Self-Supervised Fair Representation Learning without Demographics
Authors: Junyi Chai
Xiaoqian Wang
Venue: NeurIPS 2022 Accept (2022)
Keywords: fairness without demographics
reweighing
representation learning

Abstract: Fairness has become an important topic in machine learning. Generally, most literature on fairness assumes that the sensitive information, such as gender or race, is present in the training set, and uses this information to mitigate bias. However, due to practical concerns like privacy and regulation, applications of these methods are restricted. Also, although much of the literature studies supervised learning, in many real-world scenarios, we want to utilize the large unlabelled dataset to improve the model's accuracy. Can we improve fair classification without sensitive information and without labels? To tackle the problem, in this paper, we propose a novel reweighing-based contrastive learning method. The goal of our method is to learn a generally fair representation without observing sensitive attributes.Our method assigns weights to training samples per iteration based on their gradient directions relative to the validation samples such that the average top-k validation loss is minimized. Compared with past fairness methods without demographics, our method is built on fully unsupervised training data and requires only a small labelled validation set. We provide rigorous theoretical proof of the convergence of our model. Experimental results show that our proposed method achieves better or comparable performance than state-of-the-art methods on three datasets in terms of accuracy and several fairness metrics.

Self-Supervised Fair Representation Learning without Demographics
Junyi Chai, Xiaoqian Wang"
Elmore Family School of Electrical and Computer Engineering
Purdue University
West Lafayette, IN 47906 joyrangg
Abstract
Faimess has become important topic in machine learning- Generally, most literature on fairness assumes that the sensitive information, such as gender or race, is present in the training set, and uses this information to mitigate bias. However, due to practical concerns like privacy and regulation, applications of these methods are restricted. Also, although much of the literature studies supervised learning, in many real-world scenarios, we want to utilize the large unlabelled dataset to improve the model's accuracy. Can we improve fair classification without sensitive information and without labels? To tackle the problem, in this paper, we propose a novel reweighing-basd -base contrastive learning method. The goal of our method is to learn a generally fair representation without observing sensitive attributes. Our method assigns weights training samples per iteration based on their gradient directions relative to the validation samples such that the average top-k validation loss is minimized. Compared with past fairness methods without demographics, our method is built on fully unsupervised training data and requires only a small labelled validation set. provide rigorous theoretical proof of the convergence our model. Experimental results show that our proposed method achieves better or comparable performance than state-of-the-art methods on three datasets terms of accuracy and several fairness metrics.
Introduction
As machine learning systems are increasingly used for automated decision making with social impact. discrimination across different demographic groups has become an important concern (Ntoutsi et al.) 2020). There have been growing evidence of disparities across different demographic groups in real-world machine learning systems. Research on the COMPAS dataset shows a strong correlation between recidivism prediction and race, where black individuals are more likely to be classified as high risk (Larson et al. (016)). Gender bias has been identified in image captioning models (Hendricks) al., 2018), where the model is likely recognize the person in the image (without considering the person's 's appearance) as a man if the scene shows snowboarding. It is crucial to ensure that algorithm makes fair predictions without explicit or implicit consideration of biased information, so not to reveal or amplify social biases.
Due to distributional disparity, historical bias, or indirect discrimination (Hajian and Domingo Ferrer 2012). simply removing sensitive attribute during training is not enough to guarantee faimess. In response, methods (Hardt et al. 2016, Creager et al.) 2019 Bahng et al.) 2020) have been proposed achieve fairness under certain fairness notions. Generally, these methods assume one predefined sensitive attribute, and apply fairness constraints based on such information. However,
"Corresponding author.
36th Conference on Neural Information Processing Systems (NcurIPS 2022).

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in real-world scenarios. due to privacy or legal concern, it might be infeasible to collect or use the sensitive information. For example, General Data Protection Regulation (GDPR) imposes heightened prerequisites to collect and use protected features (Voigt and Von dem Bussche 2017). Besides, for many automatic decision-makinn biased against several sensitive attributes. For example, on the COMPAS dataset, we may expect the classifier to be fair with respect to both race and gender. Under such scenarios, conventional methods on fairness that are formulated with one predefined sensitive attribute and one predefined fairness metric (Hardt et al. 2016 Krasanakis et al. 2018) would fail to work, and it is important to study the problem of fairess without demographies.
systems, is important to make sure that the system is not
Current approaches on fairness without demographics (Hashimoto et al. 2018 Lahoti et al. 2020) have been following the idea of Max-Min problem. These works are proposed under a fully supervised setting. In many real-world scenarios, however, we are often given an unlabelled dataset, or only a small portion of labelled samples are available, and to improve model generalization, we always want to utilize the large unlabelled set during training. Thus we ask: Can we improve fair classification without sensitive information and without labels?
One straightforward solution to the problem is contrastive learning. Without using labels during training, contrastive learning aims to learn a compact representation in R., which minimizes the distance between positive pairs and maximizes the distance between negative pairs based on the similarity between data. However, since we can only access data without labels in contrastive learning, we would inevitably sample false negative pairs. Instead, we consider the following relaxed problem: Given small set of labelled samples and a large unlabelled set, can we improve fair classification without sensitive information using contrastive learning?
In this paper, we propose fair contrastive learning method without sensitive attributes. Compared with previous works on fairness without demographics which are fully supervised, our method follows the Min-Max fairness constraints and only requires a small set with labels. During training, we calculate the gradients of training samples at each iteration and compare them with the average gradient of validation samples with top-k validation loss. If one sample has a positive contribution to the decrease of validation loss, we would apply higher weight on the sample, and otherwise we would discard the training sample at the current iteration. In this way, we aim to approach an optimal distribution of training samples that minimizes the top-k validation loss.
We summarize our contribution as follows:
1. We formulate novel contrastive learning method with gradient-based reweighing to learn fair representations without demographics. We also theoretically prove the convergence of our method.
2. Our model effectively incorporates limited supervised information into self-supervised training and achieves comparable or better classification results than fully supervised methods.
3. We validate the effectiveness of our method in improving fairness on three benchmark datasets under various sensitive attributes.
2 Related Work
Fairness in Machine Learning: Fairness has been widely studied in machine learning area. Generally,
fairness methods can be divided into two categories: individual fairness (Mukherjee et al. 2020
I[vento 2019 Mallvii-aal et al. 2019 Petersen et al., 2021 and group fairness (Feldman al. 2015 Hardt al. (2066). Our method follows the idea of group fairness. Different fairness
notions including disparate impact (Kamiran and Calders) 2012) and equalized odds (Hardi et al.
2016) have been proposed to quantify disparities of machine learning models. Kleinberg al. (2016) argue that disparities in machine lcarning arises due to biased data, instead of biased classifiers. In response, different methods have been proposed to modify input features and eliminate potential bias in downstream tasks. [reager et al. (2019) propose to quantify the correlation between sensitive information and input features using KL. divereneee and modify the input feature using Sattiger et al. (2018) and Jang et al. (2021) propose to generate a fair dataset using generative models. CCammnn jt al. (2177) learn a mapping from training distribution to an underlying fair distribution and relax the problem to a convex optimization problem. [Tiag and Nachum (2020) adjust training labels based on the desired specific fairness constraints. Other than preprocessing, methods on fairness fall in two categorics: inprocessing and postprocessing, Zafar et al. (2017) propose to reduce the
2

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fairness constraints to linear correlation constraints, and use such regularization term during training. Kim al. (0199) learn fair classifier through adversarial training with an extra discriminator. Adel et al. 2019) propose to add one extra layer on original network and use adversarial training to achieve fairness. Chai and Wang (022) propose to learn adaptive weights to balance among different demographic groups. As for postprocessing, the methods adjust the decision threshold of a classifier based on the expected fairness constraints Hardt et al. (2016); Jang et al. (2022). All these methods require sensitive information to formulate fairness metrics. A more related problem is fair classification under noisy sensitive attribute (Gupta et al. 2018 Lamy et al.. 2019 Wang et al. 2020), where the goal is to improve fairness clean data under partially flipped training sensitive attributes.
Fairness without Demographics: Fairnsss without demographics has been less studied. Some works solve this problem by using proxy sensitive features. Grari et al. (202T) propose to approximate the sensitive attributes with VAF. Yan et al. (2020) propose to use clustering information as an approximation of sensitive information. However, such methods either require the strong assumption that the clustering information is correlated with the sensitive information, or are prone to estimation bias. Besides, such methods cannot generalize to the setting where we expect the classifier to be unbiased w.r.t. several sensitive attributes. Instead, Hashimoto et al. 2018 consider the worst- case distribution over a certain group size and propose to achieve fairnsss through distributionally robust optimization. Lahoti et al. (2020) propose to reweigh training samples adversarially based on training loss to maximize the average loss. Similar methods have also been discussed in debiased learning (Nam et al. 2020; Liu et al. 202T) which employs a biased model to explore and rectify spurious correlations in training set. Our method follows similar idea of Min-Max fairness constraints. However, in contrast to the fully supervised setting, our method requires only a small labelled validation set.
Learning representations without supervision is a long-standing task, and among these methods, constrastive learning has become increasingly popular. The main idea of contrastive learning is to learn a compact representation of input features on hypersphere such that samples of same labels are close to each other possible, while samples of different labels are as far apart as possible. In this way, the trained contrastive encoder can be readily applied to downstream classification tasks by only fine-tuning an extra linear layer on a small labelled set. vaan den Oord et al. (2018) propose to learn a representation of input features using similarity between different samples and between augmentations of same sample. Chen et al. (2200) show that strong augmentation is crucial to learn good representation and prevent the network from exploiting naive cues. [Chuang et al. (020)) propose to modify the self-supervised contrastive loss to mitigate the influence of false negative pairs. Xiao et al. (2020) propose to construct separated embedding spaces, such that each embedding space only invariant to certain augmentations. Verma et al. (2021) propose use mix-up noise for domain-agnostic augmentation, Tian et al. (2020) prove that optimal augmentations for contrastive learning should be task task-dependent and proposes semi-supervised method to learn effective views for a given task. Apart from self- suff-uueeeiied learning, Khosla et al. (2020) propose two different loss terms to incorporate contrastive loss into fully supervised learning.
Contrastive Learning:
3 Self-Supervised Fair Representation Learning without Demographics
3.1 Background
Let {(x,, y,, a.), S N) be the training set, where for the i-th sample, 2; is the input data, y: E {0, 13 is the one-hot encoding label, and a, E {0, 13 is the sensitive attribute. Let h(x))) E [0, 1] be the output of classifier, then general fair classification task can be formulated as
1
N Lots (h(a))) y.), s.1. ((h)= Se
arg min h
N
1=1
where Lets is the classification loss and d(h) is the faimess constraint. For example, ((h) max (arg max h()))) = pos) - Parag max h(m))) = pos|a)) corresponds to faimess constraint
d' of the demographic parity, where PP P(arg h(x)) = pos) is the probability that classifies data æ
to the positive (pos) class. This formulation works when the sensitive information is available in the training set. However, when such information is not available in the training set, a natural question to ask is: how should we formulate the fair classification task without the sensitive information? As
3

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with (Hashimoto et al. 2018) and (Lahoti et al., 2020). we formulate the faimess constraint with sensitive attributes unknown the following Max-Min problem: maximizing the minimum utility U amongst all sensitive groups. If we choose accuracy as the utility metric, such requirement can be seen as a relaxation of error-based fairness constraints, and the fair classification task without demographics can be formulated as
Cas (h(x))) y:). arg min arg max Kila, = a'Hl i
1
Σ
And a' can be either surrogate demographic information estimated with extra assumptions.
3.2 Contrastive Learning
Contrastive learning aims at learning a balanced representation on the unit hyper sphere of Idd based on the similarity of input features. Generally, given a training set of size N, during each iteration we sample mini-batch of size from the training set and apply random augmentation on each sample twice, resulting in a subset { S i S } For tabular data, random augmentation includes mix-up and adding Gaussian noise, while for image data, random augmentation includes mix-up, cropping and resizing, cropping, resizing and flipping, color drop, color jitter, rotation, cutout, adding Gaussian noise, Gaussian blur, and Sobel filtering as used in previous work (Chen et al. 2020). For augmentations of same sample, we want the query to match its anchor key over all other samples which are treated as negative. Let fo be contrastive encoder network with parameter which maps an input onto the unit hyper-sphere of Rd subsequently used for classification task. For an anchor ø, a common choice of contrastive loss is InfoNCE (van den Oord et al. 2018):
cxp(sim(fo(Z:), fo fo(=" 1)/T)
Leter ( 0) - log Ejer exp (sim (fo( (o(
where sim is the cosine similarity metric, T is the temperature scaling the penalties on hard negative samples, r is the positive sample, and all samples other than æ in the mini-batch are negative samples. Ideally, we would like to learn a compact representation of input features such that the embedded features of different labels are pairwise linearly separable. To determine the decision boundary for classification, a common way is to add one extra linear layer after the encoder and train the linear layer small validation set with the encoder frozen.
that controls
3.3 Problem Formulation
We now formulate our problem. Given an unlabelled training set of size N and a small validation set {(x)ad y)")) ,1 S j < M} with M < N, denote the augmentated training set (each sample augmented twice) as (æ.. 1 < < 2N), our goal is to learn fair embedding via contrastive learning without observing the sensitive information in either the training or validation set. Inspired by previous work (Hashimoto et al. 2018). we use Min-Max faimess as the surrogate training objective in contrastive learning. To specific, we propose to minimize the top-k average loss (which is a relaxation of minimizing the max loss) as follows:
2N
1(k, 0)
Σ Te
(ā;;; 0) O)k + A(ks
where A(:: 0) is the k-th largest contrastive loss among {Letr (ā;;; 0) 2- Here straightforward way is to directly apply the hinge function on contrastive loss during training. The problem with such method is that, since we treat all samples other than the reference negative, we would inevitably introduce false negative pairs in ([). which makes contrastive loss not representative enough of downstream classification loss. Besides, when the training datasets are imbalanced w.r.t. label (Larson et al. 20166] Dua and Graif 2017), we are more likely to obtain false negative pairs for part of training samples, exacerbating the sampling bias of contrastive learning. To mitigate such problem, we instead consider the validation stage and use average top-k validation loss as the training objective. Let fe be the contrastive encoder with parameter 0 and Iw be the linear layer during validation with parameter our training objective can be formulated as
A8
1
Pas (foo(()))) - (k, + + x 0.0)
(ka 0,w)
=
K
(2)

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where (k, is the k-th largest classification loss among validation samples (Lets (Sw(So( -ン) As the update of contrastive encoder affects both training and validation, we want to learn weight assignment { for training samples such that by minimizing the weighted contrastive loss we also minimizes the average top-k validation loss:
2N
0" (v) = arg min
Σ
o Cer Cer (ā,;
2N
i=1
(3)
2¹ w arg min 1a (k, 0 (v), v20ww
3.4 Weight Approximation
Directly calculating the optimal weight in (3) can be very expensive. In this subsection, introduce a surrogate weight based on the gradient similarity between the contrastive loss and the validation loss.
For the simplicity of notation, we omit the parameters the losses. That is, at iteration we denote the contrastive loss in (I) as 14.; = (ā;; ()) and denote the validation loss in (2) as Iral.
As the latent representation from the encoder fo is related with both 4, and ryall we can assign surrogate of weights by considering the similarity between the gradients contrastive loss and validation loss. We would expect higher weights on training samples whose gradient directions Val,, are closer to that of Vo4.a such that the weighted update of encoder better approximates the expected update under 7yal Inspired by Ren al. (2018), based on the inner product between gradients:
simple approximation of the optimal weight
Ut = (Volral) Voli.-
To avoid negative contrastive loss, we apply ReL.U function u, and normalize the weights on each augmented mini-batch {æ,, 1 I S 2n} that is sampled from training set:
t, max (u,,i;
2n00,i
(5)
2n Ev=1 0e + E> 01,5"
where 5(r) =1 = r= 0, and Uy is the optimal weight for the i-th training sample t-iteration
Our method effectively utilizes the gradient information of training validation samples and computes the similarity between the gradient directions as the surrogate weight. Intuitively, if one training sample provides similar direction as samples of top-k validation loss, then this training sample should be upweighted, and otherwise downweighted. In this way, unlike training the encoder only validation set, our method tries to approximate a distribution of training set such that the modified distribution is beneficial to optimization objective defined in (
3.5 Training Algorithm
The gradients in can be easily computed with automatic differentiation. Our training procedure is as follows: we first pre-train the encoder to minimize the classification loss on the small validation set following the method by (Khosla et al.] 2020p. We then use this pre-trained model as initialization and train the encoder on the training set. During each iteration, we first compute the contrasitve loss for each sample in the forward pass, and fine-tune the linear layer with encoder frozen to compute the gradients and weights 4 and (5), and the encoder then updated according to the weighted gradient descent. We summarize the detailed training process in Algorithm
5

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Algorithm Optimization Algorithm
Pre-train the encoder fo on the validation set { {(x))) y) ,155 S M); do 1. Sample a mini-batch of training samples of size n, apply random augmentation on each
for = 0, ,
sample twice and get training set (āt < < 2n];
2. Calculate contrastive loss (Letr( 0) )) as in (T) denote it as (4,))
3. Freeze fo and fine-tune the linear layer 9w on validation set;
4. Calculate validation loss (k, F,,, w) as in denote it as (y
5. Update ,t = max ((Vol)) Vole,,,
6. Update Ut,i EV Pe,, Pe,r+8(22 (5
2noi.
where 8(r) =1 > r
mn Pew))
7. Update oc+1 Oc 2n end for
Vo >
i==1 V1,3le,
2n
3.6 Convergence Proof
We now discuss the convergence of our algorithm. Although the convergence of SGD has been widely studied (Gower et al.) 2019 Nguyen al. (2088), the convergence of our algorithm is non-trivial given that our training algorithm involves two different loss functions and that the validation loss involves extra linear layer compared with contrastive loss. We show theoretically that under some mild conditions, our method converges to the critical point, and the detailed proof can be found the Appendix. Before state the convergence of our algorithm, first state the assumptions need to prove the convergence:
Assumption 3.1. We have the following two assumptions.
A. The partial derivative of validation loss pal with respect to 0 is Lipschitz continuous with constant L, i.e., Log and Vi are upper-bounded by
The contrastive loss has o-bounded gradients w.r.t. 0.
And can prove the convergence of our method under bounded learning rates an and 02. Theorem 3.2. Under Assumption
3.1 at iteration t, let the learning rate of contrastive encoder 10
I satisfies 0n &
and the learning rate of linear classifier satisfies 02 S (Pt "
E. min L. LΣ, 70,
where
Tt, =l=lV I Be, P-.=(11) B(v=((Volea)) ((olu))
then the validation loss will monotonically decrease until convergence.
4 Experiments
4.1 Experimental Setup
We validate model three benchmark datasets. Details of the datasets follows:
CelebA (Luu et al. 2015): The dataset contains 202,599 face images, each of resolution 178 218, with 40 binary attributes. We perform two different tasks on CelebA dataset: gender classification with age as sensitive attribute, and attractiveness classification with gender as sensitive attribute.
Adult (Dua and Graff (017): The dataset contains 65,123 samples with 14 attributes and one binary label indicating if an individual's incoming exceeds 50K. For Adult dataset, the goal is predict whether an individual's income exceeds 50K, and the sensitive attributes are gender and race.
COMPAS (Larson al.) 2016) The dataset contains 7,215 samples with 11 attributes. As with previous works on fairness (Zafar et al. 2017), we only select black and white

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individuals in COMPAS dataset, and the modified dataset contains 6,150 samples. For COMPAS dataset, the goal is to predict whether a defendant reoffends within two years, and the sensitive attributes are sex and race.
We implement our method in PyTorch 1.10.1 with one NVIDIA RTX-309 GPU. We use accuracy to evaluate classification performance, and evaluate fairness using two widespread metrics: disparate impact (Kamiran and Calders, 2012), equalized odds (Hardt et al. 2016). For our method, we implement the contrastive encoder using the structure from (Chen et al.
2020 and the linear classifier using logistic regression. Our method does not require sensitive information in either training or validation set. Labels are available on validation set, but not on training set. We compare our method with six related methods:
Fully supervised baseline: Fully supervised network with same structure as (Chen et al. 2020 and without fairness constraints. Labels are available both training and validation set. The difference between our method and fully supervised baseline is that the fully supervised baseline are trained with supervised contrastive loss (Khosla et al. 2020) on training and validation set.
Contrastive learning baseline: Contrastive learning method (Chen et al. 2020) without fairness constraints. Labels are only available on validation set. The difference between our method and contrastive learning baseline is that the baseline does not impose fairness constraints during training.
Distributionally robust optimization (DRO): contrastive learning baseline with distribu- tionally robust optimization (Hashimoto et al. 2018). The difference between our method and DRO is that DRO is applied on contrastive loss during training and on validation loss during validation.
Adversarially reweighted learning (ARL): contrastive learning baseline with adversarially reweighted learning (Lahoti et al., 2020). The difference between our method and ARL that ARL is only applied on validation loss during fine-tune. The adversarial network is chosen as one linear layer as suggested by the authors (L.ahoti al. 2020).
Postprocessing:
contrastive learning baseline with postprocessing (Hardt al. 2016). The fairness constraint is equalized odds. The difference between our method and postprocessing is that the latter requires sensitive information in the validation set to adjust the classification threshold w.r.t. the fairness constraint.
TAC: contrastive learning baseline with TAC (Hwang et al. 2020). The sensitive information and label are available on both training and validation set. The difference between our method and TAC is that TAC is applied on fully supervised baseline.
We repeat experiments on each dataset three times and report the average results and in each repetition randomly spilt data into 64% training data, 16% validation data and 20% test data. All the methods evaluated are trained and tested on the same data partitions each time. All hyperparameters tuned find the best validation accuracy. The values of hyperparameter in our method are set by performing cross-validation on training data in the value range of 0.1 to 10. The hyperparameters for the comparing methods are tuned as suggested in the original paper (Hardt et al. 2016 Hashimoto
et al. 2018 Hwang et al. 2020).
4.2 Experimental Results
Compared with other state-of-the-art methods on fairness without demographics, our method achieves best or comparable performance on all three datasets regarding both classification accuracy and fairness when evaluate faimess w.r.t. different sensitive groups. Unlike DRO or ARL which only applies fairness constraints during either training or validation, method effectively applies fairness constraints classification during self-supervised training. In this way, our method mitigates the problem that contrastive loss during training might not be representative enough for downstream classification loss. Besides, since directly apply weight to training samples, we are able to directly modify the update of encoder with supervised information, instead of merely adjusting the update of linear layer during fine-tune.
Classification results are shown in Tables 6
We also compare our method with conventional fairness methods where the sensitive information available. Compared with postprocessing, although our method does not require sensitive information
7

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Table 1: Results the COMPAS dataset with sensitive attribute. Postprocessing and TAC require demographic information. We evaluated Postprocessing and TAC when providing different demographic information (shown in the parenthesis). Lower Disparate Impact and lower Equalized Odds shows more fair results.
Disparate Impact (%
Equalized
Methods
Accuracy (%)
Odds (%)
Methods with Correct Demographics Methods with Wrong Demographics
Postprocessing (gender)
63.42=0.54
12.31
10.65:13.91
TAC (gender)
63.47=0.67
6.42-12.56
5.03:11.32
Postprocessing (race)
63.03=0.74
17.6411.91
17.67:12.41
TAC (race)
63.82-0.86
16.64+1.07
16.68
Fully supervised baseline
6..23=0.84
19.17:4.86
20.25:1..19
Contrastive learning baseline
6..02=0.93
19.23++2.49
20.63:1..39
Methods without Demographics
DRO
62.21=0.62
18.82:13488
16.633+.22
ARL
63.23=0.51
17.6243..3
15.37--2.73
Our method
63.67=0.55
17.53
13.34.12.00
Table 2: Results the COMPAS dataset with race as sensitive attribute.
Disparate Impact (%)
Equalized
Methods
Accuracy (%)
Odds (%)
Methods with
Postprocessing (race)
63.03=0.74
15.52+2.47
17.62:43.05
Correct Demographics
TAC (race)
63.82=0.86
5.24=2.14
4.73
Methods with
Postprocessing (sex)
63.42-0.54
2..41+1.84
30.32-+3.42
Wrong Demographics
TAC (sex)
63.47=0.67
19.8
29.72:3.60
Fully supervised baseline
65.23-0.84
22.32:4..44
38.37-17.23
Contrastive learning baseline
64.02=0.93
22.2342.66
38.3447.38
Methods without Demographics
DRO
62.21=0.62
21.41:3.89
30.43:1..64
ARL
63.23=0.51
21.37+1.71
29.46+3.53
Our method
63.67=0.55
17.46+13.73
24.43-1..18
Table Results on the Adult dataset with gender as sensitive attribute.
Disparate Impact (%)
Equalized
Methods
Accuracy (%)
Odds (%)
Methods with
Postprocessing (gender)
82,21=1.07
13.01
10.17+22.64
Correct Demographics
TAC (gender)
84.12=1.53
12.17+1.97
8.23+3.45
Methods with
Postprocessing (race)
82.07=1.21
16.0142.13
20.21
Wrong Demographics
TAC (race)
83.64=1.68
18.8343.67
21.4442.11
Fully supervised baseline
85.53-0.94
19.30#1.43
23.34:12.55
Contrastive learning baseline
84.11=1.14
19.80+2.36
22.82-22.17
Methods without Demographics
DRO
81.37=2.26
16.21+1.87
19.43+3..64
ARL
82.31=1.12
15.82+3.69
18.25+-2.67
Our method
82.76=0.73
14.81+1.47
17.63+1.66
on validation set, our method still achieves comparable performance. Compared with TAC, although our method does require labels on training set or sensitive information on training and validation set, our method still achieves comparable performance regarding accuracy on all three datasets and comparable performance regarding disparate impact on Adult and CelebA datasets. Besides, we also show results when conventional fairness methods are applied with wrong sensitive information. We observe that when there exists a high correlation between different sensitive groups, even wrong sensitive information can play as alternative demographics information to help faimess (compared fairness without demographics methods). However, since distributional disparity regarding different sensitive attributes are not identical, as shown in the tables, fairness methods with certain predefined sensitive information does not always guarantee fairness under another predefined sensitive groups. On Adult and CelebA dataset, both postprocessing and TAC applied with wrong sensitive

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Table 4: Results the Adult dataset with race sensitive attribute.
Disparate
Equalized
Methods
Accuracy (%)
Impact (%)
Odds (%)
Methods with
Postprocessing (race)
82.07 1.21
13.3442.14
11.15:33.62
Correct Demographics
TAC (race)
83.64 1.68
13.32+2.43
9.1442.25
Methods with
Postprocessing (gender)
8.73
15.1741.57
20.2112224
Wrong Demographics
TAC (gender)
84.12=1.53
14.17=1.59
20.65:+3.48
Fully supervised baseline
85.53=0.94
13.8442.54
2..33
Contrastive learning baseline
84.11=1.14
13.81+1.27
22.30+1..69
Methods without
DRO
81.37=2.26
13.52+1.67
17.35-12.04
Demographics
ARL
82.31=1.122
13.3442.32
16.43
Our method
82.76=0.73
12.21+1.59
16.46+22.21
Table 5: Results on the CelebA dataset with gender as sensitive attribute and attractive as label.
Disparate
Equalized
Methods
Accuracy (%)
Impact (%)
Odds (%)
Methods with
Postprocessing (gender)
78.32=0.87
11.24 1.88
8.67+2.34
Correct Demographics
TAC (gender)
79.32=0.61
13.21
10.23:12.96
Methods with
Postprocessing (age)
77.43-1.83
14.01+2.56
18.42++1.60
Wrong Demographics
TAC (age)
78.82-0.71
17.31+2.68
19.63++2.23
Fully supervised baseline
80.43=1.62
18.62:3.299
22.37::582
Contrastive learning baseline
79.13=0.57
18.21
20.64:15.45
Methods without Demographies
DRO
76.38-2.66
15.3343.09
17.6114.43
ARL
76.43=1.37
14.441:2.19
16.83:12.76
Our method
7..63-0.79
14.32+11.9
16.17-11.97
Table Results on the CelebA dataset with age as sensitive attribute and gender as label.
Disparate Impact (%)
Equalized
Methods
Accuracy (%)
Odds (%)
Methods with
Postprocessing (age)
86.83=0.86
11.17 1.59
8.13433.3
Correct Demographics
TAC (age)
88.12-0.92
9.45+2.09
5.27=:2.48
Methods with
Postprocessing (smiling)
86.32=0.72
14.01
12.67:2..15
Wrong Demographics
TAC (smiling)
87.76=0.96
14.33+2.93
12.25+11.75
Fully supervised baseline
89.74-0.84
16.75+4.85
14.44:14.00
Contrastive learning baseline
87.43=0.84
16.25+2.53
14.43:14.93
Methods without Demographics
DRO ARL
72.43=2.63
15.21+1.73
13.44+2233
85.54=0.73
14.6743.59
1..59+1.34
Our method
86.93=0.72
11.3442.50
10.82-12.37
information achieve trivial improvement in fairness. In comparison, method without predefined sensitive information works better under different sensitive attributes.
4.3 Trade-Off between Fairness and Accuracy
We move discuss the fairness-accuracy trade-off with Pareto frontier. Kim al. (2020) propose to characterize the trade-off's in group fairness via the muiness--oonfusee tensor z composed of eight elements, and the majority of group fairness constraints can be modeled with specific fairness matrices. By solving the optimization problem of z with model-specific constraints and linear or quadratic fairness regularization terms, we can obtain model-specific Pareto frontier indicating the trade-off any methods could achieve under such classifier, and smaller distance to the frontier indicates better fairness-accune accuraacy trade-off, and methods lie right on the curve indicates an ideal classifier. In Fig. [ the blue curve shows the model-specific frontier, where the model is chosen as contrastive learning baseline. Compared with DRO and ARL, our method lies closer the frontier and achieves better fairness- faimess--ccuracy trade-off.
best

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(d) COMPAS (race)
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(l) CelebA (age)
Figure I: Pareto frontier on Adult, CelebA and COMPAS dataset. The MS Pareto Frontier is plotted
by post-processing the contrastive learning baseline.
Conclusion
Improving fairness without accessing sensitive attributes has been challenging task. In this paper, propose a fair contrastive learning method with wradient-based reweighing to learn a fair representation for downstream classification tasks. We consider semi-supervised setting where small validation set is available, and use top-k average loss as surrogate fairness constraints. We assign weight based on gradient similarity to apply information of validation loss during self-supervised training. We theoretically prove the convergence of our method, and we show from experiments that our method improves fairness with relatively small sacrifice in classification accuracy across multiple datasets. Future directions of interest includes robustness of our method to noisy validation set, and alternative ways of sampling validation set to further improve fairness.
Acknowledgements
This work was partially supported by the EMBRIO Institute, contract #2120200, a National Science Foundation (NSF) Biology Integration Institute, Purdue's Elmore ECE Emerging Frontiers Center, and NSF IIS #1955890, IIS #2146091.
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Checklist
1. For all authors...
(a) Do the main claims made in the abstract and introduction accurately reflect the paper's
contributions and scope? [Yes]
(b) Did you describe the limitations of your work? [Yes]
(c) Did you discuss any potential negative societal impacts of your work? [N/A]
(d) Have you read the ethics review guidelines and ensured that your paper conforms to them? [Yes]
2. If you are including theoretical results...
(a) Did you state the full set of assumptions of all theoretical results? [Yes]
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14


Reviews:
[{"review_id": "irqAi15h8tN", "reviewer": "Reviewer_kdXn", "summary": "This paper studies the fairness issue in machine learning. It aims to improve fair classification without sensitive information and without labels. Specifically, this paper proposes a novel reweighing-based contrastive learning method to learn a generally fair representation without observing sensitive attributes. The idea of this paper is direct and reasonable, and the experimental results demonstrate the effectiveness of the proposed method.", "questions": "\tIn the line 132, how to obtain α^' under the situation where sensitive attributes are unknown?\n\n\tFrom the line 160 to 163, why is treating all samples as negative a problem? This sentence is not explained clearly. Could the authors give a more detail explanation or an example?\n\n\n\tThe authors describe the λ is a hyperparameter in Appendix, but in the equation 2, it looks like the λ is determined by k and k is a hyperparameter. Is the experiment in A.2 conducted on different k?\n", "limitations": "N.A", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths:\n\n1.\tThe paper is clearly written and is easy to follow.\n\n2.\tThe setting in this paper, without sensitive information and without labels, has high application value and is rarely studied before.\n\n3.\tThe method in this paper has theoretical guarantee.\n\n4.\tExtensive experiments are shown to demonstrate the effectiveness of the proposed framework.\n\nWeakness:\n\n1.\tThere is a typo in line 160, “… to is to …” —> “… is to …”.\n\n2.\tIt’s not clear why using top-k average loss. \n\n3.\tMore ablation study needs to add. It seems like there are requirements for the size of the validation set when using it as a guide. The authors had better to analyze the effect of different size of the validation set.\n\n", "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": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"ethics_review_area": ""}, "extra_text": {}}, {"review_id": "cZe3BxfCW6-", "reviewer": "Reviewer_Xdpb", "summary": "This paper introduces a novel problem “Can we improve fair classification without sensitive information and without labels?” To tackle this problem, they propose a reweighing-based contrastive learning method. Then, they provide theoretical proof of the convergence of their model. Finally, the conduct experiments on three datasets to show their proposed method achieves better performance. ", "questions": "According to the authors, there are weaknesses in this work that have not been addressed. Please refer to the main reviews.", "limitations": "1)\tMaybe due to the space limitation, the detail of the experiment is not well introduced.\n2)\tThe methods with correct demographics baselines are not the start-of-the-art fairness improved methods.\n", "rating": 7, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths:\n\n1)\tThe motivation for this paper is intuitive and well explained. Meanwhile, the paper is well organized.\n2)\tThe authors consider a semi-supervised setting where a small validation set is available, which has strong research significance.\n3)\tThe authors propose a novel contrastive learning method and can solve their proposed question well.\n4)\tThe authors provide theoretical proof of the convergence of their method.\n5)\tThe authors validate the effectiveness of our method in improving fairness on three benchmark datasets.\n\nHowever, I still have some concerns:\n\n1)\tThe authors consider a semi-supervised setting compared with DRO and ARL. However, there are many semi-supervised methods in classification. Are they can combined with DRO or ARL? why authors consider using contrastive learning methods to improve the semi-supervised setting?\n2)\tIn experiment, the authors compare their methods with DRO and ARL which are under a fully supervised setting. However, their methods get better performance in both accuracy and fairness metrics. I'm a little skeptical about this result. And in experiment analysis, the authors don’t analysis the reasons. What’s the experiment setting of DRO and ARL? Besides, the authors compared their methods with methods with correct demographics. I understand this is not the key point of this paper. But why the authors just compare with Postprocessing and TAC instead of the start-of-the-art fairness improved methods? \n", "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": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"ethics_review_area": ""}, "extra_text": {}}, {"review_id": "E5EZAJrA7Gn", "reviewer": "Reviewer_s7Zh", "summary": "This paper proposed a fair contrastive learning method with gradient-based reweighing to learn a fair representation for downstream classification tasks without accessing sensitive attributes. The top-$k$ loss is employed as a surrogate fairness constraint. The convergence of the proposed method is theoretically proved and the effectiveness of the proposed method is verified on benchmark datasets.", "questions": "1. The motivation for this work is not strong. The paper does not do a very good job of motivating why sensitive information is infeasible in real-world scenarios. I think the paper would be more compelling if the authors could provide more concrete scenarios where sensitive information is infeasible.\n\n2. The authors claimed that conventional methods on fairness would fail to work when there are more than one sensitive attributes. However, I think the sensitive attributes in previous works are not restricted to being single.\n\n3. In line 119, what are the superscripts c and s?\n\n4. In line 158, what is the subscript $+$? How does $\\ell(k,\\theta)$ calculate the top-$k$ average loss?\n\n5. It is not clear to me how the proposed method learns fair representations. Can the authors comment on how the weights help to learn fair representations in contrastive learning and how the minimization of classification loss on validation samples helps to learn the proper weights? Is there any physical meaning to the weights? Do they have ground-truth values?\n\n6. Some improvements of the proposed method are marginal. It is better to do a significance test.\n\n7. The size of the validation set seems important. It is better to do an ablation study for it.\n\n======================= After Rebuttal =========================\n\nI increased my score to borderline accept.", "limitations": "The authors have not adequately addressed the limitations and potential negative social impact of their work.", "rating": 5, "confidence": 3, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Originality: The proposed method is a combination of Min-Max fairness, importance reweighting, contrastive representation learning, and inner-product-based weight approximation. \n\nQuality: This work is technically sound. The claims are well supported.\n\nClarity: Overall this paper is well written and organized. However, there are some nations being used without clearly defined. \n\nSignificance: The proposed method is insightful and provides a new perspective on learning fair representations in an unsupervised manner.", "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": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"ethics_review_area": ""}, "extra_text": {}}, {"review_id": "AyEw91rJDwj", "reviewer": "Reviewer_4iqE", "summary": "This work introduces a contrastive method that reweighs training samples based on objective loss gradients. The proposed method is very interesting and takes the form of a training procedure (instead of defining more models or editing existing ones), which means that it is particularly suitable for reuse by non-experts. The paper is well-organized, but I think it needs a revision to improve explanations and make in-depth arguments that would help explain why the proposed approach works. The experiment methodology is sound and results are convincing compared to existing alternatives.", "questions": "Please see my comments in Strengths and Weaknesses section.", "limitations": "Please see my comments in Strengths and Weaknesses section.", "rating": 5, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "- The greatest shortcoming of the paper is that, in section 3.4, the explanation of why the particular weighting strategy was chosen is too brief and thus feels rather arbitrary. In my opinion, a couple of paragraphs are needed to corroborate why this strategy is expected to work. Two particular concerns I would personally like to see addressed (in addition to other explanations of why following gradients can improve fairness) is that gradients may be similar, but integrating over them can create huge deviations in training outcomes in terms of loss and corresponding accuracy (the authors do a nice job in showing that training converges, but is this enough?) and why should a distribution be approximated by relu-ing data instead of normalizing their sigmoid transformation, which is more typical in machine learning.\n- The paper measures specific types of fairness, but it is not explained why the proposed approach can address these in particular. Note that addressing multiple types of fairness simultaneously perfectly is known to be an impossible task unless very specific conditions are satisfied [Kleinberg et al. (2016)], which begs the question what kind of fairness objective the proposed approach is particularly good at addressing.\n\nMinor comments:\n- In section 2, please give a brief explanation of the main idea of contrastive learning.\n- \"Here a straightforward way to is to\" > incomplete sentence\n- \"The problem with such method is,\" > \"The problem with such a method is that,\"\n- It could be helpful to refer to [1] for better positioning the proposed approach in the context of AI bias literature.\n\n[1] Ntoutsi, E., Fafalios, P., Gadiraju, U., Iosifidis, V., Nejdl, W., Vidal, M. E., ... & Staab, S. (2020). Bias in data‐driven artificial intelligence systems—An introductory survey. Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery, 10(3), e1356.", "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": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"ethics_review_area": ""}, "extra_text": {}}]

Author rebuttal:

Decision: Accept