We will refer
these sensitive attribudes (SA). However, recent work (Veale & Binns 2017 Holstein et al., 2019) has highlighted many real-world scttings in which SA may not be available. For example, data subjects may abstain from providing sensitive information for privacy reasons or to evade future discrimination (Markos et al. 2017). Attributes on which the model discriminates might not be known or available during training and only identified post-deployment (Citron & Pasqualc 2014 Pasquale
2015 Veldanda et al.) 2023b)
For instance, recent. work shows that lair NLP models trained on western datasels discriminate based on last names when re-contextualized to geo-cultural settings like India (Bhatt et al. 2022). Similarly, reports suggest that Nikon's face detection models repeatedly identify Asian faces blinking, bias that was only identified retrospectively (Leslic 2020 Unfortunately, by this point, at least some harm is already incurred.
Recent work has therefore sought to train fair classifiers without SA the training set (Liu et al. 2021 Creager et al. 2021 Nam et al.) 2020 Hashimoto et al. 2018a). At their core, these methods first identify advantaged and disadvantaged groups within the training dataset; i.e., subgroups with high and low accuracy, respectively. Then, they deploy various training strategies to boost performance on vantagad groups. However, these methods are highly scnsitive the choice of hyperparameters, and can actually hurt fairness compared to baseline empirical risk minimization (ERM) without proper hyperparameter tuning (Liu et al., 2021). Hence, with the exception of GEORGE (Sohoni et al. 2020) and ARL (Lahoti et al. 2020), prior work has assumed access to SA on the validation data. However, in practical settings, SA may not be available for the same reasons they are unavailable on training data.
In this paper, we propose Antigone, a principled approach that enables hyperparameter tuning for fairness without access to SA on training and validation data. Antigone enables effective hyperparameter tuning of methods like JTT (Liu et al., (201)), AFR (Qiu al.) 2023) (that currently assume ground-truth SAs on validation data) and improves fairness when GEORGE's and ARL's own hyperparameter tuning methods are
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replaced with Antigone. Antigone works for fairness metrics including demographic parity, equal opportunity and worst sub-group accuracy.
Antigone starts with a baseline ERM model trained to predict target labels (note these target labels are known and different from SAs). Subgroups advantaged by the baseline ERM model will be over-represented in the set of correctly classified inputs; similarly, disadvantaged subgroups are over-represented in the set of incorrectly classified inputs. Hence, Antigone uses the ERM model's correctly and incorrectly classified validation data proxies for advantaged and disadvantaged subgroups, respectively. We refer to these as pseudo-sensitive attributes (PSA). Note that PSA labels are noisy; some inputs from the advantaged subgroups will be incorrectly classified, and vice-versa. Can they still be used for hyperparameter tuning? Prior work shows that under certain theoretical assumptions on label noise, called the mutually corrupted (MC) noise model, fairness measured on PSA is proportional to ground-truth fairness (Lamy et al., 2019). Thus, PSA labels on validation data can still be used to compare different models for fairness, and consequently for hyperparameter tuning.
However, this sets up a new problem: how do we tune the hyperparameters of the ERM model itself to maximize the accuracy (or minimize the noise) of our PSA? We cannot directly measure PSA accuracy or noise since we do not have any ground-truth SA labels. Here, we show formally that under the MC noise model, minimizing noise is equivalent to maximizing the Euclidean distance wetween the mean (EDM) images in the correct and incorrect classes. Since the EDM can be directly measured, we train a family of ERM models with different hyper-parameters and pick the model with the largest EDM on the validation dataset. The PSAs obtained are then used to tune hyperparameters for fairness schemes like JTT, AFR, GEORGE and ARL.
For more intuition, consider the example in I Figure on the CelebA dataset. The target label is hair color, and the (unknown) SA is gender. The baseline ERM model discriminates against blond men. The correct set for the ground-truth blond class has only 4% blond men while the incorrect set has 65% blond men. This is also reflected in the mean images for these two classes: the correct set for the ground-truth blond individuals has more female features while the incorrect set has more male features. As noted above, Antigone picks an ERM model with the largest distance between these mean images so as to maximize PSA label accuracy.
We evaluate Antigone in conjunction with three state-of-art methods, JTT (Lu et al. 2021 AFR QQu et al. 2023). GEORGE (Sohoni et al. 2020) and ARL [Lahoti et al. 2020 on binary SA using demographic parity, equal opportunity, and worst subgroup accuracy as fairness metrics across the CelebA, Waterbirds and Adult datasots. Empirically, we find that: (1) Antigone produces more accurate PSA labels on validation data compared to GEORGE's unsupervised clustering approach (Table 1}; (2) used with JTT (AFR), Antigone comes close to matching the fairness of JTT (AFR) tuned with ground-truth SA as shown Table 2
Table 5 and (3) improves the fairness of both GEORGE and ARL when Antigone's 's PSA labels are used instead of their own hyperparameter tuning methods (Tblle 3 Table 4). Specifically, the worst- worst-group accuracy increases by 4.2% and 8.6% on the CelobA and Waterbirds datasets for GEORGE, respectively, and by up to 11.6% on the Adult dataset for ARL. Ablation and sensitivity studies demonstrate the effectiveness of Antigone's e EDM metric versus alternatives (Table 1 and shed light on discrepancies between the ideal MC assumplions and its use in practice (Appendix Table 13) Overall, our key contributions are:
We propose Antigone (subsection 2.2 a new method for the often overlooked problem of hyper- parameter tuning for fair classification in setting where sensitive altributes are unavailable on both training and validation data. Antigone generates PSA labels on validation data using the correctly and incorrectly classified examples of an ERM model as proxies for advantaged and disadvantagod subgroups.
We propose an unsupervised approach to tune Antigone's own hyperparameters (spocifically, those of its ERM model) by maximizing the Euclidean distance between the mean (EDM) images of the correctly and incorrectly classified sets. We theoretically justify this choice under the MC noise model, proving that maximizing EDM minimizes PSA label noise in an idcalized setting [subsoc- tion 2.3 Empirically, we show that gap between our practical implementation and the idcalized MC noise model is small.
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Experimentally, find that Antigone based hyperparameter tuning boosts fairness for three state- of-art methods, JTT, AFR, GEORGE and ART (section 3). even surpassing their own hyperporam- eter tuning techniques. Antigone also generates more accurate PSA labels compared to GEORGE's unsupervised clustering approach (scction 4
2 Proposed Methodology
We now describe Antigone, starting with the problem formulation (Section 2.1 followed by a description of the Antigone algorithm (Section 2.2
2.1 Problem Setup
Consider data distribution over set D = X' A Y, the product of input data (X), sensitive attributes (A) and target labels ()) triplets. We are given training set D = {xf", v. yutr with N training samples, and validation set Deal = (araa agaa, " Neat with Nyal validation samples. We will assume binary sensitive attributes (AE (E,0,11) and target labels (y E {0,
Tizl
We seek to train a machine learning model, say a deep neural network (DNN), which can be represented as a parameterized function fo X' + y E {0, 1}, where f E @ are the trainable parameters, e.g.: DNN weights and biases. Standard fairness unaware empirical risk minimization (ERM) optimizes over trainable parameters to minimize average binary cross-entropy loss on D Optimized model parameters 0* are obtained by invoking training algorithm, for instance stochastic gradient descent (SGD), the training dataset and model, i.c., 8*1 MERM (D"", fo, 7), where Y E Г are hyper-parametors of the training algorithm including learning rate, training epochs etc. Hyper-paramelers are tuned by evaluating models fe--t for all 7 E I on Deal and picking the best model. More sophisticated algorithms like Bayesian optimization can also be usod. Next, we review three commonly used fairness metrics that we account for in this paper.
Demographic parity (DP): DP requires the model's outcomes to be independent of sensitive attribute. In practice, we seek to minimize the demographic parity gap:
A = PX) = 1/A = -
1|A=00 =
=
(1)
Equal opportunity (EO): EO aims to equalize only the model's true positive rates across sensitive attributes. In practice we seek to minimize
11A==,Y- -| 1|
(2)
Worst-group accuracy (WGA): WGA seeks to maximize the minimum accuracy over all sub-groups (over sensitive attributes and target labels). That is, we seek maximize:
WGA min (0.
(()(()) = v a, Y=
In all three settings, seek to train models that optimize fairness under constraint average target label accuracy, i.e., accuracy in predicting the target label. For example, for equal opportunity, we seek H* = arg mingeeee A such that P[fe(z) Y E [Acctor Accthr Acper where Accter and Acethr are user-specified lower and upper bounds on larget label accuracies, respectively.
2.2 Antigone Algorithm
We now describe the Antigone algorithm which consists of three main steps. In step 1, we train multiple ERM models that each provide pseudo sensitive attribute (PSA) labels on validation data. In step 2, we use the proposed EDM metric to pick a single ERM model from step 1 with the most accurate PSA labels. Finally, in step 3, we use the PSA labelled validation set from step tune the parameees of methods like JTT that train fair classifiers without SA labels on training data.
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Step 1: Generating PSA labels on validation set. In step 1, we use the training dataset and standard FRM training to obtain set of classifiers, 0- = MERM (D'r 7), each corresponding to different value of training eaper-parameters E T. As we discuss in Section 2.1 these include learning rate, weight decay and number of training epochs. Each classifier, which predicts the target label for a given input, generates validation set with PSA labels as follows:
DPSA {xrtar, val , , val, nal Nual VY E P, where
(4)
1, if Sor yfal
pal.y
(5)
0,
otherwise.
valyy now refers to PSA labels. In the next step, we search over the set I to find hyperparameters y E T that maximize PSA accuracy.
where ai
Step 2: Picking the most accurate PSA labeller. From Step 1, let the correct set be X =
{azal : a; mal,7 = }} and the incorrect set be X valyy 0.0. = fapal a; ag = 0}. We define Euclidean distance between the means (EDM) of these sets as:
EDM ||(xX MoMXX111.ss.. A=L.PSA) p(X ( AS0.PSA) l|2:
(6)
where u(.) represents the empirical mean of a dataset. Antigone picks 7" that maximizes EDM, i.e., 7" arg max,er EDM7. We justify this choice in two ways. Intuitively, PSA labels validation data distinguish between advantaged and disadvantaged classes, e.g., placing blond men and blond women in different groups as in Figure 1 resulting in larger differences in the mean images of the two groups. Formally, we show the optimality of this strategy under the MC noise model in Subsection 2.3
Step 3: Training a fair model. Step 2 yields D DpslA" a validation dataset with (estimated) pscudo sensi- tive attribute labels. We can provide DPSA as an input to any method that trains fair models without access to SA on training data, but requires validation set with SA labels to tune its own hyper-parameters In our experimental results, we use Desa to tune the hyper-parameters of JTT (Tiu et al. 2021). ) GEORGE (So- honi et al. 2020) and ARL (Lahoti et al., 2020).
2.3 Analyzing Antigone under Ideal MC Noise
Prior theoretical work (Lamy et al. 2019) has studied the impact of noisy sensitive attribute labels on fairness under the "mutually contaminated (MC) noise model (Scott et al. 2013). Here, it is assumed that we have access to PSA labels, XA=o,rSA X and XA=1ISSA E X, corresponding to disadvantaged (PSA- = 0) and advantaged (PSA- = 1) groups, respectively, that are contaminated (or, noisy) versions of their corresponding ground-truth SA labels, XA= E X and XA=1 E X. Specifically, P(X = 1) = (1 a P = + A = 0) and P(X[PSA = 0) = -PP = +) (1- P A = 0) decompositions are satisfied under the MC noise model, but we follow the notation described in prior work (Scott et al.
2013 Lamy et al. 2019) to denote the MC noise model in our setting as:
X XA=LPSA = (1 aA1 + a and XA=o.SA = BX + (1- AA
where a and 8 are noise parameters. With some abuse of terminology for conciseness, Equation says that fraction a of the pscudo advantaged group, XA=IPPSA is contaminated with data from the disadvantagod group, and fraction B of the pseudo disadvantaged group, XA=O.PSA, is contaminated with data from the advantaged group. We construct D by appending input instances in XA=0.PSA with their corre- sponding PSA labels (f.e., a, = 0) and target labels, respectively. We do the same for DA=LPSS. The noise can also be target dependent, in which case we use a and 8, as noise parameters for label i. Under this model, Lamy et al. (2019) show the following result::
Proposition 2.1. measured on the noisy datasets are proportional to the true DP and EO gaps. Mathematically:
Lamy et al. 2019) Under the ideal MC noise model in Equation 7 DP and EO gaps
A DP (DA= U DA=I,PSA)
B)A SP (DA=o DA=I), and
(8)
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A Ao (DA U DA==1PSA) (1 (1-00 01 31) (D))= (DA=o DA=1).
(9)
Equation 8 and Equation show that under the ideal MC noise model, the DP and EO gaps can be minimized using PSA labels instead of ground-trth SA labels, although asymptotically with infinite validation data samples. In practice, we seek to minimize the total noise + 3, or equivalently maximize the proportionality constant 1 a - 3 to obtain the most reliable fairness estimates. We show that this can be done by maximizing EDM.
Lemma 2.2. Assume PSA and PSA, correspond to the impul dala of noisy dalasels in the ideal MC model. Then, mazimizing the EDM between PSA and AA=,, i.e, [lu(XA=0, =(XA==1 mazimizes
can see that ( 1 ((XA=I.Psa)ll= (1 a () u(XA=1)ll2 I2. Here []µ(X==)) - u(Xx=1))le is the EDM between the ground truth advantaged and disad- vantaged data and is therefore a constant. Hence, maximizing EDM between XA=o,PSA and XA=L.SA maximizes a
Proof. From Equation 7
Remark 2.3. The MC noise model assumes independent label noisc. However, when using ERM classifiers to generate PSAs, this noise can be instance dependent. Although we use the simplified MC noise model to inform our practical implementation, we do not claim that Antigone inherits the MC model's theoretical guarantees. In [able 13 we do show empirically that the gap between fairness achieved with Antigone and under ideal MC noise is small.
3 Experimental Setup
3.1 Baseline Methods
We evaluate Antigone with state-of-tho-art fairness methods that work without SA training data:
JTT (Luu et al., 2021), GEORGE (Shhoni et al. (2020), ARL Lahoti et al. (2020), and AFR (Qiu et al., 2023 ). GEORGE and ARL additionally do not require SA on validation data. Below, we describe these baselines.
JTT: JTT operates two stages. In the first stage, a biased model is trained using T epochs standard ERM training to identify the incorrectly classified training examples. In the second stage, the misclassified examples are upsampled À times, and the model is trained again completion with standard ERM. The hyperparameters of stage and stage 2 classifiers, including early stopping epoch T, learning rate and weight decay for stage and upsampling factor À for stage 2, are jointly tuned using validation dataset with ground-truth SA labels. We refer to this as the Ground-Truth + JTT basclinc.
GEORGE: GEORGE is a competing approach to Antigone in that it does not assume access to SA on either training or validation data. GEORGE operates in two stages: In stage 1, an ERM model is trained until completion on the ground-truth target labels. The activation in the penultimate layer of the ERM model are clustered into & clusters to generate PSA labels on both the training and validation datasots. In Stage 2, these PSA are used train a Group DRO model SSaawa** hyper-parameter.
(020)) and tune its carly stopping
ARL: Adversarially Reweighted Learning (ARL) seeks to improve the worst-group performance without access to SA either training validation datasets. ARL framework considers a mini-max game between a learner and adversary. The goal of the learner is to output fair predictions by minimizing the weighted cross entropy classification loss function. Whereas, the adversary maximizes the weighted cross entropy loss so as to identify high loss training data points and upweight them during the training of the learner. Since ARL does not assume access to SA on validation set, it tries to maximize the target label accuracy by performing grid scarch over the joint eypor-parameter space of both learner and adversary.

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AFR: Automatic Feature Reweighting is lightweight framework that operates in two stages. In the first stage, a standard ERM model is trained on 80% of the training dataset to minimize the FRM objective. In the second stage, AFR retrains only the last layer of the ERM model using the remaining 20% of the training dataset with a weighted loss function. The weights of each sample, i, are determined by:
Ny, (xx())(6)))
(10)
AM 1= exp( (19g)
These weights emphasize the samples where the standard ERM model from stage underperforms. The hyper-parameter, Y, is used to control how much to up-weight examples with poor ground-truth target label prediction probability (ø), ensuring that examples from the disadvantaged group are given greater importance in stage 2. Additionally, AFR balances the larget class labels using Ky: which is the reciprocal of the number of examples belonging to class in the ro-training set. In stage 2, AFR also uses a regularization term to prevent the last layer from focusing only on minority examples, potentially at the cost of degrading performance on majority group examples to an unacceptable level. The strength of this regularization is controlled by the hyper-parameter т. The hyper-parameterr of the second stage are tuned using validation dataset with ground-truth SA labels. We refer to this as the Ground-Truth + AFR baseline.
3.2 Antigone + Baseline
AJT:: Here, we replace the ground-truth SA the validation dataset with PSA obtained from Antigone and use to tune JTT's syper-parameet
GEORgE: For fair comparison with GEORGE, replace its stage 1 with Antigone, and use the resulting validation PSA labels to tune the hyper-parameters of GEORGE's stage 2.
Instead of tuning the target label accuracy the validation set, we use Antigone's validation PSA labels to tune the eyper-parameters of ARL. We also tune the hyper-parameters of ARL with ground-truth SA labels and refer to as Gromd--rrut++RRI
Antigone+ ARL: ARL:
AFR: Here, our primary goal is to improve WGA, as AFR seeks to mitigate spurious cor- relations by improving WGA with the assumption of having access to ground-truth SA on the validation dataset. We substitute the ground-truth SA in the validation dataset with PSA acquired from Antigone and use it to tune AFR's hyperparameters.
3.3 Datasets and Parameter Settings
We cmpirically evaluate Antigone the CelebA and Waterbirds datascts, which allow for direct comparison with related work (Liu et al., 2021 Sohoni et al. 2020). We also evaluate Antigone on UCI Adult Dataset, tabular dataset commonly used in the fairness literature to directly compare with ARL Lahoti et al. (020 (see Appendix for more details.
CelebA Dataset: CelebA (Luu et al. 2015) is an image dataset, consisting of 202,599 celebrity face images annotated with attributes including gender, hair colour, age, smiling, etc. The task predict hair color, which is either blond Y = 1 or non-blond Y 0 and the sensitive attribute is gender A [Men, Women). In all experiments using CelebA dataset, ResNet50 architecture for a total of 50 epochs using SGD optimizer and batch size of 128. We tune JTT over the same hyper-parameters as in their paper: three pairs of lcarning rates and weight decays, (le 04, 04), (le - 04, le 02), (le - 05, le - 01) for both stages, and over ten early stopping points up to T = 50 and e (20, 50, 100} for stage 2. For Antigone, we explore over the same learning rate and weight decay values, as well as carly stopping at any of the training epochs. We report results for DP, EO and WGA fairness metrics. In each case, we seek to optimize fairness while constraining average target label accuracy to ranges (190, 91), [91, 92), [92, 93), [93, 94), 194,96 95))-
fine-tune a pre-trained
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Waterbirds Dataset: Waterbirds is syuthetically generated dataset, containing 11,788 images of wa- ter and land birds overlaid on top of either water or land backgrounds (Sagawa* et al. 2020). The task is to predict the bird type, which is either a waterbird Y = or a landbird Y = 0 and the sensitive attribute is the background A = (Water background, Land background). In all our experiments using Wa- terbirds dataset, we fine-tune ResNet50 architecture for a total of 300 epoch using the SGD optimizer and a batch size of 64. We tune JTT over the same hyper-parameters as in their paper: three pairs of learning rates and weight decays, (Ie 03, le - 04), (1e - 04, le 01), (le 05, 1.0) for both stages, and over 14 early stopping points up to T 300 and À E {20, 50, 100) for stage 2. For Antigone, over the same learning rate and weight decay values, as well as early stopping points at any of the 300 training epochs. In each case, we seek to optimize fairness while constraining average accuracy to ranges {194, 94.5), [94.5, 95), [95, 95.5), [95.5, 96), [96, 96.5)).
explore
In case of GEORGE, for both CelebA and Waterbirds datasets, we use the same architecture and early stopping stage hyper-paramcters (T 50 for CclebA and T 300 for Waterbirds) reported in their paper. For GEORGE, we replace GEORGE's stage with the Antigone model, which is identified by searching over the same hyperparameter space as in Antigone+JTT.
In case of AFR, for both CelebA and Waterbirds, we fine-tune pre-trained ResNet50 architecture and tune its hyper-parameters to minimize the cross-entrops ropy loss function in stage 1. In stage 2, we re-train the last layer by searching over the prpee-paraeetes space reported in their paper. Specifically, for CelebA, we tune over early stopping stage epochs (T 1000), 7 from 10 points linearly spaced between [1, 3), learning rate 2e 2, and I E {0.001, 0.01, 0.1). For Waterbirds, we tune over early stopping stage 2 epochs (T 500), y from 33 points linearly spaced between [4, 20), learning rate le 2, and (0,0.1, 0.2, 0.3, 0.4). For Antigone+ AFR, we tune AFR's stage hyper-parameten using Antigone's PSA, which are identified by searching over the same hyperparameter space as in Antigone+JTTT.
4 Experimental Results
Accuracy of Antigone's PSA labels: Antigone seeks to generate accurate PSA labels on validation data, referred to as pseudo label accuracy, based on the EDM criterion (Lemma 2.2 In Figure 2 we empirically validate Lemma 2.2 by plotting EDM and noisc paramcters a1 (contamination in advantaged group), 31 (contamination in disadvantaged group) and 1 - a1 - B1 (proportionality constant between true and estimated fairness) on Waterbirds dataset (similar plot for CelebA dataset in Appendix Figure 3(b) From the figure, we observe that in both cases the EDM metric indeed captures the trend in - a1 - B1, enabling early stopping at an epoch that minimizes contamination. The best carly stopping points based on EDM and oracular knowledge of 1 a1 A1 shown in blue dot and star, respectively, and very close.
EDM 1-a1 -8:
a A
Waterbirds Dataset: Waterbirds Class
0.8
0.6
0.4
0.2
0.0
50
100
150
200
250
300
Epochs
Figure 2: Euclidean Distance between Means (EDM) and noise parameters (a1, 81 and 1 1- ai - B1) for the positive target class of Waterbirds dataset. Blue dot indicates the model picked by Antigone, while black star indicates the model that maximizes 01 B.
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we compare Antigone's PSA labels' F1 Score to GEORGE with the bascline k = 5 and with k 2 clusters on CelebA and Waterbirds. We find that Antigone outperforms GEORGE on all but one sub-group in CelebA, and all Waterbirds. Table I also reports results on a version of Antigone that uses standard ERM training instead of EDM (Antigone (w/o EDM)). We find that Antigone provides higher pscudo-label accuracy compared to this baseline. Appendix Table 6 shows precision and recall of Antigone's PSA labels and reaches the same conclusion. We also study the impact of varying the fraction of disadvantaged group individuals from 5%, 20%, 35%; 50% in the CelebA dataset (see Appendix (Table 7j. As the dataset gets more balanced, the models themselves are more fairer, and PSA label accuracy reduces (as expected). Nonetheless, disadvantaged group individuals are over-represented in incorrect sets for up to 35% imbalance.
In Table
we
Table 1:
F1 scores and pseudo label accuracies (Ps. Acc.) We mark the best performance in bold. BM (blond men), BW (blond women); NBW (non-blond women) and NBM (non-blond men) for CelebA; WT (waterbirds landbkgd), WW (waterbirds waterbkgd), LW (landbirds waterbkgd) and LL (landbirds land- bkgd) for Waterbirds.
Antigone (w/o EDM)
GEORGE
GEORGE (A: = 2)
Antigone (w/ EDM)
CelebA (F1 Scores)
BM
0.28# 0.01
0.13# 0.02
0.12 0.01
0.35 0.04
BW
0.95 0.01
0.43 0.04
0.51+ 0.02
0.96 0.00
NBW
0.22+ 0.02
0.42+ 0.02
0.6 0.01
0.22+ 0.01
NBM
0.67 0.01
0.4 0.02
0.3 a 0.01
0.68 _ 0.01
Ps. Acc.
0.59+ 0.01
0.33+ 0.03
0.48+ 0.00
0.60= 0.00
Waterbirds (FI Scores)
WL
0.41+ 0.02
0.43+ 0.02
0.52= 0.01
0.76= 0.08
WW
0.72. 0.00
0.36 0.02
0.43 0.02
0.83 0.01
LW
0.58 0.02
0.44# 0.08
0.55 0.08
0.78 = 0.04
LL
0.76: 0.01
0.34 0.02
0.55 0.03
0.84:
Ps.
Acc.
0.68+ 0.01
0.30+ 0.02
0.53+ 0.08
0.81+ 0.02
Anti In Table 2. we compare the test target label accuracy and fairness achieved by Antigone with JTT (Antigone+JTT) vs. JTT using ground-truth SA Trouun-Truthh+JTTT) On DP and EO, Antigone+JTT is very close to TrunddTruth+JTT in terms of both target label accuracy and fairness, and substantially improves on standard ERM. Antigone+JIT improves WGA from 38.7% for standard ERM to 68.1% at the expense of 3% target label accuracy drop. Toundd-Truth-JTT improves WGA fur- ther up to 78.6% but with a 4.4% larget label accuracy drop. Waterbirds (Appendix Table 17) and UCI Adult (Appendix Table 12) have the same trends.
Comparison with GEORGE: As already noted in Table Antigone's PSA labels are more accurate and have higher F1 scores than GEORGE's. In Table 3) ments over GEORGE in both WGA (8.6% higher) and target label accuracy on Waterbirds. For CelebA, Seiigone+GoRRGG has a 4.2 % higher WGA but with a small drop of 0.4% in target label accuracy. Fair- ness improvement are statistically significant under paired t-tests; over 10 runs, Antigon++ always equals or betters GEORGE in terms of WGA (Appendix Figure 5).
Antioone+GFORGG shows marked improve-
Comparison with ARL: In Table 4 (full table in Appendix Table 14 we compare the target label accuracies and fairness of Antigone+ ARL vs. just ARL for different validation accuracy thresholds on the Adult UCL. ARt. has 4.5%-11.6% higher WGA than ARL alone, but with small (< 0.6%) drop in target label accuracy. Similar observations hold on DP Gap and EO Gap.
Comparison with AFR: In Table 3] we compare the test target label accuracies and WGA achieved by Antigone with AFR Antigone+AAFR vs. AFR using ground-truth SA ( Truth+ Antigone + AFR very close to Ground-Trute + AFR in terms of both target label accuracy and WGA, and substantially improves on standard FRM. On CelebA, Antigone AFR improves WGA from 41% for standard FRM to
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Table 2: (Avg. target label accuracy, Fairness) on test data for different validation accuracy thresholds 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..
(94.7, 30.1)+ (o.a,
(94.4, 59)+ (0.2,
[94, 95)
Ground-Trute + JTT
(94.7, 14.9)+ 00.4.
(94.5, 30.4)+ (0.2, 2.3)
(94.3, 62.1)+ (0.5, 5.2)
Antigone- + JTT
(93.7, 13.1)+ (0.4, 0.73
(93.6, 26.4)+ (0.4, 5.0)
(93.4, 62.6)+ (0.2, 1.0)
[93, 94)
Ground- Truth + JTT
(93.6, 13.1)+ (0.3,
(93.6, 22.7)+
(93.4, 67.9)+ (0.4, 1.90
Antigone + JTT
(92.7, 11.1)+ (0.2.
(92.3, 20.2)+
(92.7, 68.1)+ (0.4, s.n)
[92, 93)
Ground-Truth + JTT
(92.7, 11.2)+ (0.3,
(92.7, 16.9) 00.4, 2.9)
(92.7, 72.5)+ (0.2, 1.30
Antigone + JTT
(91.7, 9.6)+ (0.1, 0.83
(91.5, 16.3) + (0.3, 5.4)
(91.3, 63.2)+ (0.3, 2.0)
991, 92)
Ghound-Trrute + JTT
(91.8, 9.7)+ (0.2,
(91.8, 10.1)+ (0.3,4.11
(91.8, 77.3) + (0.1.
Antigone + JTT
(91.0, 8,3)+
(90.9, 13.1)+
(90.9, 63,1)= + (0.8, 4.4)
(90, 91)
Ground-Trute + JTT
(91.0, 8.4)+ 00.2, 0.4)
(90.7, 6.8)+ (0.4, 8.73
(91.4, 78.6) + (0.2,
ERM
(95.8, 18 18.6)+ (0.0, 0.5)
(95.8, 46.4) + 00.0, 2.2)
(95.8, 38.7)= (0.00 2.8)
Table 3: Performance of GEORGE using Antigone's validation PSA compared with GEORGE by itself. We observe that on CelebA and Waterbirds dataset, Antigone + GEORGE out-performs GEORGE, even if GEORGE assumes knowledge of number of clusters (k 2) in its clustering step. (**) indicates
p value < (.01(0.
CelebA
Waterbirds
Method
Avg Ace
WGA
Avg Acc
WGA
ERM
95.75
35.14
95.91
29.70
GEORGE
93.61
60.44
95.39
49.15
Antigone + GEORGE
93.56
62.45*
95.99**
57.73
GEORGE (k=2)
94.62
60.75
94.61
42.98
Antigone +
94.18
64.94**
95.56**
52.80*
GEORGE (k=2)
Table 4: Comparison of (Avg. target label accuracy, Fairness) between ARL using Antigone's noisy validation data, ARL alone, and ground-truth validation data on the UCI Adult dataset. Lower DP and EO gaps indicate better fairness, while higher WGA is better. Antigone + ARL consistently outperforms ARL across various validation accuracy thresholds and fairness metrics. The p-values are marked with accordingly:
for < 0.1, ** for p < 0.05, and *** for p < 0.01.
Val. Thresh.
Method
DP Gap
BO Gap
Worst-group Ace.
Antigone ARL ARL Ground-rrun Truth + ARL
(84.51, 16.84)" + (0.15, 1.00)
(84.1, 5.64) # co.08, 1.43)
(84.14, 59.68) ... (0.13, 1.27)
88455, 85)
(84.53, 19.01) caus. 6.7)
(84.53, 9.35)
10.11, 0.s8:
(84.53, 55 08) (0.13, 5.03)
(84.5, 15.86) (0.3, 199:
(84.43, 4.97) (0.17 1:3
(84.08, 62.66)
(0.an, 0.71
Antigone + ARL
(84.12, 15.55) **.
(83.7, 6.65)*
(83.47, 60.9)**
84, 84.5)
ARL Ground-Truth + ARL
(84.02, 18.35)
(84.02, 8.04)
(84.02, 55.60 55.69)
(84.23, 15.26)
(83.81, 5.57) 10.33,
(83.62, 64.74)
Antigone + ARL
(83.29, 15.13) "T" (0.21, 1.17)
(83.07, 5.36)
(0.22, 2.50)
(82.93, 62.17)" "*" (0.18, 1.03)
883.5, 84)
ARL
(83.54, 19.43) +: (0.13 3.17)
(83.54, 10.52) =: (0.12) 2.18)
(83.54, 53.72) (1.12) 2.06)
Ground- Truthh I ARL
(83.53, 14.7)
0.57:
(83.17, 4.34)
10.17, 0.50:
(83.31, 66.61) (0.24, 1.6;
Antigone + ARL
(82.98, 15.05) *** co.15,
(82.69, 5,4)
co.16, 0.15)
(82.55, 65.85) "** c0.a1, 0.58)
183, 83.5)
ARL
(83.2, 18.24) (o.33,
(83.2, 8.69) 4: (0.15. a.65)
(83.2, 5-.21) c0.13,
Ground-TTrute -rrnn + ARL
(82.86, 14.84)
coL1s, 1:30)
(83.04, 6.03)
10.13, 1.50)
(82.47, 66.75)
(0.10, 1.50)
ERM
(84.69, 18.27) (5.0 6.0
(84.69, 9.39)
(0.09, 1.112
(84.69, 53.36)
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Published in Transactions on Machine Learning Research (03/2024)
81% at the expense of 5% target label accuracy drop. Ground-Truth + AFR improves WGA further up to 82% with a 4% target label accuracy drop. Similar observations hold for the Waterbirds dataset also.
Table 5: Performance of AFR using Antigone's validation PSA compared with AFR by itself. Higher WGA is better. We observe that Antigone + AFR is close to the performance of Ground-Truth + AFR.
CelebA
Waterbirds
Method
Avg Acc
WGA
Avg Acc
WGA
ERM
0.96
0.41
0.98
0.64
Antigone + AFR
0.91 om
0.81 a 0.01
0.92 0.04
0.82 A 0.09
Ground Truth + AFR 0.92
0.82
0.93
0.84 0.02
Ablation Studies: We perform two ablation experiments to understand the benefits of Antigone's pro- posed EDM metric. We already noted in [Table 1 that Antigone with the proposed EDM metric produces higher quality PSA labels compared to a version of Antigone that picks hyper-parameters 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 average target label accuracy. Second, in Appendix Table 13 also compare Antigone+-JTT against synthetically labeled validation dataset that exactly follows the ideal MC noise model in Section 2.3 We find that on DP Gap and EO Gap fairness metrics, Antigone is results are comparable (in fact sometimes slightly better) with those derived from the ideal MC model. On WGA, the most challenging fairness metric to optimize for, we find that the ideal MC model has a best-case WGA of 73.9% compared to Antigone's 66.7%. This reflects the loss in fairness due to the gap between the assumptions of the idealized model versus Antigone's implementation: however, the reduction in fairness is marginal when compared to the ERM baseline which has only a 38% WGA.
Applicability to backbone models We conducted additional experiments to evaluate Antigone's perfor- mance using large pre-trained models. Specifically, we fine-tuned a pre-trained state-of-art large transformer model, ViT-B/16 (Dosovitskiy et al., (2020), on the Waterbirds dataset, resulting in largel label accuracy of 99% and WGA of 82% for the ERM model (refer to Appendix B.1 for more details). In Appendix Table 8 we compare Antigone-ViT-B/ 1/'ss PSA labels GEORGE with k and k 2 clusters. We find that Virigone-VVT-B/IB outperforms GEORGE. Furthermore, we compare the test target label accuracies and WGA achieved by Antigone-ViT-B/UU are consistent with prior observations and show that Antigone- Antigone-ViT-B/II ViT-B/16 can be successfully used with large pre-trained models.
AFR vs. Ground-Truth (Appendix Tabll 10p. The results
5 Limitations
Antigone has some notable limitations that we discuss here, along with potential avenues to mitigate these concerns. First, in its current form, Antigone only explicitly deals with binary sensitive attributes. In practice, multiple subgroups could in fact be over-represented in the incorrect set, and as such accounted for during hyperparameter tuning but not explicitly. We note that downstream robustness methods, like JTT, that we demonstrate Antigone in conjunction with and others like Creager et al. (021)) have the same limitation. Antigone+JTTT can improve fairness for these sub-groups as whole but cannot, for example, have different up-weighting factors for cach subgroup. However, this limitation not fundamental and can be addressed by further sub-dividing the incorrect set, via multiple rounds of Antigone+JJTT where in each round we address any remaining fairness gaps. We note also that although GEORGE addresses multiple (k) subgroups, tuning & is challenging and results for larger & are sometimes worse than k 2.
A second concern is whether the assumptions of the MC noise model, independent label noise in partic- ular, hold strictly. While they do not, we are not claiming the theoretical fairness guarantees of [amy ct al. (2019). Antigone is a practical solution to improve fairness like other works we evaluate against. In Appendix Table 13 we do compare Antigone+ JJT against synthetically labeled validation dataset that exactly follows the MC noise model and find that Antigone's reduction in fairness marginal. Tn Figure
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we also empirically validate that the proportionality constant 1 --a minimizes the gap between the true and estimated fairness values.
6 Related Work
Methods that seek to achieve fairness are of three types: pre-processing, in-processing and post-processie
algorithms. Pre-processing (Quadrianto ct al. 2019
Ryu ct al. 2018) methods focus on curating the dataset
that includes removal of sensilive information or balancing the dalasets. In-processing methods (Hashimoto
et al.
2018b Agarwal et al.) 2018 Zafar et al.) 2019
Lahoti et al. 2020 Prost et al.) 2019 Veldanda et all
2023a;
Sohoni et al. 2020 alter the training mechanism by adding fairness constrains to the loss function
by
training adversarial framework to make predictions independent of sensitive attributes (Zhang)
ett al.
2018]. Post-processing hods (Hardt et al. 2016 Wang et al. 2020b Savani et al.) 2020) alter
the outputs, for e.g. use different threshold for different sensitive attributes. In this work, we focus on in-processing 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 models without training data annotations (Liu et al., 2021 Nam et al. 2020; Hashimoto et al.)
2018a
Creager et al.
2021
Levy et al., but require
2020 Duchi & Namkoong, 2018 Nam et al.) 2022 Zhang et al.
2022
LaBonte et al.
2023
sensitive attributes on validation datasct to tune the hyperparametert
With Antigone, WC seek to remove
this restriction. Since JTT already compared against Nam et al.
2020 and Levy et al.
(020), a scalable
version of (Duchi & Namkoong 2018), we compare against JTT, although we believe Antigone can be used with these methods also.
Recently, Kirichenko et al. (022) proposed a simple and light-weight framework to improve WGA. They demonstrated that re-training the last layer of an ERM model with a small, group-balanced dataset is sufficient for achieving robustness to spurious correlations. But, ground-truth SA's are required to balance the groups and aune-byperparameters. AFR (Qiu et al., 2023) addresses this problem by retraining the last layer of an ERM model with a weighted loss that emphasizes the examples where the ERM model under-performs, automatically up-weighting the disadvantagen group without ground-truth SA labels. AFR showed that it can achieve the same target label accuracy and WGA as DFR, but AFR still requires ground- truth SA on validation dataset to tune-hyper perper-paramttrs. We show that using Antigone's 's PSA, we can get close to the performance of AFR without considering any access to ground-truth SA labels.
GEORGE (Sohoni et al. 2020 and and ARL (Lhhoti et al. 2020 are two methods that like Antigone do not require PSAs on validation data. Qualitative and empirical comparisons in section 4sshow that Antigone outperforms both. ARL is demonstrated to be effective only on smaller datasets and on simple structured network architectures. Prior works (Sohoni et al. 2020; Wang 2022) have also noted ARL does not scale well to complex work architectures (e.g.: Res and large vision datasels. On the other hand, both methods can account for multiple subgroups, although as we noted before, Antigone still helps improve ground-truth sensitive attributes. [Zhu et al. (023) is based on open-source proxy models. These proxy models are trained on distinct datasets to predict sensitive attributes. Subsequently, such off-the-shelf proxy models (Alao et al. 2021 are employed to predict unknown sensitive attributes within the dataset. Zhho et al. (2022) presume that the proxy features are known a a-priori, thereby gaining knowledge of the attributes on which the model discriminates. However, as noted in section 1 we consider a more realistic setting where no such knowledge given/known a-priori. There are also some post-processing methods to improve fairness without access to scnsitive attributes but assuming a small set of labelled data for auditing Kim et al. (2019). One could use Antigone to create this auditing dataset, albeit with noise. Evaluating Antigone with these post- post-processing methods is an avenue for future work.s
fairness for both. Another line of work makes implicit assumptions
Finally, a parallel body of work has looked al fairness with noisy sensitive altributes and incomplete infor- mation from a theoretical perspective using simplified but representative mathematical models (Lamy et al., 2019. Wang et al.) [2020a] Awasthi et al. 2021 Celis et al.) (021), and sometimes with restrictions on the classifier types, etc. Yet these methods have largely not been translated to practical implementations on large datasets and state-of-art. deep networks, which is Antigone's end goal. Antigone is one of the first
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methods to bring insights from this line of work to bear practical implementations. As side note, we observe that Lemma 2.2 adds an extra result that might be of interest to this stream of research.
7 Conclusion
We propose Antigone, method to enable hyper-paraneter tuning for fair ML models without access to sensitive attributes on training or validation sets. Antigone generates high-quality PSA labels by training a lamily of ERM models and using correctly (incorrectly) classified examples as proxies for majority (minorily) group membership. We propose a hyperparameter free approach to pick the ERM models that obtains the most accurate PSA labels, and provide theorctical justification for this choice using the idcal MC noise model. Antigone produces more accurate sensitive attributes estimates compared the state-of-art, and be used to effectively tune hyperparameters of state-of-art fairness methods. Future work will also seek to address the variance in fairness metrics (Mozannar et al. 2020) introduced by finite sample size under the ideal MC noise model, extend Antigone to non-binary sensitive attributes, and use methods such as Autotune (Koch et al., 2018 to automatically search over larger poper-parameter spaces to maximize the EDM metric.
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Rachad Alao, Miranda Bogen, Jingang Miao, Nya Mironov, and Jonathan Tannen. How Meta is working to assess fairness in relation to race the U.S. across its products and sys- wor--on--------ssss---iiiii Published in Transactions on Machine Learning Research (03/2024)
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Appendix
Availability
Code with README.txt file is available at: demographics
wittttessssstttttttttoet without,
A Experimental Setup
A.1 Compute
We trained all the models employing the JTT approach using Quadro RTX8000 (48 GB) NVIDIA GPU cards, whereas, for both GEORGE and ARL approaches, we used GeForee RTX3090 (24 GB) NVIDIA GPU cards.
A.2 CelebA Dataset
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 = or non-blond Y = 0 and the sensitive attribute is 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 bascline ERM model under-pertt mnder-performs on the blond men.
Dataset details:
Hyper-parameter settings: In all our experiments using CelebA dataset, we fine-tune pre-trained ResNet50 architecture for a total of 50 epochs using SGD optimizer and batch size of 128. We tune JTT over the same hyper-parameters as in their paper: three pairs of learning rates and weight decays, (le - 04, le 04), (1e - 04, le 02), (le 05, le - 01) for both stages, and over len early stopping points up to T = 50 and (20, 50, 100} for stage 2. For Antigone, we explore over the same learning rate and weight decay values, as well as carly stopping at any of the training epochs. We report results for DP, EO and WGA fairness metrics. In each case, we seek to optimize fairness while constraining average target label accuracy to ranges ([90, 91), (91, 92), [92, 93), [93, 94), (94,95);
A.3 Waterbirds Dataset
Dataset details: Waterbirds is a synthetically generated datasct, containing 11,788 images of water and land birds overlaid on top of either water or land backgrounds (Sagawa* et al. 2020). The task is to predict the bird type, which is either waterbird Y = or landbird Y = and the sensitive attribute is the background
{ [Water background, Land background). The dataset 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 a minority of waterbirds (landbirds) on land (water) backgrounds. Thus, the baseline ERM model under-performs on the minority group.
Hyper-parameter settings: Tn all our experiments using Waterbirds dataset, we fine-trained ResNet50 architecture for total of 300 epoch using the SGD optimizer and a batch size of 64. We tune JTT over the same hyper-parameters as in their paper: three pairs of learning rates and weight decays, (le 1e-003 03, 1e 04), (1e 04, 1e 01), (le 05, 1.0) for both stages, and over 14 early stopping points up to T = 300 and X E (20, 50, 100) for stage 2. For Antigone, we explore over the same learning rate and weight de- cay values, as well as early stopping points at any of the 300 training epochs. In each case, we seek to optimize fairness while constraining average accuracy to ranges (944,4) 94.5), (94.5, 95), [95, 95.5), [95.5, 96), [96, 96.5))
In case of GEORGE, for both CelebA and Waterbirds datasots, we use the same architecture and early stopping stage
(T 50 for CelebA and T 300 for Waterbirds) reported in their paper. For Antigone+ GEORGE, replace GEORGE's stage with the Antigone model, which is identified by
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searching over the same and determine if Singoon++FOOGGE performance is significantly greater than GEORGE by itself, we conducted & paired statistical t-test. The null hypothesis (HO) states that the mean of Antionne-GEORGH is less than or equal to the mean of GEORGE, while the alternative hypothesis (H1) states that the mean of GEORGE is greater than that of GEORGE.
space in Antigone+JJT. To establish statistical significance
A.4 UCI Adult Dataset
Dataset details: Adult dataset (Dua & Graff 2017 is used to predict if an individual's annual income is & 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 attribule is 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 21112, 9049 and 15060 instances, respectively. The dataset has twice many men as women, and only 15% of high income individuals are women. Consequently, the baseline ERM model under-perfore on the minority group.
Hyper-paramcter settings: In all our experiments using Adult dataset, we train a 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 a batch size of 256. We tune Antigone and JTT by performing grid search over learning rates E {le - 03, le 04, le- 05) and weight decays E {le 01, le - 033. For JTT, we explore over T (1,2, 5, 10, 15, 20, 30,35, 40, 45, 50, 65, 80, 95 and À E {5. 10, 20}. In cach case, we seek to optimize fairness while constraining average accuracy to ranges {[82, 82.5), [81.5, (2), (81, 81.5), [80.5, 81), [80, 80.5)
For ARL, we train for a total of 100 epochs. We choose the best learning rate and batch size by exploring all possible
for the learner and adversary in the syper-parameter search space given by batch size E {32,64 64, 12.,,2,,80, 256 512} and learning rate E {0.001, 0,01, 0.1, 2, as in their paper. The learner is a fully connected two layer food-forward network with 64 and 32 hidden units in the hidden layers, with ReLU activation function. The adversary fully connected one layer feed-forward network with 32 hidden units in the single hidden layer, with ReLU activation function. For Antigone+AARL, we use Antigone's pscudo sensitive attribute labels, for hyper-parameter tuning, identified by searching over the same hyper- parameter space as in Antigone+-JTT. We seek to optimize fairness while constraining average accuracy to ranges ([4455, 85), [84, 84.5), [83.5, 84), [83, 83.5), [82.5, 192, [82, 82.5).. A paired statistical (-test is used to establish statistical significance and determine if the fairness of Antigone-ARI is significantly greater than that of ARL alone. The null hypothesis (HO) states that the mcan fairness of Antigone+ is less than or equal to that of ARL, while the alternative hypothesis (HI) states that the mean fairness of Antigone+ ARL is greater.
B Quality of Antigone's Sensitive Attribute Labels
Antigone seeks to generate accurate PSA labels on validation data based on the EDM criterion (Lemma 2.2 In Appendix Figure 3(b) we empirically validate Lemma 2.2 by plotting EDM and noise parameters aı (contamination in ad advantaged group), 31 (contamination in disadvantaged group) and 1 -a - 31 (propor- tionality constant between true and estimated fairness) on CelebA dataset. From the figure, we observe that the EDM metric indeed captures the trend in 1 a - 31, enabling early stopping at an epoch that minimizes contamination. The best early stopping point that maximizes EDM also has a very high 1-aa a1 -1.
Lemma 2.2 shows that the EDM metric is, in thoory, proportional 1-a-8. To further validate this lemma, we consider larger hyper-parameter space, including learning rate, weight decay, and early stopping epochs, resulting in a total of 900 data points from our Waterbirds dataset. We compute the Pearson correlation cocfficient between the EDM metric and 1 - a B across these 900 different data points. The Pearson correlation coefficients are 0.90 and 0.95 for the waterbirds and landbirds classes, respectively, indicating a strong positive correlation between the EDM metric and 1 - a - B. In Appendix Figure 4 we validate Lemma 2.2 by plotting the EDM metric vs. I-a a - 3 for different syper-parameter settings.
In Appendix Table 6 we compare Antigone's PSA label's precision, recall, and F1 scores to GEORGE with the baseline k 5 and with k = 2 clusters CelebA and Waterbirds. We find that. Antigone outperforms
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Women
Men
Waterbkgd
Landbkgd
EDM
1-a--6 CelebA Dataset: Blond Class
Waterbirds
Blond
DAL AY
0.6
47%
3%
47%
3%
Non- BlonB
Landbirds
0.4
0.2
26%
24%
48%
0.0
20
CelebA Dataset
Waterbirds Dataset
Epochs
(a) Dataset Details
(b) EDM and noise parameters on Celeba
Figure Figure (a) illustrates CelebA and Waterbirds datasets along with fraction each sub-group examples in their respective training dataset. Figure (b) shows Euclidean Distance between Means (EDM) and noise parameters 01 and and ai - 31 for the positive target class of CelebA dataset. The noise parameters unknown in practice. Blue dot indicates the model that pick to generate pseudo sensitive attributes, while black star indicates the model that maximizes 1 0n - 31.
2.0
1.6
0.7
14.
EDM
0.6
EDM
1.2
0.4
0.3
a1 B1
0gg Bo
(a) Waterbirds Class
(b) Landbirds Class
Figure 4: Figure illustrates a strong positive correlation between EDM and 1 - a B with Pearson correlation coefficient of 0.90 and 0.95 for the (a) waterbirds and (b) landbirds classes, respectively, on the Waterbirds dataset.
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GEORGE. We also study the impact of varying the fraction of disadvantaged group individuals from 5%; 20%, 35%, 50% in the CelebA dataset (see Appendix Table 7). As the dataset gets more balanced, the models themselves are more fairer, and PSA label accuracy reduces (as expected). Nonetheless, disadvantaged group individuals are over-represented in incorrect sets for up to 35% imbalance.
Table 6:
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 F1 scores across different noisy groups on CelebA and Waterbirds, respectively.
Antigone (w/o EDM)
GEORGE
GEORGE
Antigone (w/ EDM)
(k 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, 0.01)
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-bloud Men
(0.00, 0.00, 0.01)
(0.01, 0.02, 0.02)
(0.01, 0.01, 0.01)
(0.0, 0.0, 0.0)
CelobA Accuracy
0.59 +:t 0.01
0.33 = 0.01
0.48 + 0.00
0.60 + 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)
0.37, 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 7: We tabulate the precision, recall, Fi-score, pseudo label accuracy of the noisy validation groups generated by varying the fraction of minority group examples in each class of CelebA dataset. We observe that Antigone has higher precision, recall, Fl score and pseudo label accuracy if the imbalance is more in the training dataset.
Fraction Minority
3%
20% Precision, Recall, F1 Score
35%
50%
Blond Men (Minority) Blond Women (Majority)
0.57, 0.40, 0.47
0.81, 0.17, 0.29
0.67, 0.15, 0.24
0.75, 0.14, 0.24
0.97, 0.98, 0.98
0.83, 0.99, 0.90
0.68, 0.96, 0.79
0.53, 0.95, 0.68
I - a1 31
0.34
0.64
0.35
0.28
Blond Ps. Ace
0.95
0.83
0.68
0.55
Non-bloud Women (Minority) Non-blond Men (Majority)
0.45, 0.26, 0.33
0.59, 0.17, 0.26
0.63, 0.18, 0.28
0.63, 0.16, 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
3g Non-blond Ps. Acc.
1
0.41
0.41
0.31
0.15
0.94
0.81
0.67
0.54
Overall Ps. Acc.
0.95
0.81
0.67
0.54
B.1 Antigone's Performance on Large Pre-trained Models
search can include model architectures. We perform additional experiments by fino-tuning a pre-trained stato-of-art large transformer model, VIT-B/16 Dosovitskiy et al. (2020), ; on the Waterbirds dataset and show that Antigone-ViT-B/1e can generate high quality PSA labels and improve down-stream fairness. We seek to maximize the EDM metric by exhaustively performing a grid search
Antigone's
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over the hyper-parameter space which inchudes learning rate {le - 03, 1c 04, le 05), weight decay E 10,1e-04, le 01,1.0,, batch size E (64,512) and gradient clipping E {False, True with threshold = 1.0).
PSA labels' F1 Score and PSA labels' accuracy to GEORGE with the baseline k = and with k 2 clusters. We find that Antigone- Barigone-ViT--B.. 16 outperforms GEORGE. The table also reports results on a version of Brrigone-ViT-B/// that uses standard ERM training instead of EDM (Antigone-ViI-BIIO (w/o EDM)). We find that Antigone- ViT-B316 (w/ EDM) provides higher pseudo-label accuracy compared to this baseline. To validate Lemma 2.2 compute the Pearson correlation coefficient between the EDM metric and 1-a-8 over larger hyper parameter space containing 14,400 different data points from our Waterbirds datasets. The Pearson correlation cocfficient is 0.88 and 0.97 for waterbirds and landbirds classes, respectively, indicating a strong positive correlation between the EDM metric and a 3.
In Appendix Table 8 we compare the quality of
Table 8: Fl scores and pseudo label accuracies (Ps. Acc.) of Barrigne-ViT--B/1 and GEORGE on Wa- terbirds datasct. We mark the best performance in bold. WL (waterbirds landbkgd), WW (waterbirds waterbkgd), LW (landbirds waterbkgd) and LL (landbirds landbkgd) for Waterbirds dataset.
Autigone- ViT-B/16 GEORGE GEORGE (k= 2)
Antigone-ViT-B/UU ViT-B/16 (w/ EDM)
(w/o EDM)
Waterbirds (F1 Scores)
WL
0.28 0.02
0.43+ a.a2
0.52+ 0.2
0.71 + 0.67
WW
0.69, 0.03
0.36. 0.02
0.43 0.02
0,67;
LW
0.18 0.05
0.44+
0.55 0.03
0.64:
LL
0.68; 0.03
0.34 0.02
0.55 0.03
0.77 : 0.00
Ps. Acc.
0.57
0.30# 0.02
0.53= u.0s
0.72:
In Appendix Table 9 we compare the test larget label accuracies and WGA achieved by Antigone-ViT-B/UI + AFR vs. Ground TrRR, where we utilize ResNet-50 as the backbone model for AFR. Furthermore, in Appendix Table 10 we also compare the test target label accuracics and WGA achieved by Antigone- VIT-B/16 + AFR-VIT-B/16 vs. -rrtue---T--------------- VIT-B/16, where we utilize ViT-B/16 the backbone model for AFR-VIT-B/16. The results consistent, with prior observations and show that Antigone-ViT: B/16 can be successfully used with large pre-trained models.
Table 9: Performance of AFR using ViT-B/6''s validation PSA compared with Ground-Truth + AFR Waterbirds dataset. Higher WGA is better. We observe that Antigone- AFR is close to the performance of Ground-Truthl AFR.
Waterbirds
Method
Avg Acc
WGA
ERM
0.98 sou
0.64
Antigone- VIT--/16 +
0.90 + 2.s
0.83 0.02
AFR
Ground- Truth + AFR
0.o3
0.84 0.02
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Table 10: Performance of AFR-VIT-B/LL using Antigone-ViT- ViT-B/16's validation PSA compared with Ground-Truth + AFR-VIT-B/II Waterbirds dataset. Higher WGA is better. We observe that Antigone- VIT-B/16 + AFR-ViT-B/16 is close to the performance of Ground-Truth + AFR-ViT-B/16.
Waterbirds
Method
Avg Ace
WGA
ERM
0.99
0.82 0.01
Antigone-VTT FTT-B/16 +
0.97 0.01
0.93 0.01
AFR-VIT-BI B/16
Ground- Truth +
0.97
0.93
AFR-VIT-B/II
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C Antigone + JTT
Appendix Table 11 and Appendix [Table 12 show the performance of Antigone in conjunction with JTT on Waterbirds and UCI Adult datasets, respectively. While we observed on the validation set that Ground- TJuth+JTT consistently exhibits higher (or equal) fairness compared to Antigone+JJTT, it is important to note that fairness measurements may differ on test sets due to potential distribution shifts Xu & Goodacre (018))
To show that Antigone is effective on multiple binary sensitive attributes, we evaluate the trained Antigone+JTT models with age as the sensitive attribute on the CelebA dataset. The baseline ERM model achieves larget label accuracy of 95.83% and worst-group accuracy (WGA) of 78.14%. Antigone improves WGA to 86.23% with a target label accuracy of 95.25%; and improves WGA further to 91.22% with target label accuracy of 93.53%. Antigone similarly improves demographic parity gap (2.21% to 1881%) and oqual opportunity gap (4.88% to 2.59%) with larget label accuracy >95%
We report the (Test average target label accuracy, Test fairness metric) for different validation accuracy thresholds on Waterbirds dataset. We observe that Antigone + JTT (our noisy sensitive attributes) improves fairness over baseline ERM model and closes the gap with Ground TruthTruthh + JTT (ground-tree -ruth sensitive attributes).
Table 11:
Val. Thresh.
Method
DP Gap
EO Gap
Worst-group
Antigone JTT
(95.8, 3.9) # (0.4, 0.4)
(96.2, 10.7) (0.3, 7.1)
(96.3, 83.0) = (0.4, 1.3)
[96, 96.5)
Groud--ruth JTT
(95.8, 3.9) 1 (0.4, 0.4)
(96.0, 7.1) 1 (0.3, 1.4)
(96.3, 83.0) 1 (0.4, 1.3)
Antigone + JTT
(95.4, 2.8) + (0.1, 0.1)
(96.0, 7.5) + (0.2, 1.5)
(96.3, 83.2) + (0.3, 0.6)
[95.5, 96)
Ground-Truth + JTT
(95.4, 2.9) = (0.4, 1.1)
(95.6, 6.0) = (U.3, 2.1)
(96.1, 83.5) = (0.5, 0.8)
Antigone JTT
(94.5, 1.5) 1. (0.6, 0.6)
(94.7, 4.2) 1 (0.9, 3.1)
(94.7, 85.9) (0.9, 1.4)
[95, 95.5)
Ground-Truth + JIT
(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) + (U.5, 1.4)
(94.2, 86.7) + (0.8, 1.8) (94.1, 88.2) + (0.6, 0.7)
[94.5, 95)
Ground-Truth + JTT
(93.6, 0.6) + (0.5, 0.5)
(93.8, 2.0) + (0.5, 1.4)
Antigone + JTT
(93.0, 1.5) = (0.6, 0.3)
(93.6, 4.8) = (1.2, 3.0)
(93.7, 87.9) = (0.5, 1.4)
[94.0, 94.5)
Ground-Truth + JTT
(03.1, 1.5) 1 (0.3, 0.4)
(93.2, 4.0) 1 (1.0, 2.1)
(93.8, 88.1) 1 (0.7, 1.1)
ERM
(97.3, 21.3) + (0.2, 1.1)
(97.3, 35.0) + (0.2, 3.4)
(97.3, 59.1) + (0.2, 3.8)
Table 12: (Avg. larget label 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 Cap
Worst-group Ace.
Antigone + JTT
(81.85, 11.76) + (0.11, 3.53)
(81.46, 2.68) + (0.24, 5.67)
(81.65, 34.58) + (0.20, 0.87)
>=82 and <82.5
Ground-Truth + JTT
(8188, 11.92) + (0.18, 3.62)
(81.49, 3.14) = (0.17, 4.97)
(81.65, 54.58) = (0.16, 0.76)
Antigone + JTT
(81.74, 11.72) # (0.15, 3.48)
(8165, 6.39) = (0.18, 1.14)
(81.56, 56.32) = (0.4, 1.22)
>-11. and <822
Ground-Truth + JTT
(81.57, 10.97) + (0.24, 3.87)
(81.75, 6.1) = (0.37, 1.85)
(81.52, 57.24) + (0.34, 1.32)
Antigone + JT'
(81.01, 9.11) + (0.19, 3.67) (81.05, 8.92) = (0.25, 3.34)
(81.14 1.43) = (0.24, 1.25)
(81.19, 34.46) # (0.25, 1.64)
>=81 and <81.5
Ground- -Tunt + JTT
(81.11, 2.63) = (0.22, 1.50)
(81.07, 55.04) = (0.34, 1.07)
Antigone + JTT
(80.71, 8.36) + (0.31, 2.54)
(80.57, 2.28) = (0.35, 1.31)
(80.63, 56.3) + (0.29, 1.81)
>=80.5 and <811
Ground-Trathh + JTT
(80.41, 7.04) + (0.4, 2.97)
(80.87, 5.93) + (0.28, 1.52)
(80.53, 56.23) + (0.23, 0.98)
Antigone + JTT
(80.09, 7.54) +: (0.26, 2.18)
(80.19, 2.54) +: (0.32, 1.39)
(80.18, 57.67) 4: (0.22, 1.73)
>00 and <80.5
Truth + JTT
(80.09, 5.63) = (0.39, 2.59)
(80.23, 6.84) (0.15, 1.85)
(79.88, 37.50) + (0.44, 1.75)
ERM
(84.82, 53.83) + (0.09, 0.20)
(84.82, 9.70) + (0.09, 0.75)
(84.82, 53.14) + (0.09, 0.58)
D Comparison with GEORGE
Appendix Figure 5) and Appendix Figure 6 shows the performance of both Antigone+GEORGE and GEORGE experiments across multiple runs on CelebA and Waterbirds datasets, respectively.
24

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Published in Transactions on Machine Learning Research (03/2024)
Table 13: Antigone + JTT vs Ideal MC Model + JTT (Avg. target label accuracy, Fairness) comparison on test data for different validation accuracy thresholds on the CelebA dataset. Lower DP and EO gaps are better. Higher WGA is better.
DP Cap
EO Gap
WGA
Antigone + JTT
(94.9, 14.7)
(94.6, 33.7)
(94.5, 61.7)
[94, 95)
Ideal MC JTT
(94.9, 14.7)
(94.4 34.1)
(94.4, 58.3)
Antigone JTT
(93.7, 12.2)
(93.9, 30.3)
(93.3, 60.0)
[93, 94)
Ideal MC + JTT
(93.7, 12.2)
(93.5, 26.3)
(93.7, 65.0)
Autigone + JTT
(93.1, 12.1)
(92.4, 22.9)
(92.9, 65.6)
[92, 93)
Ideal MC JTT
(93.1, 12.1)
(93.0, 22.7)
(93.2, 69.4)
Autigone + JTT
(91.9, 9.3)
(91.1, 13.9)
(91.1, 66.7)
[91, 92)
Ideal MC JTT
(91.9, 9.3)
(92.2, 19.1)
(91.8, 73.9)
Autigone JTT
(91.1, 7.9)
(91.1, 13.9)
(91.1, 66.7)
[90, 91)
Ideal MC + JTT
(90.9, 8)
(90.4, 18.9)
(91.4, 72.2)
E
Comparison with ARL
Appendix Table 14 shows the performance of Antigone+ART. on UCT Adult dataset.
Table 14: Comparison of (Avg. target label accuracy, Fairness) between ARL using Antigone's noisy valida- tion data, ARL alone, and ground-truth validation data on the UCI Adult dataset. Lower DP and EO gaps indicate better fairness, while higher WGA is better. Antigone + ARL consistently outperforms ARL across various validation accuracy thresholds and fairness metrics (as shown in bold). The p-values are marked with accordingly: * for p 0.1, ** for p < 0.05. *** for p < 0.01, and *... for p < 0.001.
Val. Thresh.
Method
DP Gap
EO Cap
Worst-group Acc.
Autigone + ARL
(84.51, 16.84)* (0.15 1.00)
(84.1, 5.64) *** + 10.00. 1:43)
(84.14, 59.68)** 10:10, 1.27)
84.55 85)
ARL Ground-Truth ARL
(84.53, 19.01) = 1015, BOT)
(84.53, 9.35)
00133, 0.00)
(84.53, 55.08) a 00.13, 3.00:
(81.5, 15.86) 1 (9.14, 1.0))
(84.43, 1.97)
00.17. 1.2
(84108, 62.66) c0.32, 0.71;
Autigone + ARL
(84.12, 15.55)
(0.21, 1.14)
(83.7, 6.65)"
(0.22, 1.03
(83.47, 60.9)" (0.22,
84, 84.5)
ARL
(84.02, 18.35) (0.77 1.00
(84.02, 8.04)
(0.17, 1.21)
(84.02, (5.69) (6.17, 2,00:
Cround-Truth ARL
(84.23, 15.26) (0.12, 0.01
(83.81, 5.37) (0.12, 1.54)
(83.62, 64.74) 06.14, 0.55;
Autigone + ARL
(83.29, 15.13) (
Law)
(83.07, 5.36)
(82.93, 62.17)" "77 (0.18, 1.03)
88.55 84)
ARL Ground-Truth ARL
(83.54, 19.43)
(83.54, 10.52)
(83.54, 53.72)
9.60;
(83.53, 14.7) (649,, o.y)
(83.17, 4.34)
(0.13, a.00)
(83.31, G0.61) (0.26, 1:4)
Autigone ARL ARL
(82.98, 15.05) " (0.18, 1.45)
(82.69, 5.4) 10.10, 0.15)
(82.55, 65.85) *** (0.31, 0.58)
88, 83.5)
(83.2, 18.24) (8:13, 2.45)
(83.2, 8.69)
(0.12, 3.08)
(83.2, 54.21) 10.22, 4.93)
Ground-Trute ARL
(82.86, 14.84) e (0.3) 1.25)
(83.04, 6.03)
(0.13, L.50)
(82.47, 66.75) 4: 06.16, 1::0;
Antigone + ARL
(82.69, 14.16)****
(OLYT, 1.22)
(82.32, 8.23) + c0.10, 2.44)
(82.12, 66.93)
(O) (0.30, 1.00)
82.5, 83)
ARL
(82.71, 20.27)
(0av, nor
(82.71, 10.32) a (0-27, 9119)
(82.71, 54.4) -0 9.99
Ground Trutth ARL
(82.63, 13.79) (0.3,, 1.523
(82.21, 4.31) (0-as, 2.04)
(81.91, 69.08) + 06.21, L.5e:
Antigone + ARL
(82.3, 13.63) ****
(81.88, 8.76) +
139,,, 66.61)**
(0.50, 1,073
82, 82.5)
ARL Ground Truth + ART.
(82.16, 21.63)
(0.35
(82. 16, 13.55)
(0-300
(82.16, 52.82)
(82.34, 13:21)
(81.5 3.39)
(81.35, 69.98)
ERM
(84.69, 18.27)
(84.69, 9.39)
(84.69, 53.36) L.V:
25

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Published in Transactions on Machine Learning Research (03/2024)
68
66
64
WGA
62
60
58
2
5
8
10
Trail Number
GEORGE (k 5)
GEORGE (k 2)
Antigone+GEORGE (K 5)
Antigone+GEORGE (k= 2)
Figure 5: Figure illustrates the performance of Antigone+-GORGE and GEORGE in terms of target label accuracy and WGA across multiple trials for both k = and = 2 on the CelebA dataset.
65
60
55
50
WGA
45
40
35
30
25
2
5
8
10
Trail Number
GEORGE (k =
GEORGE (k= 2)
Antigone+GEORGE (k 5)
Antigone+GEORGE (k
Figure 6: Figure illustrates the performance of Anoigone-GEORGE and GEORGE in terms of target label accuracy and WGA across multiple trials for both k = and = 2 on the Waterbirds dataset.
26


Reviews:
[{"review_id": "ea5tssR9Ow", "reviewer": "Reviewer_j4jz", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "The strengths of this paper are as follows.\n\n1. The studied problem is of great importance. The fairness problem is always a concern, especially for data involving sensitive attributes.\n2. The proposed method achieves the best performance on three datasets.\n3. The paper is written well.\n\n\nThe weaknesses of this paper are as follows.\n1. The baselines are a bit out-of-date. There is only one baseline published after 2020 (JTT), and there is no recent method to be considered in the experiments. Actually, JTT has a lot of follow-up papers, and the authors should consider them both in the related work section and experiments section.\n2. It is concerned whether the method can be generally and widely used. The proposed method should be evaluated on more backbone models, especially for these pretrained large models, for more extensive evaluation.\n3. The predicted pseudo may still reveal the fairness issue.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This paper studies the problem of fair machine learning by proposing a proxy-based method that first generates pseudo sensitive attributes on the validation data as proxy data. Here, the generation process can help the method not be restricted by the existing methods' assumptions that the sensitive attributes are known on the validation data. The authors conduct experiments on three datasets, and the results show superior performance of the proposed Autigone method.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "Please answer my questions, with corresponding changes, in the above-mentioned weaknesses.", "broader_impact_concerns": "N/A", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "kYlzrCimlc", "reviewer": "Reviewer_46BP", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths: \n1) Anti-gone is a simple procedure for constructing a fair classifier without access to sensitive attributes, who's main additional computational cost involves training potentially many ERM models with different hyper-parameters.\n\n2) Anti-gone appears to work quite well in the provided experiments -- in particular, for example, JTT with antigone appears to perform nearly as well as JTT with ground-truth sensitive attribute labels. \n\nWeaknesses:\n1) The formal justification of the Antigone is based on an implausible mutually contaminated noise model (Section 2.3). It would be useful for the authors to provide some sense of the extent to which the mutually contaminated noise model may be violated in the empirical experiments. Concretely, the mutually contaminated noise model's key restriction is that P(A = a | X = x, PSA = p) does not vary across values of the feature (see Remark 2.3). Could you report in the experiments the extent to which this holds or does not hold? This is, in principle, a falsifiable assumption and it would be useful to see whether antigone's performance degrades as this is violated more.\n\n2) Relatedly, I found the statement of the mutually contaminated noise model in Equation 7 difficult to interpret. Should that be a statement about the joint distribution of (X, A, PSA)? That is P(X | PSA = 1), P(X | PSA = 0) satisfies that decomposition? \n\n2) The only illustration of different hyperparameters in the experiments appears to the be the number of epochs used for training and possible early start times. It would be useful/important to understand how antigone performs for other choices of function classes and/or hyperparameters. Among neural networks, there are many other hyperparameters we could consider such as the learning rate -- how does antigone perform when we only consider alternative learning rates? For example, many prediction models are simply based on threshold rules of a possibly regularized risk assessment -- can we apply antigone for the choice of regularization parameter? Random forests are often used for classification in fair machine learning, yet there are also many hyperparameters in the learning algorithm -- can we apply antigone for the choice of these hyperparameters? If antigone is tailored for the sorts of classifiers illustrated in the experiments, that should be clarified.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "The paper proposes a new method (antigone) for training fair algorithms without access to sensitive attributes at either test or validation time. The core idea is to produce pseudo-sensitive attributes (PSA) by training many different ERM classification models with differing hyperparameters. We then define the PSA to be the labels associated with the ERM classifier that generates the largest difference in average feature values between the positive and negative class. These PSA can then be used as input to any model that estimates a fair classifier without access to sensitive attributes on the train set but requires access to sensitive attributes on the test set. The authors provide theoretical justification for antigone using the mutually contaminated noise model (Section 2.3). The authors report that the methods work well in experiments based on standard datasets.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "See my discussion of weakness above.", "broader_impact_concerns": "I have no concerns about the broader impact of this paper.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "EZn0kOW3Qv", "reviewer": "Reviewer_yigd", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "**Strengths.** The main strength of this paper is the clarity of the approach. The method proposed here is simple, but well justified in theory with very good experimental results. Moreover, the authors put much effort in explaining the design of their experiments, the choice of their setup, and conducting fair comparison with previous methods.\n\n**Weaknesses.** As noted by the authors, Antigone is limited by the use of binary sensitive attributes, which is a main issue for related methods. Moreover, the selection made at the validation phase requires to train as much models as the number of hyperparameter values: in the experiments, this is done for a small number of values. However, in practice, one could consider higher range, and in this case, the authors do not provide a strategy that could reduce the complexity of their approach.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "In this paper, the authors propose an algorithmic framework to train fair classifiers, i.e., classifiers which correct bias arising from sensitive data attributes (SA) such as gender or race, under the assumption that these attributes are not provided at any stage of the procedure (either training or validation). In practice, this setting is motivated by the fact that data subjects may abstain from providing sensitive information when data is collected. Contrary to most of the previous works which assumed that the SA were given at validation phase to conduct hyper-parameter tuning [1,2], this approach provides a hyper-parameter tuning procedure which is more in line with reality. In particular, their method works with binary SA.\n\nThe authors propose the algorithm Antigone, which works in three steps. Given a range of hyper-parameter values, they first train an Empirical Risk Minimization (ERM) model for each of these values, which then provides proxies for the SA labels by comparing the prediction given by the ERM model to the true output (denoted PSA). Then, in validation phase, they select the model which maximizes the \"Euclidean distance between the means\" (EDM): this quantity simply refers to the squared distance between the mean of the pseudo-advantaged inputs (PSA-labeled 0) and the mean of the pseudo-disadvantaged inputs (PSA-labeled 1). This criterion consists in the main contribution of the paper and originates from the assumption of \"mutually contamined\" noise model, which states that the PSA labelization is a noisy version of the SA labelization [3]. Finally, the selected ERM model can be used as input to any method that trains fair models without access to SA on training data but requires SA for the validation. This algorithm works in the three commonly fairness settings: demographic parity, equal opportunity and worst-group accuracy.\n\nIn practice, the authors compare Antigone with state-of-the art methods that do not require  SA on the training dataset: JTT [1], which requires SA at validation phase; GEORGE [4] and ARL [5], which do not require SA at validation phase. They propose several numerical experiments in high-dimensional setting involving neural networks, where the hyper-parameter are learning rate, weight decay and early-stopping points. In particular, the results justify the use of their EDM criterion, as well as the superiority of their method.\n\n[1] Just train twice: improving group robustness without training group information. Liu et al., 2021. \n\n[2] Environment inference for invariant learning. Creager et al., 2021.\n\n[3] Noise-tolerant fair classification. Lamy et al. 2019.\n\n[4] No sub-class left behind [...]. Sohoni et al., 2020\n\n[5] Fairness without demographics through adversarially reweighted learning. Lahoti et al., 2020.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "I would simply recommend the authors to conduct several experiments on the model of Figure 1, to validate Lemma 2.2 in multiple settings.", "broader_impact_concerns": "None", "additional_comments": "", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Meta-review: This paper introduces Antigone, a novel approach for training fair models without the need to access sensitive attributes during the validation phase. Instead of accessing these sensitive labels, Antigone creates pseudo reference labels from multiple different ERM classification models with varying hyperparameters. Reviewers agree that Antigone's methodology is both straightforward and clearly articulated (yigd, 46BP). Additionally, experiments indicate the method's applicability across diverse models (46BP, j4jz). During the rebuttal process, the authors provided further clarification on the interpretations of the equations and the experimental setup regarding the categories of hyperparameters considered. While the review by j4jz highlights concerns regarding the performance of the proposed methods when applied to recent backbone models, upon examining the paper, review comments, and rebuttals, the action editor read the paper&rebuttal and believes that some of these concerns are addressed in the rebuttal.  For instance, the authors have conducted additional analyses on AFR from ICML’23, as well as on various model architectures, including ViT-B/16, within their rebuttals. The authors are advised to expand upon this by including a comprehensive discussion and comparison with the backbone models, such as those developed in the follow-up works of JTT, in their camera-ready submission.
Decision: Accept (poster)